Heroes Factory (GW1 - bis)
Jean Monéger
2025-06-02
Introduction
Recently, entire occupations have been granted the label of “Heroes”. For example, during the recent COVID-19 pandemic, as well as in previous health crises (such as the SARS and H1N1 pandemics), healthcare workers were applauded – sometimes literally – as ‘heroes’. Military personnel in the US, but also in the UK, are also often called ‘heroes’. So are police, firefighters, and other first responders. But how malleable is this perception of heroism in these occupations? Can we manipulate the public perception toward recognising “heroism” in occupations not typically perceived as such (e.g., psychiatrists)?
In this study, we tested how malleable the perception of heroism in an occupation is. Specifically, we hypothesised two core components of heroism perception:
Perception of physical threat contributes to the perception of heroism
Altruistic motivations of the group’s member contribute to the perception of heroism
Rationale
Franco et al. (2011) provided the general and, to their own admission, overly simplistic definition of heroism as “to act in a prosocial manner despite personal risk” (p.99). Altruism and exposure to danger are indeed two core elements that are consistently found in the lay people’s prototype of a hero (Kinsella et al., 2015). Regarding physical threat, Sternstorm & Curtis (2012) observed that altruistic actions were distinguished between being merely altruistic vs heroic as a direct function of the level of physical danger. The more dangerous the action, the more heroic rather than altruistic.
As emphasised by Sternstorm & Curtis (2012), altruism may not be a sufficient element to the perception of heroism, but it might be necessary element nonetheless. However, to our knowledge, there is a lack of experimental evidence for this influence of altruism on the perception of heroism.
Manipulations
We manipulated the description of the target occupations as exposed to physical risks (vs Boredom) and having altruistic motivations (vs self-centered motivations).
The first one (MC1) will use attributes ratings for each occupation regarding how much participants perceive them to be “brave” (physical threat manipulation check) and “Selfless” (motivation type manipulation check). [Personality attributes evaluation]
The second manipulation check (MC2) will use self-reported evaluation of how much participants perceive each occupation as being “exposed to physical risks” and “effectively helping people”. [Physical ‘objective’ evaluation]
MC1 will be successful if 1) Occupations described as involving a Physical threat are perceived as significantly “braver” than occupations described as involving boredom, and 2) occupations described as involving an altruistic motivation are perceived as significantly less “selfish” than occupations not described as involving altruistic motivations.
MC2 will be successful if 1) Occupations described as involving a Physical threat are perceived as significantly more exposed to physical risks than occupations described as involving Boredom, and 2) occupations described as involving an altruistic motivation are perceived as significantly helping more people than occupations not described as involving altruistic motivations.
Hypotheses
H1a - Describing an occupation as exposed to physical threats (vs Boredom) will increase perception of heroism across all types of occupations
H1b - Describing an occupation as having altruistic motivations (vs Self-centered) will increase perception of heroism across all types of occupations
H2a: Perceived heroism will be positively predicted by perceived bravery across all types of occupations
H2b: Perceived heroism will be positively predicted by perceived altruism across all types of occupations
H3a: Perceived heroism will be positively predicted by perceived physical risk across all types of occupations
H3b: Perceived heroism will be positively predicted by perceived help provided to others across all types of occupations
Methods
After reading the Consent form and confirming their participation, reporting their Prolific ID, and answering a commitment check (Geisen, 2022 [avaiblable at https://www.qualtrics.com/blog/attention-checks-and-data-quality/]; Peer et al., 2024), participants read a description of one of the target occupation (randomly selected, between-participant). Each description consisted in a short 3-paragraph long description of the occupation. The first paragraphs briefly described the targeted occupation. The two following paragraphs were our manipulations: one emphasized the type of risk associated with the occupation (Physical vs None) and the other emphasized the motivation of the workers (Altruistic vs self-centered). These two paragraphs were displayed in a random order. Conditions were randomly assigned to participants.
The descriptions were followed by three Comprehension checks questions. Participants had 2 chances of getting the comprehension check right - after which, they were redirected toward a page asking them to return their survey. Participants succeeding in the comprehension checks completed a scale measuring to what extent, in their personal opinion, the target occupations are “heroes”. Once completed, participants rated 4 manipulation checks. They then reported their general attitude toward the target group (covariate) using a 5 point scale from “Very negative” to “Very positive”.
At the end of the study, participants completed some demographics regarding their gender, age, and occupation. They finally answered to 1 final manipulation check regarding the credibility of our deception. They were then debriefed and thanked.
Occupation Descriptions. Each description consisted in 3 paragraphs with the two last ones (randomised order) emphasising Physical threat (vs None) and Altruistic motivations (vs self-centered motivations, see Material on OSF project). We used deceptive information to manipulate risk and motivations. Specifically we reported false results from a survey indicating that “83% of XXX thought that their life was at risk in the past 12 months” (vs “83% of XXX reported being bored most of the time”), and “74% of XXX identified”Helping people” as their primary motivation” (vs “74% of XXX identified”self-improvement” as their primary motivation”).
Moral role attribution. Participants evaluated to what extent they agreed with the target occupations being described as “Heroes” using a 5-point Likert scale from “Strongly disagree” to “Strongly agree”.
Character attribution Evaluation. Participants evaluated the applicability of two adjectives using two 7 points bipolar scales. One ranged from cowardly to brave, and the other ranged from Selfish to selfless.
Situation Evaluation. Participants then rated to what extent they believed the target occupation is objectively associated to physical danger, and to what extent the people in this profession are helpful. Both questions used 7-point Likert scales from “Not at all” to “Extremely”.
General attitude. Participants reported their general attitude toward the target occupation using a 7-point-scale from “Very negative” to “Very positive”.
Comprehension checks. Participants responded to three multiple choice questions asking them about the content of the vignette they just read (see material for details). They had two chances of getting all comprehension checks correct - after which they were asked to return their survey. The comprehension checks were displayed right beneath the descriptions and consisted in easy questions about the content of the vignette.
Credibility check. Participants answered the following question: “In your opinion, how believable was the information that you read at the beginning of this study, about the target occupation’s motivation and working conditions?” from 1- Very unbelievable to 7 - Very believable.
Loading data
Please adjust the path if you are running this script in your local machine.
DF_HeroFactory_April2025.csv is our main data frame. It
is publicly accessible from our OSF webpage (https://osf.io/jdhbf/?view_only=db07323e133247b29ce0c8fe6bfe40dc).
A second data frame is required to reproduce some descriptives
statistics: Demog_Hero_factory_2025.csv, also available on
the OSF webpage of the project.
Both of these data frame can be re-computed from the Qualtrics output using the Data Wrangling code chunk presented in the Appendix section of the report.
Set <- read.csv("DF_HeroFactory_April2025.csv", comment.char="#")
Demographics <- read.csv("Demog_Hero_factory_2025.csv")In this report, I use some packages to format data, plot results, and run robust analyses. Installed packages are detailed in the code chunk below.
if(!require("dplyr")) install.packages("dplyr")
if(!require("tidyr")) install.packages("tidyr")
if(!require("stringr")) install.packages("stringr")
if(!require("ggplot2")) install.packages("ggplot2")
if(!require("emmeans")) install.packages("emmeans")
if(!require("data.table")) install.packages("data.table")
if(!require("PerformanceAnalytics")) install.packages("PerformanceAnalytics")
if(!require("interactions")) install.packages("interactions")
if(!require("car")) install.packages("car")
if(!require("effectsize")) install.packages("effectsize")
if(!require("RColorBrewer")) install.packages("RColorBrewer")
if(!require("effectsize")) install.packages("effectsize")
if(!require("report")) install.packages("report")
if(!require("ordinal")) install.packages("ordinal")
if(!require("robustbase")) install.packages("robustbase")
if(!require("olsrr")) install.packages("olsrr")
if(!require("knitr")) install.packages("knitr")
if(!require("kableExtra")) install.packages("kableExtra")
if(!require("gt")) install.packages("gt")
if(!require("lavaan")) install.packages("lavaan")Results (as registered)
We aimed to collect answers from 1360 representative UK residents. A final sample of 1362 participants completed our survey. Because two of the participants timed out (IDs: “5cb6f38ffdc7fa0013f809a3”, “5cf84c0f4b639a0016a45a54”), they were not included toward the completion of our representative sample. They were thus excluded from our analyses.
Our sample included 692 women, 653 men, 11 others, and 4 who preferred not indicating their gender. The mean age was 46.55 year old (SD = 15.36).
Most of them (n = 1242) did not report a job relevant to the study. However, several participants (n = 4) reported impossible responses: “None of the above” and any other job from the list. They were removed from our descriptive analyses of job distribution (see plot below). Note that some participants reported several past occupations that were relevant to the study (e.g., Police officers & Firefighters).
Demographics$flag_inconsistent <- (Demographics$Job_match_6 == "None of the above") &
(Demographics$Job_match_1 != "" | Demographics$Job_match_2 != "" | Demographics$Job_match_3 != "" |
Demographics$Job_match_4 != "" | Demographics$Job_match_5 != "")
paste0("1360 participants took part in the study. Mean age in the sample is ", mean(as.numeric(Set$Age)), ", SD = ", sd(as.numeric(Set$Age)))## [1] "1360 participants took part in the study. Mean age in the sample is 46.5455882352941, SD = 15.359732853326"## Gender
Set %>% group_by(Gender) %>% summarise(N=n()) %>%
ggplot(aes(x=Gender,y=N,fill=Gender))+
geom_bar(stat = 'identity',color='black')+
scale_y_continuous(labels = scales::comma_format(accuracy = 2))+
geom_text(aes(label=N),vjust=-0.25,fontface='bold')+
theme_bw()+
theme(axis.text = element_text(color='black',face='bold'),
axis.title = element_text(color='black',face='bold'),
legend.text = element_text(color='black',face='bold'),
legend.title = element_text(color='black',face='bold')) +
ggtitle("Gender distribution")
## Occupations
#colnames(Set)
jobs <- unlist(Demographics[-which(Demographics$flag_inconsistent == T), 4:10]) # Make a long list of all jobs that were named
jobs <- jobs[jobs != ""] # Remove empty strings
job_df <- as.data.frame(table(jobs))
colnames(job_df) <- c("Job", "Count")
ggplot(job_df, aes(x = Job, y = Count, fill = Job)) +
geom_bar(stat = 'identity',color='black')+
scale_y_continuous(labels = scales::comma_format(accuracy = 2))+
geom_text(aes(label=Count),vjust=-0.25,fontface='bold')+
theme_bw()+
theme(axis.text = element_text(color='black',face='bold'),
axis.title = element_text(color='black',face='bold'),
legend.text = element_text(color='black',face='bold'),
legend.title = element_text(color='black',face='bold')) +
ggtitle("Job distribution")
Plots
Descriptively, most jobs were evaluated as relatively heroic. Below are visual representations of the perception of our target occupations (firefighters [F], Nurses [N], police officers [P], Psychiatrists [Ps] and Welders [W]).
# 1. Create a summary dataframe for facet annotations (mean and SD)
df_summary <- Set %>%
group_by(Job) %>%
summarize(
mean_score = mean(Heroism, na.rm = TRUE),
sd_score = sd(Heroism, na.rm = TRUE),
.groups = "drop"
)
# 2. Create the ggplot using the long format data
ggplot(Set, aes(x = Heroism)) +
geom_histogram(aes(fill = after_stat(count)),
binwidth = 1,
color = "black", show.legend = FALSE) +
facet_grid( ~ Job, scales = "free") +
scale_fill_gradientn(
colours = brewer.pal(9, "YlOrBr"),
name = "Count"
) +
labs(
title = "Histograms of Variable by Occupation",
x = "Score",
y = "Count"
) +
# Annotate each facet with the mean and standard deviation
geom_text(data = df_summary,
aes(x = 7, y = Inf,
label = paste0("Mean = ", round(mean_score, 2),
"\nSD = ", round(sd_score, 2))),
vjust = 1.5, hjust = 1.1, size = 3) +
theme_classic() +
theme(panel.grid.major.y = element_line(linewidth = 0.5),
panel.grid.minor.y = element_line(linewidth = 0.5))
Additional descriptions of our main variables show a tendency to
perceive occupations favorably.
Set$Credibility <- as.numeric(Set$Credibility)
df_long <- Set %>%
pivot_longer(
cols = c(Heroism, Danger, Helpfulness, Selfless, Brave, Attitude, Credibility),
names_to = "Variable",
values_to = "Score"
)
# 2. Compute summary statistics by Job and Variable
df_long2<- subset(df_long, df_long$Variable != "Credibility")
df_summary <- df_long %>%
group_by(Job, Variable) %>%
summarize(
mean_score = mean(Score, na.rm = TRUE),
sd_score = sd(Score, na.rm = TRUE),
.groups = "drop"
)
df_summary2 <- df_long2 %>%
group_by(Job, Variable) %>%
summarize(
mean_score = mean(Score, na.rm = TRUE),
sd_score = sd(Score, na.rm = TRUE),
.groups = "drop"
)
# 3. Create the ggplot using the long format data
ggplot(df_long2, aes(x = Score)) +
geom_histogram(aes(fill = after_stat(count)),
binwidth = 1,
color = "black", show.legend = FALSE) +
facet_grid(Variable ~ Job, scales = "free") +
scale_fill_gradientn(
colours = brewer.pal(9, "YlOrBr"),
name = "Count"
) +
labs(
title = "Histograms of Variable by Occupation",
x = "Score",
y = "Count"
) +
# Annotate each facet with the mean and standard deviation
geom_text(data = df_summary2,
aes(x = 7, y = Inf,
label = paste0("Mean = ", round(mean_score, 2),
"\nSD = ", round(sd_score, 2))),
vjust = 1.5, hjust = 1.1, size = 3) +
theme_classic() +
theme(
panel.grid.major.y = element_line(linewidth = 0.5),
panel.grid.minor.y = element_line(linewidth = 0.5)
)
Manipulation checks
We are manipulating the description of the target occupations as exposed to high physical risks (vs no physical risk) and having altruistic motivations (vs self-centered motivations) in vignettes.
Two manipulation checks were used:
Character attribution: Participants rated how brave and selfless the target occupation was, as a manipulation check for our Risk and Motivation manipulations respectively. This manipulation check focuses on character attributions rather that verifiable objective evaluation.
Situation attribution: Participants rated how dangerous and helpful the occupations were, as a manipulation check for our Risk and Motivation manipulations respectively. This manipulation check focuses on the evaluation of a situation, objectively - in contrast to a character evaluation.
Each manipulation check is presented in the two tabs below.
Manipulation check 1: Character attribution
This tab contains:
- Perception of bravery Does our Risk manipulation influence perceived Bravery?
- Perception of selflessness Does our Motivation manipulation influence perceived Selflessness?
Perception of bravery
The Risk type (physical vs Boredom) should predict the perception of bravery.
##
## Welch Two Sample t-test
##
## data: Set$Brave by Set$Risk
## t = -5.206, df = 1357, p-value = 2.227e-07
## alternative hypothesis: true difference in means between group B and group R is not equal to 0
## 95 percent confidence interval:
## -0.4931945 -0.2232317
## sample estimates:
## mean in group B mean in group R
## 5.622781 5.980994## Cohen's d | 95% CI
## --------------------------
## -0.28 | [-0.39, -0.18]
##
## - Estimated using pooled SD.## standardGeneric for "summary" defined from package "base"
##
## function (object, ...)
## standardGeneric("summary")
## <environment: 0x11fc8d980>
## Methods may be defined for arguments: object
## Use showMethods(summary) for currently available ones.my_sum <- Set %>%
group_by(Risk) %>%
summarise(
n=n(),
mean=mean(Brave),
sd=sd(Brave)
) %>%
mutate( se=sd/sqrt(n))
# Standard deviation
ggplot(my_sum) +
geom_bar( aes(x=Risk, y=mean), stat="identity", fill="forestgreen", alpha=0.5) +
geom_errorbar( aes(x=Risk, ymin=mean-se, ymax=mean+se), width=0.4, colour="orange", alpha=0.9, size=1.5) +
ggtitle("Brave ~ Risk type (B = Boredom; R = High risk); bars are SE")## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
## Set$Risk: B
## [1] 1.278198
## ------------------------------------------------------------
## Set$Risk: R
## [1] 1.259083## [1] 1.280748The Welch Two Sample t-test testing the difference of Bravery by Risk condition (mean in group Boredom = 5.62, mean in group Risk = 5.98) suggests that the effect is negative, statistically significant, and medium sized (difference = -0.36, 95% CI [-0.49, -0.22], t(1357.02) = -5.21, p < .001; Cohen’s d = -0.28, 95% CI [-0.39, -0.18])
==> Success Manipulation Check. Yes, Our manipulation of Physical risks influenced Bravery evaluations. This is a medium effect, d = 0.28.
Perception of selflessness
The Motivation type (Altruistic vs Self-centered) should predict the perception of Altruism, defined as the average between “Caring” scores and reverse-coded “Selfless” scores.
##
## Welch Two Sample t-test
##
## data: Set$Selfless by Set$Help
## t = 4.7993, df = 1336.6, p-value = 1.771e-06
## alternative hypothesis: true difference in means between group H and group S is not equal to 0
## 95 percent confidence interval:
## 0.2034586 0.4847767
## sample estimates:
## mean in group H mean in group S
## 5.669118 5.325000my_sum <- Set %>%
group_by(Help) %>%
summarise(
n=n(),
mean=mean(Brave),
sd=sd(Brave)
) %>%
mutate( se=sd/sqrt(n))
# Standard deviation
ggplot(my_sum) +
geom_bar( aes(x=Help, y=mean), stat="identity", fill="forestgreen", alpha=0.5) +
geom_errorbar( aes(x=Help, ymin=mean-se, ymax=mean+se), width=0.4, colour="orange", alpha=0.9, size=1.5) +
ggtitle("Selfless ~ Help type (H = Helping; S = Self improve); bars are SE")
The Welch Two Sample t-test testing the difference of
Selflessness by Motivation condition (mean in group Helping People =
5.67, mean in group Self-improvement = 5.33) suggests that the effect is
positive, statistically significant, and medium sized (difference =
0.34, 95% CI [0.20, 0.48], t(1336.56) = 4.80, p < .001; Cohen’s d =
0.26, 95% CI [0.15, 0.37])
==> Success. Yes, motivation types did predict perception of selflessness. This is a medium effect, d = 0.26
Manipulation check 2: Situation attribution
This tab contains:
- Perceived Risk Does our Risk manipulation influence perceived Physical risk?
- Perceived helpfulness Does our Motivation manipulation influence perceived helpfulness?
Perceived Risk
To what extent do you believe the target occupation is exposed to physical danger – Risk type should increase evaluation of physical risks
##
## Welch Two Sample t-test
##
## data: Set$Danger by Set$Risk
## t = -18.15, df = 1190.5, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group B and group R is not equal to 0
## 95 percent confidence interval:
## -1.294546 -1.041971
## sample estimates:
## mean in group B mean in group R
## 5.113905 6.282164my_sum <- Set %>%
group_by(Risk) %>%
summarise(
n=n(),
mean=mean(Danger),
sd=sd(Danger)
) %>%
mutate( se=sd/sqrt(n))
# Standard deviation
ggplot(my_sum) +
geom_bar( aes(x=Risk, y=mean), stat="identity", fill="forestgreen", alpha=0.5) +
geom_errorbar( aes(x=Risk, ymin=mean-se, ymax=mean+se), width=0.4, colour="orange", alpha=0.9, size=1.5) +
ggtitle("Danger ~ Risk type (B = Boredom; R = High risk); bars are SE")
The Welch Two Sample t-test testing the difference of
Situation Danger by Risk condition (mean in group Boredom = 5.11, mean
in group Risk = 6.28) suggests that the effect is negative,
statistically significant, and large (difference = -1.17, 95% CI [-1.29,
-1.04], t(1190.54) = -18.15, p < .001; Cohen’s d = -0.99, 95% CI
[-1.10, -0.87])
==> Success. Yes, Risk condition did predict perception of Danger – this is a very large effect.
Perceived helpfulness
To what extent do you believe the target occupation helps people? – Motivation type should increase evaluation of help provided
##
## Welch Two Sample t-test
##
## data: Set$Helpfulness by Set$Help
## t = 5.0127, df = 1289.5, p-value = 6.113e-07
## alternative hypothesis: true difference in means between group H and group S is not equal to 0
## 95 percent confidence interval:
## 0.1852758 0.4235477
## sample estimates:
## mean in group H mean in group S
## 6.107353 5.802941my_sum <- Set %>%
group_by(Help) %>%
summarise(
n=n(),
mean=mean(Helpfulness),
sd=sd(Helpfulness)
) %>%
mutate( se=sd/sqrt(n))
# Standard deviation
ggplot(my_sum) +
geom_bar( aes(x=Help, y=mean), stat="identity", fill="forestgreen", alpha=0.5) +
geom_errorbar( aes(x=Help, ymin=mean-se, ymax=mean+se), width=0.4, colour="orange", alpha=0.9, size=1.5) +
ggtitle("Helpfulness ~ Motivation type (H = Helping; S = Self-improve); bars are SE")
The Welch Two Sample t-test testing the difference of
Helpfulness by Motivation condition (mean in group Helping people =
6.11, mean in group Self-improvement = 5.80) suggests that the effect is
positive, statistically significant, and medium sized (difference =
0.30, 95% CI [0.19, 0.42], t(1289.51) = 5.01, p < .001; Cohen’s d =
0.27, 95% CI [0.16, 0.38])
==> Success. Yes, Motivation condition did predict helpfulness – this is medium effect, d = 0.27.
Credibility analyses
We included a credibility check. Participants were asked at the end of the study, “to what extent they found the information presented believable”. Scores range from 1 to 7. We can check the distribution of the credibility rating:
my_sum <- Set %>%
group_by(Job) %>%
summarise(
n=n(),
mean=mean(Credibility),
sd=sd(Credibility)
) %>%
mutate( se=sd/sqrt(n))
# Standard deviation
ggplot(my_sum) +
geom_bar( aes(x=Job, y=mean), stat="identity", fill="forestgreen", alpha=0.5) +
geom_errorbar( aes(x=Job, ymin=mean-se, ymax=mean+se), width=0.4, colour="orange", alpha=0.9, size=1.5) +
ggtitle("Credibility (bars are SE) by job condition")
Cred <- subset(df_long, df_long$Variable == "Credibility")
df_summary <- Cred %>%
group_by(Job) %>%
summarize(
mean_score = mean(Score, na.rm = TRUE),
sd_score = sd(Score, na.rm = TRUE),
.groups = "drop"
)
ggplot(Cred, aes(x = Score)) +
geom_histogram(aes(fill = after_stat(count)),
binwidth = 1,
color = "black", show.legend = FALSE) +
facet_grid( ~ Job, scales = "free") +
scale_fill_gradientn(
colours = brewer.pal(9, "YlOrBr"),
name = "Count"
) +
labs(
title = "Frequency of Responses for the Credibility item, for each occupation condition",
x = "Score",
y = "Count"
) +
# Annotate each facet with the mean and standard deviation
geom_text(data = df_summary,
aes(x = 7, y = Inf,
label = paste0("Mean = ", round(mean_score, 2),
"\nSD = ", round(sd_score, 2))),
vjust = 1.5, hjust = 1.1, size = 3) +
theme_classic() +
theme(
panel.grid.major.y = element_line(linewidth = 0.5),
panel.grid.minor.y = element_line(linewidth = 0.5)
)
The study was overall quite credible. In the
exploratory section, we will further assess to what extent credibility
rating influenced our effects.
Principal analyses
On the basis of our manipulation checks, it can be stated that our manipulations (both physical risks and motivation type) were successful in changing evaluations of bravery, selflessness, danger, and helpfulness. We proceed with our main registered hypotheses. This section contains analyses regarding:
- H1: the effect of our manipulations on heroism
- H2: the effect of perceived selflessness and perceived bravery on heroism
- H3: the effect of perceived risk and perceived helpfulness on heroism
Hypotheses 1: Manipulation as predictors
This tab contains:
- H1 Model comparison testing the influence of job as a covariate
- H1 Model Comparison Attitude testing the influence of Attitude for a possible halo effect
- H1 Main registered model How does our manipulations predict Heroism
- H1 Outliers analyses Comparison of betas between robust and non robust mixed models
- H1 Job interaction There is an effect of job - so we took a look at the occupation level by subsetting our data frame.
- H1 Occupation Decomposition How does our manipulation influenced each occupation?
- H1 Conclusion
From registration:
***Statistical Technique***
A model comparison approach will be used to assess the effects of our manipulations and qualify the variance part of Heroism perception explained by our manipulation (dummy coded -0.5 and 0.5) and by normative evaluation effects (i.e., baseline differences in heroism perceptions across occupations), and by a general halo effect relating to general attitude.
We will use two steps to evaluate the effects of our manipulation of perceived heroism:
A first regression model (Model 1) to assess:
- The effect of the Risk type (dummy coded -0.5 for the No risk condition, and 0.5 for the High risk condition) on the attribution of Heroism across all occupations (H1a)
- The effect of the Motivation type (dummy coded - 0.5 for the self-centered condition, and 0.5 for the altruistic condition) on the attribution of Heroism across all occupations (H1b)
- Their interaction (exploratory analysis)
A second model with Job type as a moderator (Model 2):
- The effect of the Risk type (dummy coded -0.5 for the No risk condition, and 0.5 for the High risk condition) on the attribution of Heroism across all occupations (H1a)
- The effect of the Motivation type (dummy coded - 0.5 for the self-centered condition, and 0.5 for the altruistic condition) on the attribution of Heroism across all occupations (H1b)
- Their interaction (exploratory analysis)
- A higher order interaction when considering Job type (to control for potential higher order interaction - we will further explore the effects within each occupation condition in independent OLS regression models, see Registered R script, section "Further explorations")
We will compare the two models (with and without accounting for the occupation condition) to quantify the extent to which the effect of our manipulation is explained by normative differences in occupation type: A significant reduction in the other predictors' main effect sizes when controlling for Job Type would indicate that these effects are partially dependent on normative evaluations of the job type.
We will base our conclusions regarding the effects of our manipulations irrespective of the job types (i.e., across all jobs) on the Model 1. Model 2 is used to quantify normative evaluation effects in our effects.
Because we have clear registered predictions for the two main effects, but not for any interaction, we will use one-tailed tests for the main effects, but two-tailed tests for the interactions.
H1 Model comparison
We will compare the two models (with and without accounting for the occupation condition) to quantify the extent to which the effect of our manipulation is explained by normative differences in occupation type: A significant reduction in the other predictors’ main effect sizes when controlling for Job Type would indicate that these effects are partially dependent on normative evaluations of the job type.
We will base our conclusions regarding the effects of our manipulations irrespective of the job types (i.e., across all jobs) on the Model 1. Model 2 is used to quantify normative evaluation effects in our effects.
mod <-lm(Heroism ~ Risk_dummy * Help_dummy, data = Set)
mod_cov<-lm(Heroism ~ Risk_dummy * Help_dummy + Job, data = Set)
anova(mod, mod_cov)## Analysis of Variance Table
##
## Model 1: Heroism ~ Risk_dummy * Help_dummy
## Model 2: Heroism ~ Risk_dummy * Help_dummy + Job
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 1356 2906.4
## 2 1352 2437.6 4 468.79 65.004 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Model comparison indicates that Heroism rate are significantly driven by normative ratings: model using Job as a covariate is associated to a significantly lower RSS (RSS = 2378.1 16) than the model not using a covariate (RSS = 2906.4, F = 18.603, p < .000001).
H1 Model Comparison Attitude
To test whether a halo effect could account for any observed effect, we also did a model comparison with attitudes as a covariate:
##
## Call:
## lm(formula = Heroism ~ Risk_dummy * Help_dummy + Attitude, data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.1585 -0.4928 -0.0421 0.8415 3.6071
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.196735 0.148368 1.326 0.185
## Risk_dummy 0.276350 0.059317 4.659 3.49e-06 ***
## Help_dummy -0.008258 0.059290 -0.139 0.889
## Attitude 0.831791 0.025076 33.171 < 2e-16 ***
## Risk_dummy:Help_dummy 0.012139 0.118064 0.103 0.918
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.088 on 1355 degrees of freedom
## Multiple R-squared: 0.4647, Adjusted R-squared: 0.4631
## F-statistic: 294.1 on 4 and 1355 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Model 1: Heroism ~ Risk_dummy * Help_dummy
## Model 2: Heroism ~ Risk_dummy * Help_dummy + Attitude
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 1356 2906.4
## 2 1355 1603.9 1 1302.4 1100.3 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1An overwhelming importance of attitudes in predicting Heroism ratings. It emphasises the need to control for attitudes.
==> JOB and ATTITUDE explain Heroism above and beyond our experimental manipulations
H1 Main registered model
Below, we present some plots showing QQ-plot (normality of the residuals), fitted vs predicted residuals (heteroscedasticity) and Cook’s distance of predicted values. These diagnostics flags major concerns about normality of the residuals and the influence of some observations (Cook’s d plot). This further warrants some robust analyses (see the robust model). In the mean time, we also present the OLS results.
##
## Call:
## lm(formula = Heroism ~ Risk_dummy * Help_dummy, data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.3246 -0.8994 0.1006 1.1006 2.3373
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.0199 0.0397 126.448 < 2e-16 ***
## Risk_dummy 0.4777 0.0794 6.017 2.29e-09 ***
## Help_dummy 0.1841 0.0794 2.319 0.0205 *
## Risk_dummy:Help_dummy -0.1051 0.1588 -0.662 0.5082
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.464 on 1356 degrees of freedom
## Multiple R-squared: 0.03004, Adjusted R-squared: 0.0279
## F-statistic: 14 on 3 and 1356 DF, p-value: 5.444e-09## We fitted a linear model (estimated using OLS) to predict Heroism with
## Risk_dummy and Help_dummy (formula: Heroism ~ Risk_dummy * Help_dummy). The
## model explains a statistically significant and weak proportion of variance (R2
## = 0.03, F(3, 1356) = 14.00, p < .001, adj. R2 = 0.03). The model's intercept,
## corresponding to Risk_dummy = 0 and Help_dummy = 0, is at 5.02 (95% CI [4.94,
## 5.10], t(1356) = 126.45, p < .001). Within this model:
##
## - The effect of Risk dummy is statistically significant and positive (beta =
## 0.48, 95% CI [0.32, 0.63], t(1356) = 6.02, p < .001; Std. beta = 0.16, 95% CI
## [0.11, 0.21])
## - The effect of Help dummy is statistically significant and positive (beta =
## 0.18, 95% CI [0.03, 0.34], t(1356) = 2.32, p = 0.021; Std. beta = 0.06, 95% CI
## [9.45e-03, 0.11])
## - The effect of Risk dummy × Help dummy is statistically non-significant and
## negative (beta = -0.11, 95% CI [-0.42, 0.21], t(1356) = -0.66, p = 0.508; Std.
## beta = -0.02, 95% CI [-0.07, 0.03])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.We fitted a linear model (estimated using OLS) to predict Heroism with Risk_dummy and Help_dummy (formula: Heroism ~ Risk_dummy * Help_dummy). The model explains a statistically significant proportion of variance (R2 = 0.03, F(3, 1356) = 14.00, p < .001, adj. R2 = 0.03). Within this model:
- The effect of Risk dummy is statistically significant and positive (beta = 0.48, 95% CI [0.32, 0.63], t(1356) = 6.02, p < .001; Std. beta = 0.16, 95% CI [0.11, 0.21])
- The effect of Help dummy is statistically significant and positive (beta = 0.18, 95% CI [0.03, 0.34], t(1356) = 2.32, p = 0.021; Std. beta = 0.06, 95% CI [9.45e-03, 0.11])
- The effect of Risk dummy × Help dummy is statistically non-significant (beta = -0.11, 95% CI [-0.42, 0.21], t(1356) = -0.66, p = 0.508; Std. beta = -0.02, 95% CI [-0.07, 0.03])
## Type 3 ANOVAs only give sensible and informative results when covariates
## are mean-centered and factors are coded with orthogonal contrasts (such
## as those produced by `contr.sum`, `contr.poly`, or `contr.helmert`, but
## *not* by the default `contr.treatment`).## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## -----------------------------------------------------
## Risk_dummy | 0.03 | [0.01, 1.00]
## Help_dummy | 3.95e-03 | [0.00, 1.00]
## Risk_dummy:Help_dummy | 3.23e-04 | [0.00, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].Model Linearity?
Because the main outcome is an ordinal variable (using integrals), it is unclear whether the model is linear or not. We can fit a cumulative link model, ideal for ordinal outcomes, to assess to what extent this changes our inferences.
# # Fitted values from your model
# fitted_vals <- fitted(mod)
#
# # Plot observed values against fitted values
# plot(fitted_vals, Set$Heroism,
# xlab = "Fitted Values",
# ylab = "Observed Heroes",
# main = "Observed vs Fitted Values")
# abline(0, 1, col = "blue", lty = 2)
summary(clm(ordered(Heroism) ~ Risk_dummy * Help_dummy, data = Set, link = "logit"))## formula: ordered(Heroism) ~ Risk_dummy * Help_dummy
## data: Set
##
## link threshold nobs logLik AIC niter max.grad cond.H
## logit flexible 1360 -2328.78 4675.56 5(0) 5.44e-08 3.8e+01
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## Risk_dummy 0.59565 0.09725 6.125 9.07e-10 ***
## Help_dummy 0.20359 0.09628 2.115 0.0345 *
## Risk_dummy:Help_dummy -0.10979 0.19233 -0.571 0.5681
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Threshold coefficients:
## Estimate Std. Error z value
## 1|2 -3.83582 0.18501 -20.733
## 2|3 -2.66230 0.10855 -24.527
## 3|4 -1.84560 0.07873 -23.444
## 4|5 -0.71009 0.05811 -12.220
## 5|6 0.42414 0.05592 7.584
## 6|7 1.50898 0.07038 21.441Using a Cumulative Link model does not change our results whatsoever.
==> Success. Both our Risk and Motivation manipulations positively influenced perceived heroism. They did not interact. Results were robust to a model adapted to ordinal variables. Importantly, the effect size of the Motivation manipulation is particularly modest: d = 0.12 95%CI[0.02, 0.23]
## [1] "Cohen's d for the effect of risk is:"## Cohen's d | 95% CI
## ------------------------
## 0.33 | [0.22, 0.43]
##
## - Estimated using pooled SD.## [1] "Cohen's d for the effect of Motivation is:"## Cohen's d | 95% CI
## ------------------------
## 0.12 | [0.02, 0.23]
##
## - Estimated using pooled SD.H1 Outliers analyses
Note on Outlier management: As registered,
We compared the outputs from our models to the outputs of a robust model
using a smoothed Huber function to down-weight extreme residuals. Robust
models used the default parameters from the lmrob command
in the robustbase package – that is a set of parameters
resulting in a 95% efficiency (assuming normal residual distribution and
no contamination). This model is robust to the presence of extreme
values and less sensitive to deviations from normality assumption
Cook’s distance plot does show that there are some influential cases:
(Note that in all Cook’s d barplots, the threshold for identifying influential cases is 4/N = 0.003 – this is an usual way of finding influential cases based on Cook’s distance but… it’s a rule of thumb).
This warrant the use of robust models, or at the very least, a model comparison with robust models.
##
## Call:
## lmrob(formula = Set$Heroism ~ Set$Risk_dummy * Set$Help_dummy)
## \--> method = "MM"
## Residuals:
## Min 1Q Median 3Q Max
## -4.40872 -0.96122 0.03878 1.03878 2.25711
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.10065 0.04178 122.071 < 2e-16 ***
## Set$Risk_dummy 0.49720 0.08155 6.097 1.41e-09 ***
## Set$Help_dummy 0.16863 0.08137 2.072 0.0384 *
## Set$Risk_dummy:Set$Help_dummy -0.09939 0.16268 -0.611 0.5413
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Robust residual standard error: 1.462
## Multiple R-squared: 0.03149, Adjusted R-squared: 0.02935
## Convergence in 10 IRWLS iterations
##
## Robustness weights:
## 93 weights are ~= 1. The remaining 1267 ones are summarized as
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3432 0.8792 0.9545 0.9088 0.9852 0.9972
## Algorithmic parameters:
## tuning.chi bb tuning.psi refine.tol
## 1.548e+00 5.000e-01 4.685e+00 1.000e-07
## rel.tol scale.tol solve.tol zero.tol
## 1.000e-07 1.000e-10 1.000e-07 1.000e-10
## eps.outlier eps.x warn.limit.reject warn.limit.meanrw
## 7.353e-05 1.819e-12 5.000e-01 5.000e-01
## nResample max.it best.r.s k.fast.s k.max
## 500 50 2 1 200
## maxit.scale trace.lev mts compute.rd fast.s.large.n
## 200 0 1000 0 2000
## psi subsampling cov
## "bisquare" "nonsingular" ".vcov.avar1"
## compute.outlier.stats
## "SM"
## seed : int(0)paste0("Weights applied to residuals - a value of zero would mean that the observation was discarded, a value of 1 means no re-weighting")## [1] "Weights applied to residuals - a value of zero would mean that the observation was discarded, a value of 1 means no re-weighting"
Our inferences remain unchanged by downweighting extreme residuals. No large discrepancy.
H1 Job interaction
We registered that we would explore any higher-order interaction with occupation type.
The effect of Risk was qualified by occupation type:
## Analysis of Variance Table
##
## Response: Heroism
## Df Sum Sq Mean Sq F value Pr(>F)
## Risk_dummy 1 77.59 77.587 43.7176 5.464e-11 ***
## Help_dummy 1 11.49 11.489 6.4737 0.01106 *
## Job 4 468.56 117.141 66.0053 < 2.2e-16 ***
## Risk_dummy:Help_dummy 1 1.17 1.166 0.6569 0.41779
## Risk_dummy:Job 4 45.35 11.338 6.3885 4.314e-05 ***
## Help_dummy:Job 4 8.85 2.212 1.2462 0.28941
## Risk_dummy:Help_dummy:Job 4 5.25 1.312 0.7391 0.56531
## Residuals 1340 2378.13 1.775
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1H1 Occupation Decomposition
Because, we observed that occupation influenced the effect of the
risk manipulation, there is a solid ground to test our hypothesis within
each job. In the table below, we report results from the model
lm(Heroism ~ Risk_dummy + Help_dummy, data = ...) for each
occupation.
Nurses <- subset(Set, Set$Job == "N")
Pol <- subset(Set, Set$Job == "P")
Firef <- subset(Set, Set$Job == "F")
Psych <- subset(Set, Set$Job == "Ps")
Psych <- subset(Set, Set$Job == "Ps")
# Regression results data frame
regression_results <- data.frame(
Group = rep(c("Nurses", "Police", "Firefighters", "Psychiatrists", "Welders"), each = 3),
Effect = rep(c("Risk dummy", "Help dummy", "Risk dummy × Help dummy"), times = 5),
Beta = c(0.20, 0.05, -0.51,
0.24, 0.12, 0.01,
0.29, 0.00586, 0.02,
0.52, 0.36, -0.29,
1.18, 0.40, 0.18),
CI = c("[-0.15, 0.54]", "[-0.30, 0.39]", "[-1.20, 0.18]",
"[-0.08, 0.56]", "[-0.19, 0.44]", "[-0.63, 0.65]",
"[0.01, 0.56]", "[-0.27, 0.28]", "[-0.53, 0.57]",
"[0.19, 0.86]", "[0.02, 0.70]", "[-0.97, 0.38]",
"[0.87, 1.49]", "[0.08, 0.71]", "[-0.44, 0.80]"),
t_value = c(1.12, 0.27, -1.46,
1.49, 0.77, 0.03,
2.04, 0.04, 0.06,
3.05, 2.11, -0.86,
7.46, 2.50, 0.57),
p_value = c(0.264, 0.789, 0.146,
0.137, 0.442, 0.973,
0.042, 0.967, 0.950,
0.002, 0.035, 0.392,
"<0.001", 0.013, 0.568),
Std_Beta = c(0.07, 0.02, -0.09,
0.09, 0.05, 0.00207,
0.12, 0.00252, 0.00384,
0.18, 0.13, -0.05,
0.41, 0.14, 0.03),
Std_CI = c("[-0.05, 0.19]", "[-0.10, 0.14]", "[-0.21, 0.03]",
"[-0.03, 0.21]", "[-0.07, 0.17]", "[-0.12, 0.12]",
"[4.40e-03, 0.24]", "[-0.12, 0.12]", "[-0.12, 0.12]",
"[0.06, 0.30]", "[7.95e-03, 0.24]", "[-0.17, 0.07]",
"[0.30, 0.52]", "[0.03, 0.25]", "[-0.08, 0.14]"),
stringsAsFactors = FALSE
)
# Create the effect sizes data frame
effect_sizes <- data.frame(
Group = rep(c("Nurses", "Police", "Firefighters", "Psychiatrists", "Welders"), each = 2),
Effect = rep(c("Risk", "Motivation"), times = 5),
Cohen_d = c(0.14, 0.03,
0.18, 0.09,
0.25, 0.00593,
0.37, 0.25,
0.89, 0.27),
CI = c("[-0.10, 0.37]", "[-0.20, 0.27]",
"[-0.06, 0.42]", "[-0.14, 0.33]",
"[0.01, 0.49]", "[-0.23, 0.24]",
"[0.13, 0.61]", "[0.01, 0.49]",
"[0.64, 1.14]", "[0.03, 0.51]"),
stringsAsFactors = FALSE
)
regression_results_gt <- regression_results %>%
gt(groupname_col = "Group") %>% # automatically groups rows by the Group column
fmt_number(
columns = c("Beta", "t_value", "Std_Beta"),
decimals = 2
) %>%
tab_header(title = "Regression Results Summary")
## Create the gt table for effect sizes:
effect_sizes_gt <- effect_sizes %>%
gt(groupname_col = "Group") %>%
# Format numeric columns to display 2 decimals
fmt_number(
columns = c("Cohen_d"), # add any other numeric columns you want to format
decimals = 2
) %>%
tab_header(
title = "Effect Sizes (Cohen's d)"
) %>%
cols_label(
Effect = "Effect",
Cohen_d = "Cohen's d",
CI = "95% CI"
)
# Display the tables in an HTML document (in R Markdown, simply putting the table object in a code chunk will render it)
regression_results_gt| Regression Results Summary | ||||||
| Effect | Beta | CI | t_value | p_value | Std_Beta | Std_CI |
|---|---|---|---|---|---|---|
| Nurses | ||||||
| Risk dummy | 0.20 | [-0.15, 0.54] | 1.12 | 0.264 | 0.07 | [-0.05, 0.19] |
| Help dummy | 0.05 | [-0.30, 0.39] | 0.27 | 0.789 | 0.02 | [-0.10, 0.14] |
| Risk dummy × Help dummy | −0.51 | [-1.20, 0.18] | −1.46 | 0.146 | −0.09 | [-0.21, 0.03] |
| Police | ||||||
| Risk dummy | 0.24 | [-0.08, 0.56] | 1.49 | 0.137 | 0.09 | [-0.03, 0.21] |
| Help dummy | 0.12 | [-0.19, 0.44] | 0.77 | 0.442 | 0.05 | [-0.07, 0.17] |
| Risk dummy × Help dummy | 0.01 | [-0.63, 0.65] | 0.03 | 0.973 | 0.00 | [-0.12, 0.12] |
| Firefighters | ||||||
| Risk dummy | 0.29 | [0.01, 0.56] | 2.04 | 0.042 | 0.12 | [4.40e-03, 0.24] |
| Help dummy | 0.01 | [-0.27, 0.28] | 0.04 | 0.967 | 0.00 | [-0.12, 0.12] |
| Risk dummy × Help dummy | 0.02 | [-0.53, 0.57] | 0.06 | 0.95 | 0.00 | [-0.12, 0.12] |
| Psychiatrists | ||||||
| Risk dummy | 0.52 | [0.19, 0.86] | 3.05 | 0.002 | 0.18 | [0.06, 0.30] |
| Help dummy | 0.36 | [0.02, 0.70] | 2.11 | 0.035 | 0.13 | [7.95e-03, 0.24] |
| Risk dummy × Help dummy | −0.29 | [-0.97, 0.38] | −0.86 | 0.392 | −0.05 | [-0.17, 0.07] |
| Welders | ||||||
| Risk dummy | 1.18 | [0.87, 1.49] | 7.46 | <0.001 | 0.41 | [0.30, 0.52] |
| Help dummy | 0.40 | [0.08, 0.71] | 2.50 | 0.013 | 0.14 | [0.03, 0.25] |
| Risk dummy × Help dummy | 0.18 | [-0.44, 0.80] | 0.57 | 0.568 | 0.03 | [-0.08, 0.14] |
Table below synthetise the effect sizes (Cohen’s d) for each model.
| Effect Sizes (Cohen's d) | ||
| Effect | Cohen's d | 95% CI |
|---|---|---|
| Nurses | ||
| Risk | 0.14 | [-0.10, 0.37] |
| Motivation | 0.03 | [-0.20, 0.27] |
| Police | ||
| Risk | 0.18 | [-0.06, 0.42] |
| Motivation | 0.09 | [-0.14, 0.33] |
| Firefighters | ||
| Risk | 0.25 | [0.01, 0.49] |
| Motivation | 0.01 | [-0.23, 0.24] |
| Psychiatrists | ||
| Risk | 0.37 | [0.13, 0.61] |
| Motivation | 0.25 | [0.01, 0.49] |
| Welders | ||
| Risk | 0.89 | [0.64, 1.14] |
| Motivation | 0.27 | [0.03, 0.51] |
It turns out that our manipulation was fully effective only in the psychiatrists and welders conditions. These two roles are assumed to be “not typically heroic”. As such, we explain these differences between roles as relating to the stereotypes of these occupations being more malleable than the others. People might have weaker opinions of psychiatrists and welders opinions.
H1 Conclusion
Hypothesis 1 received support. However, the Motivation manipulation had a very small effect on heroism perception (eta2 < 1%; d= 0.12). Moreover, when looking into each specific jobs - it turns out that Psychiatrists and Welders (least stereotyped jobs) are driving these effects. Other, typically heroized, occupations were unaffected by our manipulations.
There was NO interaction between the manipulations of risk and motivation. The two effects are independent - motivation type did not influence the independent effect of the risk manipulation.
Hypotheses 2: Character attributions as predictors
This tab contains:
- H2 Model comparison with job testing the influence of job as a covariate
- H2 Model comparison with attitude testing the influence of job as a covariate
- H2 Main registered model How does selflessness and bravery predict Heroism
- H2 Outliers analyses Comparison of betas between robust and non robust mixed models
- H2 Decomposition of the effects within job We tests our main effects in each occupation
- H2 Conclusion
From registration:
We will use three steps to evaluate the effects of our manipulation of perceived heroism:
A first regression model to assess:
- The effect of the bravery perceptions on Heroism attribution across all occupations (H2a)
- The effect of the selflessness perceptions on Heroism attribution across all occupations (H2b)
- Their interaction (exploratory analysis)
A second model with Job type as covariate and moderator:
- The effect of the bravery perceptions on Heroism attribution across all occupations (H2a)
- The effect of the selflessness perceptions on Heroism attribution across all occupations (H2b)
- Their interaction (exploratory analysis)
- A higher order interaction when considering Job type (to control for potential higher order interaction - should occupation interact with any variable, we would further explore the interactions when decomposing by job types in independent OLS regression models, see Registered R script, section "Further explorations")
We will compare the two models to quantify the extent to which the effects of measured bravery and selflessness are explained by normative differences in occupation type: A significant reduction in the other predictors' main effect sizes when controlling for Job Type would indicate that these effects are partially dependent on normative evaluations of the job type.
A third model will be computed to control for a possible halo effect explaining positive correlations, using General attitude as a covariate (Model 3):
- The effect of the bravery perceptions on Heroism attribution across all occupations (H2a)
- The effect of the selflessness perceptions on Heroism attribution across all occupations (H2b)
- Their interaction (exploratory analysis)
- The effect of General attitude (covariate)
We will compare Model 1 and Model 3 to assess to what extent our effects are conditioned by a general halo effect -- that is heroism is explained by general attitude rather than our key variables. A significant reduction in the other predictors' main effect sizes when controlling for General attitude would indicate that these effects are partially dependent on the participant's attitude of the target occupation.
We will base our conclusions regarding the effects of our manipulations irrespective of the job types (i.e., across all jobs) on the Model 1. Model 2 is used to quantify normative evaluation effects in our effects, and Model 3 to quantify halo effects involved in our results.H2 Model comparison with job
We compare a model with job as a covariate to a model that does not account for job. This will test the importance of the normative effect of jobs in heroism.
Set$Selfless_scale <- scale(Set$Selfless)
Set$Brave_scale <- scale(Set$Brave)
Set$Danger_scale <- scale(Set$Danger)
Set$Helpful_scale <- scale(Set$Helpfulness)
Set$Attitude_scale <- scale(Set$Attitude)
(mod<-lm(Heroism ~ Selfless_scale * Brave_scale , data = Set))##
## Call:
## lm(formula = Heroism ~ Selfless_scale * Brave_scale, data = Set)
##
## Coefficients:
## (Intercept) Selfless_scale
## 4.8831 0.5745
## Brave_scale Selfless_scale:Brave_scale
## 0.5844 0.2073## Analysis of Variance Table
##
## Model 1: Heroism ~ Selfless_scale * Brave_scale
## Model 2: Heroism ~ Selfless_scale * Brave_scale + Job
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 1356 1766.3
## 2 1352 1663.6 4 102.74 20.874 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Here also, the heroism rate is driven by normative evaluations of the job – including jobs as covariate leads to a better fit (RSS = 1766.3, vs RSS = 1663.6, F = 20.874, p < .000001) ___
H2 Model comparison with attitude
To account for a possible Halo effect, let’s see if attitudes play a role in explaining heroism.
##
## Call:
## lm(formula = Heroism ~ Selfless_scale * Brave_scale, data = Set)
##
## Coefficients:
## (Intercept) Selfless_scale
## 4.8831 0.5745
## Brave_scale Selfless_scale:Brave_scale
## 0.5844 0.2073##
## Call:
## lm(formula = Heroism ~ Selfless_scale * Brave_scale + Attitude_scale,
## data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.4204 -0.4442 0.1491 0.5796 2.8274
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.91561 0.03090 159.075 < 2e-16 ***
## Selfless_scale 0.29629 0.04015 7.379 2.76e-13 ***
## Brave_scale 0.34209 0.04221 8.104 1.18e-15 ***
## Attitude_scale 0.67719 0.03679 18.408 < 2e-16 ***
## Selfless_scale:Brave_scale 0.15862 0.02058 7.708 2.46e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.021 on 1355 degrees of freedom
## Multiple R-squared: 0.5284, Adjusted R-squared: 0.527
## F-statistic: 379.6 on 4 and 1355 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Model 1: Heroism ~ Selfless_scale * Brave_scale
## Model 2: Heroism ~ Selfless_scale * Brave_scale + Attitude_scale
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 1356 1766.3
## 2 1355 1413.0 1 353.35 338.85 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Massively so: the model using attitude as a covariant explained heroism way better (RSS = 1413) than the model omitting this variable (RSS = 1766), F = 339, p < .00001. It will be important to control for attitude in our conclusions.
==> JOB and ATTITUDE explain Heroism above and beyond the ratings of selflessness and bravery ___
H2 Main registered model
##
## Call:
## lm(formula = Heroism ~ Selfless_scale * Brave_scale, data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.2958 -0.4015 0.2531 0.7042 4.1631
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.88313 0.03448 141.62 <2e-16 ***
## Selfless_scale 0.57453 0.04157 13.82 <2e-16 ***
## Brave_scale 0.58440 0.04483 13.04 <2e-16 ***
## Selfless_scale:Brave_scale 0.20734 0.02281 9.09 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.141 on 1356 degrees of freedom
## Multiple R-squared: 0.4105, Adjusted R-squared: 0.4092
## F-statistic: 314.8 on 3 and 1356 DF, p-value: < 2.2e-16## 2.5 % 97.5 %
## (Intercept) 4.8154906 4.9507726
## Selfless_scale 0.4929716 0.6560860
## Brave_scale 0.4964587 0.6723356
## Selfless_scale:Brave_scale 0.1625999 0.2520898## We fitted a linear model (estimated using OLS) to predict Heroism with
## Selfless_scale and Brave_scale (formula: Heroism ~ Selfless_scale *
## Brave_scale). The model explains a statistically significant and substantial
## proportion of variance (R2 = 0.41, F(3, 1356) = 314.76, p < .001, adj. R2 =
## 0.41). The model's intercept, corresponding to Selfless_scale = 0 and
## Brave_scale = 0, is at 4.88 (95% CI [4.82, 4.95], t(1356) = 141.62, p < .001).
## Within this model:
##
## - The effect of Selfless scale is statistically significant and positive (beta
## = 0.57, 95% CI [0.49, 0.66], t(1356) = 13.82, p < .001; Std. beta = 0.39, 95%
## CI [0.33, 0.44])
## - The effect of Brave scale is statistically significant and positive (beta =
## 0.58, 95% CI [0.50, 0.67], t(1356) = 13.04, p < .001; Std. beta = 0.39, 95% CI
## [0.33, 0.45])
## - The effect of Selfless scale × Brave scale is statistically significant and
## positive (beta = 0.21, 95% CI [0.16, 0.25], t(1356) = 9.09, p < .001; Std. beta
## = 0.14, 95% CI [0.11, 0.17])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.mean_selfless <- mean(Set$Selfless_scale, na.rm = TRUE)
sd_selfless <- sd(Set$Selfless_scale, na.rm = TRUE)
Set$Selfless_p1sd <- Set$Selfless_scale - (mean_selfless + sd_selfless)
Set$Selfless_m1sd <- Set$Selfless_scale - (mean_selfless - sd_selfless)
model_p1sd <- lm(Heroism ~ Brave_scale * Selfless_p1sd, data = Set)
report(model_p1sd)## We fitted a linear model (estimated using OLS) to predict Heroism with
## Brave_scale and Selfless_p1sd (formula: Heroism ~ Brave_scale * Selfless_p1sd).
## The model explains a statistically significant and substantial proportion of
## variance (R2 = 0.41, F(3, 1356) = 314.76, p < .001, adj. R2 = 0.41). The
## model's intercept, corresponding to Brave_scale = 0 and Selfless_p1sd = 0, is
## at 5.46 (95% CI [5.35, 5.56], t(1356) = 101.77, p < .001). Within this model:
##
## - The effect of Brave scale is statistically significant and positive (beta =
## 0.79, 95% CI [0.68, 0.90], t(1356) = 13.79, p < .001; Std. beta = 0.39, 95% CI
## [0.33, 0.45])
## - The effect of Selfless p1sd is statistically significant and positive (beta =
## 0.57, 95% CI [0.49, 0.66], t(1356) = 13.82, p < .001; Std. beta = 0.39, 95% CI
## [0.33, 0.44])
## - The effect of Brave scale × Selfless p1sd is statistically significant and
## positive (beta = 0.21, 95% CI [0.16, 0.25], t(1356) = 9.09, p < .001; Std. beta
## = 0.14, 95% CI [0.11, 0.17])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.## We fitted a linear model (estimated using OLS) to predict Heroism with
## Brave_scale and Selfless_m1sd (formula: Heroism ~ Brave_scale * Selfless_m1sd).
## The model explains a statistically significant and substantial proportion of
## variance (R2 = 0.41, F(3, 1356) = 314.76, p < .001, adj. R2 = 0.41). The
## model's intercept, corresponding to Brave_scale = 0 and Selfless_m1sd = 0, is
## at 4.31 (95% CI [4.20, 4.42], t(1356) = 79.21, p < .001). Within this model:
##
## - The effect of Brave scale is statistically significant and positive (beta =
## 0.38, 95% CI [0.29, 0.46], t(1356) = 8.98, p < .001; Std. beta = 0.39, 95% CI
## [0.33, 0.45])
## - The effect of Selfless m1sd is statistically significant and positive (beta =
## 0.57, 95% CI [0.49, 0.66], t(1356) = 13.82, p < .001; Std. beta = 0.39, 95% CI
## [0.33, 0.44])
## - The effect of Brave scale × Selfless m1sd is statistically significant and
## positive (beta = 0.21, 95% CI [0.16, 0.25], t(1356) = 9.09, p < .001; Std. beta
## = 0.14, 95% CI [0.11, 0.17])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.## Type 3 ANOVAs only give sensible and informative results when covariates
## are mean-centered and factors are coded with orthogonal contrasts (such
## as those produced by `contr.sum`, `contr.poly`, or `contr.helmert`, but
## *not* by the default `contr.treatment`).## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## ----------------------------------------------------------
## Selfless_scale | 0.12 | [0.10, 1.00]
## Brave_scale | 0.11 | [0.09, 1.00]
## Selfless_scale:Brave_scale | 0.06 | [0.04, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].
We replicate our previous study: selflessness and bravery account for heroism.
Here there is a synergy regarding individual perceptions: the more we believe an occupation is brave, the more we see them as heroic, but it is particularly true for occupations we also perceive to be selfless.
Accounting for a possible halo effects by controlling for attitude, does not change our inferences (nor does accounting for job’s normative effects):
##
## Call:
## lm(formula = Heroism ~ Selfless_scale * Brave_scale + Attitude_scale,
## data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.4204 -0.4442 0.1491 0.5796 2.8274
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.91561 0.03090 159.075 < 2e-16 ***
## Selfless_scale 0.29629 0.04015 7.379 2.76e-13 ***
## Brave_scale 0.34209 0.04221 8.104 1.18e-15 ***
## Attitude_scale 0.67719 0.03679 18.408 < 2e-16 ***
## Selfless_scale:Brave_scale 0.15862 0.02058 7.708 2.46e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.021 on 1355 degrees of freedom
## Multiple R-squared: 0.5284, Adjusted R-squared: 0.527
## F-statistic: 379.6 on 4 and 1355 DF, p-value: < 2.2e-16## We fitted a linear model (estimated using OLS) to predict Heroism with
## Selfless_scale, Brave_scale and Attitude_scale (formula: Heroism ~
## Selfless_scale * Brave_scale + Attitude_scale). The model explains a
## statistically significant and substantial proportion of variance (R2 = 0.53,
## F(4, 1355) = 379.60, p < .001, adj. R2 = 0.53). The model's intercept,
## corresponding to Selfless_scale = 0, Brave_scale = 0 and Attitude_scale = 0, is
## at 4.92 (95% CI [4.85, 4.98], t(1355) = 159.07, p < .001). Within this model:
##
## - The effect of Selfless scale is statistically significant and positive (beta
## = 0.30, 95% CI [0.22, 0.38], t(1355) = 7.38, p < .001; Std. beta = 0.20, 95% CI
## [0.15, 0.25])
## - The effect of Brave scale is statistically significant and positive (beta =
## 0.34, 95% CI [0.26, 0.42], t(1355) = 8.10, p < .001; Std. beta = 0.23, 95% CI
## [0.17, 0.29])
## - The effect of Attitude scale is statistically significant and positive (beta
## = 0.68, 95% CI [0.61, 0.75], t(1355) = 18.41, p < .001; Std. beta = 0.46, 95%
## CI [0.41, 0.50])
## - The effect of Selfless scale × Brave scale is statistically significant and
## positive (beta = 0.16, 95% CI [0.12, 0.20], t(1355) = 7.71, p < .001; Std. beta
## = 0.11, 95% CI [0.08, 0.13])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.Assumption checks
Below, some plots diagnose normality of residuals (QQ plot), homoscedasticity (predicted vs fitted plot), and presence of influential cases (Cooks d plot).
Model Linearity
Because our main DV is ordinal, it is worth checking if a more relevant test (Cumulative Link model) changes our inferences.
# Fitted values from your model
fitted_vals <- fitted(mod)
# Plot observed values against fitted values
plot(fitted_vals, Set$Heroism,
xlab = "Fitted Values",
ylab = "Observed Heroes",
main = "Observed vs Fitted Values")
abline(0, 1, col = "blue", lty = 2)
library(ordinal)
# Fit a cumulative link mixed model
Set$Heroes_ord <- factor(Set$Heroism, ordered = TRUE)
# Now fit the cumulative link mixed model
clm_mod <- clm(Heroes_ord ~ Brave_scale * Selfless_scale, data = Set, link = "logit")
# Summarize the cumulative link mixed model
summary(clm_mod)## formula: Heroes_ord ~ Brave_scale * Selfless_scale
## data: Set
##
## link threshold nobs logLik AIC niter max.grad cond.H
## logit flexible 1360 -1939.75 3897.50 6(0) 3.94e-11 5.4e+01
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## Brave_scale 0.98821 0.07960 12.41 <2e-16 ***
## Selfless_scale 1.12946 0.07918 14.26 <2e-16 ***
## Brave_scale:Selfless_scale 0.45021 0.04471 10.07 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Threshold coefficients:
## Estimate Std. Error z value
## 1|2 -4.56671 0.19789 -23.08
## 2|3 -3.30968 0.12539 -26.39
## 3|4 -2.37036 0.09618 -24.64
## 4|5 -0.87703 0.07253 -12.09
## 5|6 0.88164 0.07410 11.90
## 6|7 2.55186 0.10281 24.82Using cumulative link regression does not influence our results.
Consistent with our predictions, Heroes are significantly selfless and Brave. An interaction can be observed, seemingly synergetic: the two variables encourage themselves. However, we note that the effectsize associated to the interaction is quite modest
H2 Outliers analyses
Cook’s distance plot does show high studentized residuals:
This warrant the use of robust models, or at the very least, a model comparison with robust models.
Outlier analyses through model comparison with a robust model:
##
## Call:
## lmrob(formula = Heroism ~ Brave_scale * Selfless_scale, data = Set)
## \--> method = "MM"
## Residuals:
## Min 1Q Median 3Q Max
## -5.5042 -0.5042 0.1853 0.5754 4.6326
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.97647 0.05490 90.653 < 2e-16 ***
## Brave_scale 0.52584 0.06403 8.212 5.03e-16 ***
## Selfless_scale 0.72545 0.06639 10.927 < 2e-16 ***
## Brave_scale:Selfless_scale 0.20698 0.09187 2.253 0.0244 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Robust residual standard error: 0.8809
## Multiple R-squared: 0.5328, Adjusted R-squared: 0.5318
## Convergence in 41 IRWLS iterations
##
## Robustness weights:
## 8 observations c(289,471,487,512,626,798,1095,1150)
## are outliers with |weight| = 0 ( < 7.4e-05);
## 57 weights are ~= 1. The remaining 1295 ones are summarized as
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.01441 0.84180 0.96150 0.87600 0.97890 0.99890
## Algorithmic parameters:
## tuning.chi bb tuning.psi refine.tol
## 1.548e+00 5.000e-01 4.685e+00 1.000e-07
## rel.tol scale.tol solve.tol zero.tol
## 1.000e-07 1.000e-10 1.000e-07 1.000e-10
## eps.outlier eps.x warn.limit.reject warn.limit.meanrw
## 7.353e-05 2.302e-11 5.000e-01 5.000e-01
## nResample max.it best.r.s k.fast.s k.max
## 500 50 2 1 200
## maxit.scale trace.lev mts compute.rd fast.s.large.n
## 200 0 1000 0 2000
## psi subsampling cov
## "bisquare" "nonsingular" ".vcov.avar1"
## compute.outlier.stats
## "SM"
## seed : int(0)Robust models did not change our main effects, but the interaction does appear weakened when accouting for extreme residuals.
H2 Decomposition of the effects within job
We registered an exploration of the effects within each occupation if there was any higher order interaction involving type of occupation.
Let’s see if there is an higher-order job interaction:
## Analysis of Variance Table
##
## Response: Heroism
## Df Sum Sq Mean Sq F value Pr(>F)
## Selfless_scale 1 981.91 981.91 807.4118 < 2.2e-16 ***
## Brave_scale 1 140.47 140.47 115.5086 < 2.2e-16 ***
## Job 4 139.60 34.90 28.6981 < 2.2e-16 ***
## Selfless_scale:Brave_scale 1 70.78 70.78 58.2030 4.463e-14 ***
## Selfless_scale:Job 4 2.50 0.63 0.5143 0.7252524
## Brave_scale:Job 4 7.72 1.93 1.5871 0.1752918
## Selfless_scale:Brave_scale:Job 4 23.79 5.95 4.8902 0.0006457 ***
## Residuals 1340 1629.60 1.22
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Job does have a (somewhat small) influence on our interaction.
As registered: Decomposition of the effects in each job.
To do this, we conduct Ordinary Least Squares Regression (as there is no need for random intercept anymore).
For each analysis, I report the shape of the interaction and compare the partial eta^2 of each predictors.
Firefighters
## [1] "Firefighter analysis"Firef<-subset(Set, Set$Job == "F")
summary(FireMod<-lm(Heroism ~ Brave_scale * Selfless_scale, data = Firef))##
## Call:
## lm(formula = Heroism ~ Brave_scale * Selfless_scale, data = Firef)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.0064 -0.5562 0.4438 0.4438 2.0932
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.12141 0.08912 57.464 < 2e-16 ***
## Brave_scale 0.65106 0.12642 5.150 5.04e-07 ***
## Selfless_scale 0.52142 0.09609 5.426 1.28e-07 ***
## Brave_scale:Selfless_scale 0.22611 0.04327 5.226 3.48e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.883 on 269 degrees of freedom
## Multiple R-squared: 0.4237, Adjusted R-squared: 0.4173
## F-statistic: 65.92 on 3 and 269 DF, p-value: < 2.2e-16## Type 3 ANOVAs only give sensible and informative results when covariates
## are mean-centered and factors are coded with orthogonal contrasts (such
## as those produced by `contr.sum`, `contr.poly`, or `contr.helmert`, but
## *not* by the default `contr.treatment`).## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## ----------------------------------------------------------
## Brave_scale | 0.09 | [0.04, 1.00]
## Selfless_scale | 0.10 | [0.05, 1.00]
## Brave_scale:Selfless_scale | 0.09 | [0.04, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].## Warning: 1.38158931300079 is outside the observed range of Selfless_scale## JOHNSON-NEYMAN INTERVAL
##
## When Selfless_scale is OUTSIDE the interval [-4.32, -1.91], the slope of
## Brave_scale is p < .05.
##
## Note: The range of observed values of Selfless_scale is [-3.37, 1.13]
##
## SIMPLE SLOPES ANALYSIS
##
## Slope of Brave_scale when Selfless_scale = -0.2860620 (- 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.59 0.12 4.86 0.00
##
## Slope of Brave_scale when Selfless_scale = 0.5477637 (Mean):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.77 0.14 5.55 0.00
##
## Slope of Brave_scale when Selfless_scale = 1.3815893 (+ 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.96 0.16 5.86 0.00## Warning: 1.38158931300079 is outside the observed range of Selfless_scale
In firefighters: there is a large Bravery/heroism association — The interaction is significant and synergetic
NHS
## [1] "HC analysis"HCrole<- subset(Set, Set$Job == "N")
HCrole$Brave <- scale(HCrole$Brave)
HCrole$Selfless <- scale(HCrole$Selfless)
summary(HCMod<-lm(Heroism ~ Brave * Selfless, data = HCrole))##
## Call:
## lm(formula = Heroism ~ Brave * Selfless, data = HCrole)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.5977 -0.4969 0.4023 0.5031 2.9977
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.30036 0.07737 68.510 < 2e-16 ***
## Brave 0.52032 0.11409 4.560 7.78e-06 ***
## Selfless 0.63472 0.10974 5.784 2.04e-08 ***
## Brave:Selfless 0.23868 0.04575 5.217 3.66e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.135 on 267 degrees of freedom
## Multiple R-squared: 0.3875, Adjusted R-squared: 0.3806
## F-statistic: 56.31 on 3 and 267 DF, p-value: < 2.2e-16## Type 3 ANOVAs only give sensible and informative results when covariates
## are mean-centered and factors are coded with orthogonal contrasts (such
## as those produced by `contr.sum`, `contr.poly`, or `contr.helmert`, but
## *not* by the default `contr.treatment`).## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## ----------------------------------------------
## Brave | 0.07 | [0.03, 1.00]
## Selfless | 0.11 | [0.06, 1.00]
## Brave:Selfless | 0.09 | [0.04, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].## Warning: 0.999999999999999 is outside the observed range of Selfless## JOHNSON-NEYMAN INTERVAL
##
## When Selfless is OUTSIDE the interval [-3.55, -1.27], the slope of Brave is
## p < .05.
##
## Note: The range of observed values of Selfless is [-3.55, 0.93]
##
## SIMPLE SLOPES ANALYSIS
##
## Slope of Brave when Selfless = -1.000000e+00 (- 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.28 0.11 2.59 0.01
##
## Slope of Brave when Selfless = 2.371002e-16 (Mean):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.52 0.11 4.56 0.00
##
## Slope of Brave when Selfless = 1.000000e+00 (+ 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.76 0.14 5.59 0.00## Warning: 0.999999999999999 is outside the observed range of Selfless
In Healthcare workers, Heroism is largely associated to selflessness (11%), less so to bravery (7%). The interaction indicates a large synergy (9%).
Police officers
## [1] "Police Officers"Pol<- subset(Set, Set$Job == "P")
Pol$Brave <- scale(Pol$Brave)
Pol$Selfless <- scale(Pol$Selfless)
summary(PolMod<-lm(Heroism ~ Brave * Selfless, data = Pol))##
## Call:
## lm(formula = Heroism ~ Brave * Selfless, data = Pol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.7383 -0.4540 0.1713 0.5759 3.8594
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.55066 0.07291 62.416 < 2e-16 ***
## Brave 0.39739 0.08614 4.613 6.15e-06 ***
## Selfless 0.45904 0.08437 5.441 1.20e-07 ***
## Brave:Selfless -0.04020 0.05025 -0.800 0.424
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.087 on 268 degrees of freedom
## Multiple R-squared: 0.3453, Adjusted R-squared: 0.338
## F-statistic: 47.12 on 3 and 268 DF, p-value: < 2.2e-16## Type 3 ANOVAs only give sensible and informative results when covariates
## are mean-centered and factors are coded with orthogonal contrasts (such
## as those produced by `contr.sum`, `contr.poly`, or `contr.helmert`, but
## *not* by the default `contr.treatment`).## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## ----------------------------------------------
## Brave | 0.07 | [0.03, 1.00]
## Selfless | 0.10 | [0.05, 1.00]
## Brave:Selfless | 2.38e-03 | [0.00, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].## JOHNSON-NEYMAN INTERVAL
##
## When Selfless is INSIDE the interval [-7.00, 2.26], the slope of Brave is p
## < .05.
##
## Note: The range of observed values of Selfless is [-3.13, 1.64]
##
## SIMPLE SLOPES ANALYSIS
##
## Slope of Brave when Selfless = -1.000000e+00 (- 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.44 0.09 4.83 0.00
##
## Slope of Brave when Selfless = 1.404871e-16 (Mean):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.40 0.09 4.61 0.00
##
## Slope of Brave when Selfless = 1.000000e+00 (+ 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.36 0.11 3.30 0.00
In Police officers, heroism levels are largely predicted by Bravery estimates (eta2 = 7%), and selflessness (eta2 = 10%). There is no interaction in the Police condition: eta2 = 0.2%
Psychiatrists
## [1] "Psy analysis"PsyRole<- subset(Set, Set$Job == "Ps")
PsyRole$Brave <- scale(PsyRole$Brave)
PsyRole$Selfless <- scale(PsyRole$Selfless)
summary(PsyMod<-lm(Heroism ~ Brave * Selfless, data = PsyRole))##
## Call:
## lm(formula = Heroism ~ Brave * Selfless, data = PsyRole)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2357 -0.6637 0.2474 0.7643 3.2342
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.35846 0.07809 55.813 < 2e-16 ***
## Brave 0.71198 0.09378 7.592 5.33e-13 ***
## Selfless 0.25024 0.08883 2.817 0.005212 **
## Brave:Selfless 0.19676 0.05354 3.675 0.000287 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.174 on 266 degrees of freedom
## Multiple R-squared: 0.3369, Adjusted R-squared: 0.3294
## F-statistic: 45.05 on 3 and 266 DF, p-value: < 2.2e-16## Type 3 ANOVAs only give sensible and informative results when covariates
## are mean-centered and factors are coded with orthogonal contrasts (such
## as those produced by `contr.sum`, `contr.poly`, or `contr.helmert`, but
## *not* by the default `contr.treatment`).## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## ----------------------------------------------
## Brave | 0.18 | [0.11, 1.00]
## Selfless | 0.03 | [0.01, 1.00]
## Brave:Selfless | 0.05 | [0.01, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].## JOHNSON-NEYMAN INTERVAL
##
## When Selfless is OUTSIDE the interval [-7.37, -2.33], the slope of Brave is
## p < .05.
##
## Note: The range of observed values of Selfless is [-3.00, 1.42]
##
## SIMPLE SLOPES ANALYSIS
##
## Slope of Brave when Selfless = -1.000000e+00 (- 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.52 0.09 5.62 0.00
##
## Slope of Brave when Selfless = -2.564307e-16 (Mean):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.71 0.09 7.59 0.00
##
## Slope of Brave when Selfless = 1.000000e+00 (+ 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.91 0.12 7.44 0.00
Psychiatrists heroism is largely derived from both Bravery (18%) but not by selflessness (2%). The interaction is modest (5%) but indicates synergy.
Welders
## [1] "Welders analysis"Weld<- subset(Set, Set$Job == "W")
Weld$Brave <- scale(Weld$Brave)
Weld$Selfless <- scale(Weld$Selfless)
summary(WeldMod<-lm(Heroism ~ Brave * Selfless, data = Weld))##
## Call:
## lm(formula = Heroism ~ Brave * Selfless, data = Weld)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.8247 -0.7899 0.1753 0.7481 4.6123
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.59765 0.07732 59.465 < 2e-16 ***
## Brave 0.45945 0.08770 5.239 3.26e-07 ***
## Selfless 0.52031 0.08193 6.351 9.03e-10 ***
## Brave:Selfless 0.18801 0.05764 3.262 0.00125 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.205 on 270 degrees of freedom
## Multiple R-squared: 0.3087, Adjusted R-squared: 0.3011
## F-statistic: 40.2 on 3 and 270 DF, p-value: < 2.2e-16## Type 3 ANOVAs only give sensible and informative results when covariates
## are mean-centered and factors are coded with orthogonal contrasts (such
## as those produced by `contr.sum`, `contr.poly`, or `contr.helmert`, but
## *not* by the default `contr.treatment`).## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## ----------------------------------------------
## Brave | 0.09 | [0.04, 1.00]
## Selfless | 0.13 | [0.07, 1.00]
## Brave:Selfless | 0.04 | [0.01, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].## JOHNSON-NEYMAN INTERVAL
##
## When Selfless is OUTSIDE the interval [-5.63, -1.43], the slope of Brave is
## p < .05.
##
## Note: The range of observed values of Selfless is [-3.85, 1.29]
##
## SIMPLE SLOPES ANALYSIS
##
## Slope of Brave when Selfless = -1.000000e+00 (- 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.27 0.09 3.16 0.00
##
## Slope of Brave when Selfless = 2.791765e-16 (Mean):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.46 0.09 5.24 0.00
##
## Slope of Brave when Selfless = 1.000000e+00 (+ 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.65 0.12 5.35 0.00
Small interaction. Both variables contribute to heroism. ___
H2 Conclusion
Support for Hypotheses 2. Perception of heroism is linked to perception of bravery and selflessness. The effect sizes are quite large for our main effects. We can note that the interaction between the two attributes is quite small (this varies across jobs, with police officers not benefitting from this interactive effect). When using robust regressions (which is encouraged by the presence of very influential cases in the model), the interaction is also significantly weakened (p = .02, eta2 < 1%). Both Selflessness and Bravery contribute to heroism, but they appear to do so independently.
That said, there are discrepancies with our previous experiment. In our previous study, we found that bravery contributed to heroism in the firefighter and soldier condition significantly more than selflessness, and conversely for nurses. In contrast, in this study, the only occupation showing a marked difference between the two predictors was Psychiatrists.
Hypotheses 3: Situation attributions as predictors
This tab contains:
- H3 Model comparison with job testing the influence of job as a covariate
- H3 Model comparison with attitude testing the influence of job as a covariate
- H3 Main registered model How does Helpfulness and Danger predict Heroism
- H3 Outliers analyses Comparison of betas between robust and non robust mixed models
- H3 Decomposition of the effects within job We tests our main effects in each occupation
- H3 Conclusion
We repeat the analyses using the attributes rating (Manipulation check #2) as predictors, from registration:
We will use three steps to evaluate the effects of our manipulation of perceived heroism:
A first regression model to assess:
- The effect of the perceived exposure to physical threat on Heroism attribution across all occupations (H3a)
- The effect of the perceived help to others on Heroism attribution across all occupations (H3b)
- Their interaction (exploratory analysis)
A second model with Job type as covariate and moderator:
- The effect of the perceived exposure to physical threat on Heroism attribution across all occupations (H3a)
- The effect of the perceived help to others on Heroism attribution across all occupations (H3b)
- Their interaction (exploratory analysis)
- A higher order interaction when considering Job type (to control for potential higher order interaction - should occupation interact with any variable, we would further explore the interactions when decomposing by job types in independent OLS regression models, see Registered R script, section "Further explorations")
We will compare the two models to quantify the extent to which the effects of measured bravery and selflessness are explained by normative differences in occupation type: A significant reduction in the other predictors' main effect sizes when controlling for Job Type would indicate that these effects are partially dependent on normative evaluations of the job type.
A third model will be computed to control for a possible halo effect explaining positive correlations, using General attitude as a covariate (Model 3):
- The effect of the perceived exposure to physical threat on Heroism attribution across all occupations (H3a)
- The effect of the perceived help to others on Heroism attribution across all occupations (H3b)
- Their interaction (exploratory analysis)
- The effect of General attitude (covariate)
We will compare Model 1 and Model 3 to assess to what extent our effects are conditioned by a general halo effect -- that is heroism is explained by general attitude rather than our key variables. A significant reduction in the other predictors' main effect sizes when controlling for General attitude would indicate that these effects are partially dependent on the participant's attitude of the target occupation.
We will base our conclusions regarding the effects of our manipulations irrespective of the job types (i.e., across all jobs) on the Model 1. Model 2 is used to quantify normative evaluation effects in our effects, and Model 3 to quantify halo effects involved in our results.
H3 Model comparison with job
Set$Danger_scale <- scale(Set$Danger)
Set$Helpfulness_scale <- scale(Set$Helpfulness)
(mod<-lm(Heroism ~ Helpfulness_scale * Danger_scale , data = Set))##
## Call:
## lm(formula = Heroism ~ Helpfulness_scale * Danger_scale, data = Set)
##
## Coefficients:
## (Intercept) Helpfulness_scale
## 5.0023 0.7401
## Danger_scale Helpfulness_scale:Danger_scale
## 0.3562 0.0433## Analysis of Variance Table
##
## Model 1: Heroism ~ Helpfulness_scale * Danger_scale
## Model 2: Heroism ~ Helpfulness_scale * Danger_scale + Job
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 1356 1812.3
## 2 1352 1719.4 4 92.891 18.261 1.272e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Here also, the heroism rate is driven by normative evaluations of the job – including jobs as covariate leads to a better fit (RSS = 1812.3, vs RSS = 1719.4, F = 18.26, p < .000001) ___
H3 Model comparison with attitude
To account for a possible Halo effect, let’s see if attitudes play a role in explaining heroism.
##
## Call:
## lm(formula = Heroism ~ Helpfulness_scale * Danger_scale, data = Set)
##
## Coefficients:
## (Intercept) Helpfulness_scale
## 5.0023 0.7401
## Danger_scale Helpfulness_scale:Danger_scale
## 0.3562 0.0433##
## Call:
## lm(formula = Heroism ~ Helpfulness_scale * Danger_scale + Attitude_scale,
## data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.3125 -0.4388 0.1466 0.6875 2.9213
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.98466 0.03007 165.753 < 2e-16 ***
## Helpfulness_scale 0.34542 0.03916 8.820 < 2e-16 ***
## Danger_scale 0.22601 0.03256 6.941 6.03e-12 ***
## Attitude_scale 0.70355 0.03910 17.993 < 2e-16 ***
## Helpfulness_scale:Danger_scale 0.08330 0.02389 3.487 0.000505 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.039 on 1355 degrees of freedom
## Multiple R-squared: 0.5118, Adjusted R-squared: 0.5104
## F-statistic: 355.1 on 4 and 1355 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Model 1: Heroism ~ Helpfulness_scale * Danger_scale
## Model 2: Heroism ~ Helpfulness_scale * Danger_scale + Attitude_scale
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 1356 1812.3
## 2 1355 1462.8 1 349.49 323.74 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Massively so: the model using attitude as a covariant explained heroism way better (RSS = 1462.8) than the model omitting this variable (RSS = 1812.3), F = 323.74, p < .00001. It will be important to control for attitude in our conclusions.
==> JOB and ATTITUDE explain Heroism above and beyond ratings of physical danger and helpfulness.
H3 Main registered model
##
## Call:
## lm(formula = Heroism ~ Helpfulness_scale * Danger_scale, data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.0765 -0.5704 0.1585 0.8965 3.6948
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.00226 0.03344 149.575 <2e-16 ***
## Helpfulness_scale 0.74007 0.03610 20.502 <2e-16 ***
## Danger_scale 0.35615 0.03533 10.082 <2e-16 ***
## Helpfulness_scale:Danger_scale 0.04330 0.02647 1.636 0.102
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.156 on 1356 degrees of freedom
## Multiple R-squared: 0.3952, Adjusted R-squared: 0.3938
## F-statistic: 295.3 on 3 and 1356 DF, p-value: < 2.2e-16## 2.5 % 97.5 %
## (Intercept) 4.936657149 5.06786894
## Helpfulness_scale 0.669252945 0.81088079
## Danger_scale 0.286851890 0.42545283
## Helpfulness_scale:Danger_scale -0.008619894 0.09522744## We fitted a linear model (estimated using OLS) to predict Heroism with
## Helpfulness_scale and Danger_scale (formula: Heroism ~ Helpfulness_scale *
## Danger_scale). The model explains a statistically significant and substantial
## proportion of variance (R2 = 0.40, F(3, 1356) = 295.33, p < .001, adj. R2 =
## 0.39). The model's intercept, corresponding to Helpfulness_scale = 0 and
## Danger_scale = 0, is at 5.00 (95% CI [4.94, 5.07], t(1356) = 149.58, p < .001).
## Within this model:
##
## - The effect of Helpfulness scale is statistically significant and positive
## (beta = 0.74, 95% CI [0.67, 0.81], t(1356) = 20.50, p < .001; Std. beta = 0.50,
## 95% CI [0.45, 0.55])
## - The effect of Danger scale is statistically significant and positive (beta =
## 0.36, 95% CI [0.29, 0.43], t(1356) = 10.08, p < .001; Std. beta = 0.24, 95% CI
## [0.19, 0.29])
## - The effect of Helpfulness scale × Danger scale is statistically
## non-significant and positive (beta = 0.04, 95% CI [-8.62e-03, 0.10], t(1356) =
## 1.64, p = 0.102; Std. beta = 0.03, 95% CI [-5.81e-03, 0.06])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.## Type 3 ANOVAs only give sensible and informative results when covariates
## are mean-centered and factors are coded with orthogonal contrasts (such
## as those produced by `contr.sum`, `contr.poly`, or `contr.helmert`, but
## *not* by the default `contr.treatment`).## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## --------------------------------------------------------------
## Helpfulness_scale | 0.24 | [0.21, 1.00]
## Danger_scale | 0.07 | [0.05, 1.00]
## Helpfulness_scale:Danger_scale | 1.97e-03 | [0.00, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].We replicated the previous study, in particular:
- A main effect of Danger ; beta = 0.74, 95% CI [0.67, 0.81], t(1356) = 20.50, p < .001; Std. beta = 0.50, 95% CI [0.45, 0.55]
- A main effect of Helpfulness; beta = 0.36, 95% CI [0.29, 0.43], t(1356) = 10.08, p < .001; Std. beta = 0.24, 95% CI [0.19, 0.29]
- No interaction between these features (p = .1)
## Warning: 1.00000000000001 is outside the observed range of Helpfulness_scale
Here there is no interaction regarding evaluation of danger and helpfulness.
Accounting for a possible halo effects by controlling for attitude, does not change our main inferences:
##
## Call:
## lm(formula = Heroism ~ Helpfulness_scale * Danger_scale + Attitude_scale,
## data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.3125 -0.4388 0.1466 0.6875 2.9213
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.98466 0.03007 165.753 < 2e-16 ***
## Helpfulness_scale 0.34542 0.03916 8.820 < 2e-16 ***
## Danger_scale 0.22601 0.03256 6.941 6.03e-12 ***
## Attitude_scale 0.70355 0.03910 17.993 < 2e-16 ***
## Helpfulness_scale:Danger_scale 0.08330 0.02389 3.487 0.000505 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.039 on 1355 degrees of freedom
## Multiple R-squared: 0.5118, Adjusted R-squared: 0.5104
## F-statistic: 355.1 on 4 and 1355 DF, p-value: < 2.2e-16## We fitted a linear model (estimated using OLS) to predict Heroism with
## Helpfulness_scale, Danger_scale and Attitude_scale (formula: Heroism ~
## Helpfulness_scale * Danger_scale + Attitude_scale). The model explains a
## statistically significant and substantial proportion of variance (R2 = 0.51,
## F(4, 1355) = 355.15, p < .001, adj. R2 = 0.51). The model's intercept,
## corresponding to Helpfulness_scale = 0, Danger_scale = 0 and Attitude_scale =
## 0, is at 4.98 (95% CI [4.93, 5.04], t(1355) = 165.75, p < .001). Within this
## model:
##
## - The effect of Helpfulness scale is statistically significant and positive
## (beta = 0.35, 95% CI [0.27, 0.42], t(1355) = 8.82, p < .001; Std. beta = 0.23,
## 95% CI [0.18, 0.28])
## - The effect of Danger scale is statistically significant and positive (beta =
## 0.23, 95% CI [0.16, 0.29], t(1355) = 6.94, p < .001; Std. beta = 0.15, 95% CI
## [0.11, 0.20])
## - The effect of Attitude scale is statistically significant and positive (beta
## = 0.70, 95% CI [0.63, 0.78], t(1355) = 17.99, p < .001; Std. beta = 0.47, 95%
## CI [0.42, 0.53])
## - The effect of Helpfulness scale × Danger scale is statistically significant
## and positive (beta = 0.08, 95% CI [0.04, 0.13], t(1355) = 3.49, p < .001; Std.
## beta = 0.06, 95% CI [0.02, 0.09])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.However, the interaction is now significant. Weirdly enough.
## Warning: 1.00000000000001 is outside the observed range of Helpfulness_scale
So: the part of heroism which is not predicted by attitude,
is predicted by helpfulness and danger perceptions, that worked together
in a synergetic way.
Assumption checks
Model Linearity
# Fitted values from your model
fitted_vals <- fitted(mod)
# Plot observed values against fitted values
plot(fitted_vals, Set$Heroism,
xlab = "Fitted Values",
ylab = "Observed Heroes",
main = "Observed vs Fitted Values")
abline(0, 1, col = "blue", lty = 2)
library(ordinal)
# Fit a cumulative link mixed model
Set$Heroes_ord <- factor(Set$Heroism, ordered = TRUE)
# Now fit the cumulative link mixed model
clm_mod <- clm(Heroes_ord ~ Danger_scale * Helpfulness_scale, data = Set, link = "logit")
# Summarize the cumulative link mixed model
summary(clm_mod)## formula: Heroes_ord ~ Danger_scale * Helpfulness_scale
## data: Set
##
## link threshold nobs logLik AIC niter max.grad cond.H
## logit flexible 1360 -1974.77 3967.55 6(0) 1.56e-11 5.8e+01
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## Danger_scale 0.64401 0.05983 10.764 < 2e-16 ***
## Helpfulness_scale 1.27886 0.06532 19.580 < 2e-16 ***
## Danger_scale:Helpfulness_scale 0.18919 0.04359 4.341 1.42e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Threshold coefficients:
## Estimate Std. Error z value
## 1|2 -5.00003 0.21767 -22.97
## 2|3 -3.60312 0.13650 -26.40
## 3|4 -2.55879 0.10059 -25.44
## 4|5 -0.98444 0.07063 -13.94
## 5|6 0.67737 0.06771 10.01
## 6|7 2.16274 0.08871 24.38Using cumulative link regression does not influence our main predictions, BUT, an interaction between Danger and Helpfulness appear. This might be something to explore?
Consistent with our predictions, Heroes are significantly Helpful and in Dangerous situations. Looking at the effect sizes, it would appear that Heroism is MOSTLY driven by perception of Helpfulness (eta2 = 42%) rather than danger (eta2 = 8%). Heroes help people, they’re not necessary in danger. These two effects seem, on a surface level, to work independently. However, an interaction can be observed, seemingly synergetic, but only when accounting for a halo effect OR when using CML model: the two variables encourage themselves. However, we note that the effectsize associated to this interaction is quite modest: eta 2 = 0.8%
H3 Outliers analyses
Cook’s distance plot does show high studentized residuals:
This warrant the use of robust models, or at the very least, a model comparison with robust models.
Outlier analyses through model comparison with a robust model:
##
## Call:
## lmrob(formula = Heroism ~ Danger_scale * Helpfulness_scale, data = Set)
## \--> method = "MM"
## Residuals:
## Min 1Q Median 3Q Max
## -5.35359 -0.61788 0.01426 0.64641 3.96659
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.10176 0.03226 158.125 < 2e-16 ***
## Danger_scale 0.39099 0.04168 9.380 < 2e-16 ***
## Helpfulness_scale 0.83700 0.03579 23.385 < 2e-16 ***
## Danger_scale:Helpfulness_scale 0.10235 0.02523 4.056 5.27e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Robust residual standard error: 0.9275
## Multiple R-squared: 0.5241, Adjusted R-squared: 0.523
## Convergence in 11 IRWLS iterations
##
## Robustness weights:
## 14 observations c(128,306,363,379,471,626,689,798,936,1036,1150,1230,1305,1309)
## are outliers with |weight| = 0 ( < 7.4e-05);
## 113 weights are ~= 1. The remaining 1233 ones are summarized as
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.02519 0.84750 0.95620 0.88450 0.97740 0.99800
## Algorithmic parameters:
## tuning.chi bb tuning.psi refine.tol
## 1.548e+00 5.000e-01 4.685e+00 1.000e-07
## rel.tol scale.tol solve.tol zero.tol
## 1.000e-07 1.000e-10 1.000e-07 1.000e-10
## eps.outlier eps.x warn.limit.reject warn.limit.meanrw
## 7.353e-05 2.841e-11 5.000e-01 5.000e-01
## nResample max.it best.r.s k.fast.s k.max
## 500 50 2 1 200
## maxit.scale trace.lev mts compute.rd fast.s.large.n
## 200 0 1000 0 2000
## psi subsampling cov
## "bisquare" "nonsingular" ".vcov.avar1"
## compute.outlier.stats
## "SM"
## seed : int(0)Robust models did not change our main effects, but the interaction does appear STRONGER when accouting for extreme residuals. It might be worth investigating. The absence of interaction might be driven by outliers.
In particular, the interaction is there: when accounting for attitude, when using CML model, and when using robust model.
H3 Decomposition of the effects within job
We registered an exploration of the effects within each occupation if there was any higher order interaction involving type of occupation.
Let’s see if there is an higher-order job interaction:
## Analysis of Variance Table
##
## Response: Heroism
## Df Sum Sq Mean Sq F value Pr(>F)
## Helpfulness_scale 1 1048.23 1048.23 835.1014 < 2.2e-16 ***
## Danger_scale 1 132.29 132.29 105.3915 < 2.2e-16 ***
## Job 4 96.32 24.08 19.1846 2.332e-15 ***
## Helpfulness_scale:Danger_scale 1 0.15 0.15 0.1158 0.733699
## Helpfulness_scale:Job 4 21.04 5.26 4.1901 0.002241 **
## Danger_scale:Job 4 13.56 3.39 2.7001 0.029333 *
## Helpfulness_scale:Danger_scale:Job 4 2.80 0.70 0.5581 0.693133
## Residuals 1340 1681.99 1.26
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Job does have a (somewhat small) influence on our main predictions (the effect of danger and the effect of helpfulness).
As registered: Decomposition of the effects in each job.
To do this, we conduct Ordinary Least Squares Regression (as there is no need for random intercept anymore).
For each analysis, I report the shape of the interaction and compare the partial eta^2 of each predictors.
Firefighters
## [1] "Firefighter analysis"Firef<-subset(Set, Set$Job == "F")
summary(FireMod<-lm(Heroism ~ Danger_scale * Helpfulness_scale, data = Firef))##
## Call:
## lm(formula = Heroism ~ Danger_scale * Helpfulness_scale, data = Firef)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.3549 -0.3549 0.3133 0.6451 1.7724
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.39064 0.08984 60.005 < 2e-16 ***
## Danger_scale 0.33814 0.10843 3.118 0.00202 **
## Helpfulness_scale 0.64213 0.12138 5.290 2.53e-07 ***
## Danger_scale:Helpfulness_scale 0.04147 0.05537 0.749 0.45454
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9777 on 269 degrees of freedom
## Multiple R-squared: 0.2935, Adjusted R-squared: 0.2856
## F-statistic: 37.24 on 3 and 269 DF, p-value: < 2.2e-16## Type 3 ANOVAs only give sensible and informative results when covariates
## are mean-centered and factors are coded with orthogonal contrasts (such
## as those produced by `contr.sum`, `contr.poly`, or `contr.helmert`, but
## *not* by the default `contr.treatment`).## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## --------------------------------------------------------------
## Danger_scale | 0.03 | [0.01, 1.00]
## Helpfulness_scale | 0.09 | [0.05, 1.00]
## Danger_scale:Helpfulness_scale | 2.08e-03 | [0.00, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].## Warning: 1.23764448941848 is outside the observed range of Helpfulness_scale## JOHNSON-NEYMAN INTERVAL
##
## When Helpfulness_scale is INSIDE the interval [-1.40, 4.85], the slope of
## Danger_scale is p < .05.
##
## Note: The range of observed values of Helpfulness_scale is [-4.39, 0.92]
##
## SIMPLE SLOPES ANALYSIS
##
## Slope of Danger_scale when Helpfulness_scale = -0.1400676 (- 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.33 0.11 3.02 0.00
##
## Slope of Danger_scale when Helpfulness_scale = 0.5487884 (Mean):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.36 0.11 3.34 0.00
##
## Slope of Danger_scale when Helpfulness_scale = 1.2376445 (+ 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.39 0.12 3.27 0.00## Warning: 1.23764448941848 is outside the observed range of Helpfulness_scale
In firefighters: Heroism is driven bu Helpfulness, and then Danger. No interaction.
NHS
## [1] "HC analysis"HCrole<- subset(Set, Set$Job == "N")
HCrole$Danger <- scale(HCrole$Danger)
HCrole$Helpfulness <- scale(HCrole$Helpfulness)
summary(HCMod<-lm(Heroism ~ Danger * Helpfulness, data = HCrole))##
## Call:
## lm(formula = Heroism ~ Danger * Helpfulness, data = HCrole)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.0583 -0.5187 0.1772 0.6729 3.0262
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.49175 0.07663 71.667 < 2e-16 ***
## Danger 0.34346 0.07931 4.331 2.10e-05 ***
## Helpfulness 0.65103 0.08681 7.499 9.52e-13 ***
## Danger:Helpfulness -0.01819 0.06774 -0.268 0.789
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.153 on 267 degrees of freedom
## Multiple R-squared: 0.3683, Adjusted R-squared: 0.3612
## F-statistic: 51.9 on 3 and 267 DF, p-value: < 2.2e-16## Type 3 ANOVAs only give sensible and informative results when covariates
## are mean-centered and factors are coded with orthogonal contrasts (such
## as those produced by `contr.sum`, `contr.poly`, or `contr.helmert`, but
## *not* by the default `contr.treatment`).## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## --------------------------------------------------
## Danger | 0.07 | [0.03, 1.00]
## Helpfulness | 0.17 | [0.11, 1.00]
## Danger:Helpfulness | 2.70e-04 | [0.00, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].## Warning: 1 is outside the observed range of Helpfulness## JOHNSON-NEYMAN INTERVAL
##
## When Helpfulness is INSIDE the interval [-2.81, 1.91], the slope of Danger
## is p < .05.
##
## Note: The range of observed values of Helpfulness is [-4.32, 0.71]
##
## SIMPLE SLOPES ANALYSIS
##
## Slope of Danger when Helpfulness = -1.000000e+00 (- 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.36 0.10 3.61 0.00
##
## Slope of Danger when Helpfulness = 1.712447e-16 (Mean):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.34 0.08 4.33 0.00
##
## Slope of Danger when Helpfulness = 1.000000e+00 (+ 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.33 0.11 3.00 0.00## Warning: 1 is outside the observed range of Helpfulness
Similar conclusions for nurses, Help> Danger. No interactin.
Police
## [1] "Police Officers"Pol<- subset(Set, Set$Job == "P")
Pol$Danger <- scale(Pol$Danger)
Pol$Helpfulness <- scale(Pol$Helpfulness)
summary(PolMod<-lm(Heroism ~ Danger * Helpfulness, data = Pol))##
## Call:
## lm(formula = Heroism ~ Danger * Helpfulness, data = Pol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.8871 -0.5108 0.0161 0.8233 3.0095
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.48612 0.07166 62.599 <2e-16 ***
## Danger 0.14025 0.08008 1.751 0.081 .
## Helpfulness 0.76996 0.08153 9.444 <2e-16 ***
## Danger:Helpfulness 0.06749 0.05547 1.217 0.225
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.053 on 268 degrees of freedom
## Multiple R-squared: 0.3859, Adjusted R-squared: 0.379
## F-statistic: 56.13 on 3 and 268 DF, p-value: < 2.2e-16## Type 3 ANOVAs only give sensible and informative results when covariates
## are mean-centered and factors are coded with orthogonal contrasts (such
## as those produced by `contr.sum`, `contr.poly`, or `contr.helmert`, but
## *not* by the default `contr.treatment`).## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## --------------------------------------------------
## Danger | 0.01 | [0.00, 1.00]
## Helpfulness | 0.25 | [0.18, 1.00]
## Danger:Helpfulness | 5.49e-03 | [0.00, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].## JOHNSON-NEYMAN INTERVAL
##
## When Helpfulness is INSIDE the interval [0.53, 1.33], the slope of Danger
## is p < .05.
##
## Note: The range of observed values of Helpfulness is [-3.03, 1.46]
##
## SIMPLE SLOPES ANALYSIS
##
## Slope of Danger when Helpfulness = -1.000000e+00 (- 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.07 0.09 0.81 0.42
##
## Slope of Danger when Helpfulness = 4.612324e-17 (Mean):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.14 0.08 1.75 0.08
##
## Slope of Danger when Helpfulness = 1.000000e+00 (+ 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.21 0.10 2.00 0.05
In Police officers, heroism levels are predicted by Helpfulness estimates (eta2 = 25%). However, Danger does not predict heroism. There is no interaction to report neither.
Psychiatrists
## [1] "Psy analysis"PsyRole<- subset(Set, Set$Job == "Ps")
PsyRole$Danger <- scale(PsyRole$Danger)
PsyRole$Helpfulness <- scale(PsyRole$Helpfulness)
summary(PsyMod<-lm(Heroism ~ Danger * Helpfulness, data = PsyRole))##
## Call:
## lm(formula = Heroism ~ Danger * Helpfulness, data = PsyRole)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4511 -0.6129 0.1978 0.6907 2.3997
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.46569 0.07640 58.454 < 2e-16 ***
## Danger 0.18022 0.07926 2.274 0.0238 *
## Helpfulness 0.73211 0.08436 8.678 4.1e-16 ***
## Danger:Helpfulness 0.02080 0.06115 0.340 0.7340
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.188 on 266 degrees of freedom
## Multiple R-squared: 0.3213, Adjusted R-squared: 0.3136
## F-statistic: 41.97 on 3 and 266 DF, p-value: < 2.2e-16## Type 3 ANOVAs only give sensible and informative results when covariates
## are mean-centered and factors are coded with orthogonal contrasts (such
## as those produced by `contr.sum`, `contr.poly`, or `contr.helmert`, but
## *not* by the default `contr.treatment`).## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## --------------------------------------------------
## Danger | 0.02 | [0.00, 1.00]
## Helpfulness | 0.22 | [0.15, 1.00]
## Danger:Helpfulness | 4.35e-04 | [0.00, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].## Warning: 1 is outside the observed range of Helpfulness## JOHNSON-NEYMAN INTERVAL
##
## When Helpfulness is INSIDE the interval [-0.51, 1.13], the slope of Danger
## is p < .05.
##
## Note: The range of observed values of Helpfulness is [-4.62, 1.00]
##
## SIMPLE SLOPES ANALYSIS
##
## Slope of Danger when Helpfulness = -1.000000e+00 (- 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.16 0.10 1.57 0.12
##
## Slope of Danger when Helpfulness = -2.297031e-16 (Mean):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.18 0.08 2.27 0.02
##
## Slope of Danger when Helpfulness = 1.000000e+00 (+ 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.20 0.10 2.04 0.04## Warning: 1 is outside the observed range of Helpfulness
Psychiatrists heroism is largely derived from both Helpfulness (22%) but not so much by Danger (2%). The interaction is not significant.
Welders
## [1] "Welders analysis"Weld<- subset(Set, Set$Job == "W")
Weld$Danger <- scale(Weld$Danger)
Weld$Helpfulness <- scale(Weld$Helpfulness)
summary(WeldMod<-lm(Heroism ~ Danger * Helpfulness, data = Weld))##
## Call:
## lm(formula = Heroism ~ Danger * Helpfulness, data = Weld)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.6892 -0.6892 0.0038 0.7559 2.9158
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.69611 0.07579 61.961 < 2e-16 ***
## Danger 0.42995 0.07669 5.606 5.11e-08 ***
## Helpfulness 0.54876 0.07616 7.206 5.78e-12 ***
## Danger:Helpfulness -0.05174 0.07329 -0.706 0.481
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.213 on 270 degrees of freedom
## Multiple R-squared: 0.2996, Adjusted R-squared: 0.2918
## F-statistic: 38.5 on 3 and 270 DF, p-value: < 2.2e-16## Type 3 ANOVAs only give sensible and informative results when covariates
## are mean-centered and factors are coded with orthogonal contrasts (such
## as those produced by `contr.sum`, `contr.poly`, or `contr.helmert`, but
## *not* by the default `contr.treatment`).## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## --------------------------------------------------
## Danger | 0.10 | [0.05, 1.00]
## Helpfulness | 0.16 | [0.10, 1.00]
## Danger:Helpfulness | 1.84e-03 | [0.00, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].## JOHNSON-NEYMAN INTERVAL
##
## When Helpfulness is INSIDE the interval [-4.66, 1.92], the slope of Danger
## is p < .05.
##
## Note: The range of observed values of Helpfulness is [-3.55, 1.23]
##
## SIMPLE SLOPES ANALYSIS
##
## Slope of Danger when Helpfulness = -1.00000e+00 (- 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.48 0.10 4.84 0.00
##
## Slope of Danger when Helpfulness = 3.99113e-17 (Mean):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.43 0.08 5.61 0.00
##
## Slope of Danger when Helpfulness = 1.00000e+00 (+ 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.38 0.11 3.37 0.00
No interaction, more contribution from Helpfulness.
H3 Conclusion
Support for Hypotheses 3. Perception of heroism is linked to perception of Danger and Helpfulness. The effect sizes are quite large for our main effects, with a definite advantage of Helpfulness. This effect can be due to the fact that police officers can be villainized despite everyone agreeing that they are objectively in risky situations. In a nutshell, people can disagree on bravery and heroism, but it would be counterfactual to disagree on the risk involved in occupations. This can make this dimension less predictive of heroism (but note that the contribution of risk perception to heroism remains quite significant).
We can note that interactions between the two attributes is small and negligeable (a comparison between additive and interactive model further emphasise this point, see Is the model additive or interactive). Both helpfulness and risk contribute to heroism, but Helpfulness is consistently a better predictor of heroism. This is true in all job.
Conclusion
We aimed to assess the effect of our manipulation of risk exposure and altruism on heroism. Our two manipulation checks indicated a general success. Our manipulation had positive significant effects on perceived bravery, selflessness, Danger, helpfulness.
HYPOTHESIS 1 was globally supported. However, the effect of our Motivation manipulation was small. Looking at the job level, our manipulations were only successful for Welders and Psychiatrists – the two least stereotyped occupations.
Replicating the previous study, we found strong support that perceiving heroism is strongly related to the perception of bravery and selflessness and to the perception of Risk and helpfulness. Again, this was not fully accounted by general attitude (Halo effect) and was relatively observed across each occupation.
The two components (Physical risk and Motivation) appears relatively independent: Both our manipulation and the perception of physical danger/helpfulness, did not interact. Only the more subjective character attribution of selflessness and bravery somehow interacted to predict heroism (with the exception of Police officers).
Regarding the Situation attribution (Danger & Helpfulness), heroism was largely driven by helpfulness. Effect sizes of danger, although significant in virtually all occupations (with the exception of police officers), were quite small.
summary(testmod<-lm(Heroism ~ Helpful_scale + Danger_scale + Brave_scale + Selfless_scale, data = Set))##
## Call:
## lm(formula = Heroism ~ Helpful_scale + Danger_scale + Brave_scale +
## Selfless_scale, data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.3177 -0.4796 0.1518 0.6823 3.6512
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.02132 0.02879 174.423 < 2e-16 ***
## Helpful_scale 0.49803 0.03544 14.052 < 2e-16 ***
## Danger_scale 0.20038 0.03385 5.920 4.08e-09 ***
## Brave_scale 0.28065 0.04050 6.930 6.47e-12 ***
## Selfless_scale 0.33371 0.04109 8.122 1.02e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.062 on 1355 degrees of freedom
## Multiple R-squared: 0.4903, Adjusted R-squared: 0.4888
## F-statistic: 325.9 on 4 and 1355 DF, p-value: < 2.2e-16## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## ----------------------------------------------
## Helpful_scale | 0.13 | [0.10, 1.00]
## Danger_scale | 0.03 | [0.01, 1.00]
## Brave_scale | 0.03 | [0.02, 1.00]
## Selfless_scale | 0.05 | [0.03, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].When looking at eta squared in a competitive model of all manipulation checks, Helpful appears to be the largest contributor to heroism (13%), followed by selflessness (5%). Finally Bravery (3%) and Danger (3%). Being a Hero is first and foremost about being helpful, it would appear.
In the next sections, we explore further those two aspects: the additive vs interactive nature of altruism and risk taking, and the relative contribution of each component in each occupation.
Exploratory analyses
Some exploratory analyses were registered (see ‘Additional comments’ section on OSF registration)
The following exploratory analyses were conducted:
- Testing main results when excluding participants whose occupation are relevant to our study (registered)
- Correlation matrix between all our measures (registered)
Further not-registered analyses:
- Testing interactive vs Additive components in our data frame
- Assessing whether heroism components (risk and altruism) acts in an interactive or additive fashion
Without Relevant Job participants
Additional sensitivity analyses will be conducted when excluding participants whose occupations are directly relevant or similar to the target occupations of the study.
# e.g.,
# Add the General attitudes to the target df
df_Roles_Excl <- subset(Set, Set$Part_Job=="None of the above")
anova(mod<-lm(Heroism ~ Risk_dummy * Help_dummy * Job, data = df_Roles_Excl))## Analysis of Variance Table
##
## Response: Heroism
## Df Sum Sq Mean Sq F value Pr(>F)
## Risk_dummy 1 82.28 82.276 47.7464 7.789e-12 ***
## Help_dummy 1 9.33 9.326 5.4120 0.02016 *
## Job 4 429.50 107.375 62.3123 < 2.2e-16 ***
## Risk_dummy:Help_dummy 1 3.29 3.293 1.9111 0.16710
## Risk_dummy:Job 4 45.15 11.288 6.5508 3.243e-05 ***
## Help_dummy:Job 4 10.43 2.608 1.5134 0.19592
## Risk_dummy:Help_dummy:Job 4 5.67 1.416 0.8219 0.51118
## Residuals 1222 2105.72 1.723
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Analysis of Variance Table
##
## Response: Heroism
## Df Sum Sq Mean Sq F value Pr(>F)
## Brave_scale 1 848.28 848.28 722.4792 < 2.2e-16 ***
## Selfless_scale 1 226.26 226.26 192.7071 < 2.2e-16 ***
## Job 4 110.65 27.66 23.5602 < 2.2e-16 ***
## Brave_scale:Selfless_scale 1 44.17 44.17 37.6191 1.159e-09 ***
## Brave_scale:Job 4 2.12 0.53 0.4516 0.771299
## Selfless_scale:Job 4 7.21 1.80 1.5350 0.189667
## Brave_scale:Selfless_scale:Job 4 17.88 4.47 3.8076 0.004403 **
## Residuals 1222 1434.79 1.17
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Analysis of Variance Table
##
## Response: Heroism
## Df Sum Sq Mean Sq F value Pr(>F)
## Danger_scale 1 564.65 564.65 470.1323 < 2.2e-16 ***
## Helpful_scale 1 542.94 542.94 452.0542 < 2.2e-16 ***
## Job 4 78.64 19.66 16.3682 4.536e-13 ***
## Danger_scale:Helpful_scale 1 0.09 0.09 0.0791 0.7785979
## Danger_scale:Job 4 12.57 3.14 2.6161 0.0337985 *
## Helpful_scale:Job 4 23.45 5.86 4.8810 0.0006601 ***
## Danger_scale:Helpful_scale:Job 4 1.36 0.34 0.2830 0.8891173
## Residuals 1222 1467.68 1.20
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Does not appear to change anything.
Correlations
library(PerformanceAnalytics)
PerformanceAnalytics::chart.Correlation(Set[, c("Heroism", "Selfless", "Brave", "Danger", "Helpfulness", "Attitude")], method = "spearman")
Is the model additive or interactive
It appears that all interactions are weak. Perhaps Altruism and Risk work independently on heroism and not that synergetically. In the following section, I compare additive and interactive solutions to see which model result in the best fit.
In this section we will compare an additive
model (Outcome ~ IV1 + IV2) and an interactive model
(Outcome ~ IV1 * IV2)
H1 - Risk manip and Motiv manip
modInt<-lm(Heroism ~ Risk_dummy * Help_dummy, data = Set)
modAdd<-lm(Heroism ~ Risk_dummy + Help_dummy, data = Set)
paste0("Comparison between additive vs interactive models")## [1] "Comparison between additive vs interactive models"## Analysis of Variance Table
##
## Model 1: Heroism ~ Risk_dummy * Help_dummy
## Model 2: Heroism ~ Risk_dummy + Help_dummy
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 1356 2906.4
## 2 1357 2907.3 -1 -0.93901 0.4381 0.5082## [1] "additive model"## Analysis of Variance Table
##
## Response: Heroism
## Df Sum Sq Mean Sq F value Pr(>F)
## Risk_dummy 1 77.59 77.587 36.2140 2.271e-09 ***
## Help_dummy 1 11.49 11.489 5.3625 0.02072 *
## Residuals 1357 2907.31 2.142
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## ------------------------------------------
## Risk_dummy | 0.03 | [0.01, 1.00]
## Help_dummy | 3.94e-03 | [0.00, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].## [1] "Interactive model"## Analysis of Variance Table
##
## Response: Heroism
## Df Sum Sq Mean Sq F value Pr(>F)
## Risk_dummy 1 77.59 77.587 36.1990 2.289e-09 ***
## Help_dummy 1 11.49 11.489 5.3603 0.02075 *
## Risk_dummy:Help_dummy 1 0.94 0.939 0.4381 0.50815
## Residuals 1356 2906.37 2.143
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Type 3 ANOVAs only give sensible and informative results when covariates
## are mean-centered and factors are coded with orthogonal contrasts (such
## as those produced by `contr.sum`, `contr.poly`, or `contr.helmert`, but
## *not* by the default `contr.treatment`).## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## -----------------------------------------------------
## Risk_dummy | 0.03 | [0.01, 1.00]
## Help_dummy | 3.95e-03 | [0.00, 1.00]
## Risk_dummy:Help_dummy | 3.23e-04 | [0.00, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].Additive Model: Main Bravery effect (eta^2 = 3%), Main Selflessness effect (eta^2 < 1%) Interactive Model: Main Bravery effect (eta^2 = 3%), Main Selflessness effect (eta^2 < 1%), Interaction (eta^2 < 1%).
==> The interactive model provides a better fit.
H2 - Bravery and Selflessness
modInt<-lm(Heroism ~ Brave_scale * Selfless_scale, data = Set)
modAdd<-lm(Heroism ~ Brave_scale + Selfless_scale, data = Set)
paste0("Comparison between additive vs interactive models")## [1] "Comparison between additive vs interactive models"## Analysis of Variance Table
##
## Model 1: Heroism ~ Brave_scale * Selfless_scale
## Model 2: Heroism ~ Brave_scale + Selfless_scale
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 1356 1766.3
## 2 1357 1874.0 -1 -107.64 82.636 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## [1] "additive model"## Analysis of Variance Table
##
## Response: Heroism
## Df Sum Sq Mean Sq F value Pr(>F)
## Brave_scale 1 883.92 883.92 640.06 < 2.2e-16 ***
## Selfless_scale 1 238.47 238.47 172.68 < 2.2e-16 ***
## Residuals 1357 1874.00 1.38
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## ----------------------------------------------
## Brave_scale | 0.07 | [0.05, 1.00]
## Selfless_scale | 0.11 | [0.09, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].## [1] "Interactive model"## Analysis of Variance Table
##
## Response: Heroism
## Df Sum Sq Mean Sq F value Pr(>F)
## Brave_scale 1 883.92 883.92 678.567 < 2.2e-16 ***
## Selfless_scale 1 238.47 238.47 183.068 < 2.2e-16 ***
## Brave_scale:Selfless_scale 1 107.64 107.64 82.636 < 2.2e-16 ***
## Residuals 1356 1766.35 1.30
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Type 3 ANOVAs only give sensible and informative results when covariates
## are mean-centered and factors are coded with orthogonal contrasts (such
## as those produced by `contr.sum`, `contr.poly`, or `contr.helmert`, but
## *not* by the default `contr.treatment`).## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## ----------------------------------------------------------
## Brave_scale | 0.11 | [0.09, 1.00]
## Selfless_scale | 0.12 | [0.10, 1.00]
## Brave_scale:Selfless_scale | 0.06 | [0.04, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].Additive Model: Main Bravery effect (eta^2 = 7%), Main Selflessness effect (eta^2 = 11%) Interactive Model: Main Bravery effect (eta^2 = 11%), Main Selflessness effect (eta^2 = 12%), Interaction (eta^2 = 6%).
==> The interactive model provides a better fit.
H2 - Risk and Helpfulness
modAdd<-lm(Heroism ~ scale(Danger) + scale(Helpfulness), data = Set)
modInt<-lm(Heroism ~ scale(Danger) * scale(Helpfulness), data = Set)
paste0("Comparison between additive vs interactive models")## [1] "Comparison between additive vs interactive models"## Analysis of Variance Table
##
## Model 1: Heroism ~ scale(Danger) * scale(Helpfulness)
## Model 2: Heroism ~ scale(Danger) + scale(Helpfulness)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 1356 1812.3
## 2 1357 1815.9 -1 -3.5773 2.6767 0.1021## [1] "Additive model"## Analysis of Variance Table
##
## Response: Heroism
## Df Sum Sq Mean Sq F value Pr(>F)
## scale(Danger) 1 604.52 604.52 451.76 < 2.2e-16 ***
## scale(Helpfulness) 1 576.00 576.00 430.45 < 2.2e-16 ***
## Residuals 1357 1815.86 1.34
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## --------------------------------------------------
## scale(Danger) | 0.07 | [0.05, 1.00]
## scale(Helpfulness) | 0.24 | [0.21, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].## [1] "Interactive model"## Analysis of Variance Table
##
## Response: Heroism
## Df Sum Sq Mean Sq F value Pr(>F)
## scale(Danger) 1 604.52 604.52 452.3202 <2e-16 ***
## scale(Helpfulness) 1 576.00 576.00 430.9811 <2e-16 ***
## scale(Danger):scale(Helpfulness) 1 3.58 3.58 2.6767 0.1021
## Residuals 1356 1812.28 1.34
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Type 3 ANOVAs only give sensible and informative results when covariates
## are mean-centered and factors are coded with orthogonal contrasts (such
## as those produced by `contr.sum`, `contr.poly`, or `contr.helmert`, but
## *not* by the default `contr.treatment`).## # Effect Size for ANOVA (Type III)
##
## Parameter | Eta2 (partial) | 95% CI
## ----------------------------------------------------------------
## scale(Danger) | 0.07 | [0.05, 1.00]
## scale(Helpfulness) | 0.24 | [0.21, 1.00]
## scale(Danger):scale(Helpfulness) | 1.97e-03 | [0.00, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].Additive Model: Main Danger effect (eta^2 = 7%), Main Helpfulness effect (eta^2 = 24%) Interactive Model: Main Risk effect (eta^2 = 7%), Main Helpfulness effect (eta^2 = 24%), Interaction (eta^2 < 0.1%).
Here it is clearly additive. Interaction is associated to a worst fit.
==> This replicates our previous study
Job Analysis and Manipulation : Interactive vs Additive components of heroism?
To assess additivity vs interactivity of our manipulation within jobs - we built an additive and an interactive model and compare their fit to the data (as previously done), for each occupation
Firefighters
##
## Call:
## lm(formula = Heroism ~ Risk_dummy + Help_dummy, data = Firef)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.7986 -0.7927 0.2014 0.9220 1.2073
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.938262 0.069730 85.161 <2e-16 ***
## Risk_dummy 0.285241 0.139459 2.045 0.0418 *
## Help_dummy 0.005829 0.139459 0.042 0.9667
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.152 on 270 degrees of freedom
## Multiple R-squared: 0.01527, Adjusted R-squared: 0.007972
## F-statistic: 2.093 on 2 and 270 DF, p-value: 0.1253##
## Call:
## lm(formula = Heroism ~ Risk_dummy * Help_dummy, data = Firef)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.7941 -0.7941 0.2029 0.9265 1.2059
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.938246 0.069859 85.003 <2e-16 ***
## Risk_dummy 0.285273 0.139718 2.042 0.0421 *
## Help_dummy 0.005861 0.139718 0.042 0.9666
## Risk_dummy:Help_dummy 0.017690 0.279436 0.063 0.9496
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.154 on 269 degrees of freedom
## Multiple R-squared: 0.01528, Adjusted R-squared: 0.004299
## F-statistic: 1.391 on 3 and 269 DF, p-value: 0.2457## Analysis of Variance Table
##
## Model 1: Heroism ~ Risk_dummy + Help_dummy
## Model 2: Heroism ~ Risk_dummy * Help_dummy
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 270 358.39
## 2 269 358.38 1 0.0053391 0.004 0.9496paste0("Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive")## [1] "Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive"##
## Linear hypothesis test:
## Risk_dummy - Help_dummy = 0
##
## Model 1: restricted model
## Model 2: Heroism ~ Risk_dummy + Help_dummy
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 271 361.04
## 2 270 358.39 1 2.6544 1.9998 0.1585In firefighters, No model stands out as a better fit. In the interactive fit (chosen for parsimony reasons), Risk manip and motiv manip provide equal contributions to heroism… weirdly enough because only risk manip reaches significance.
Nurses
##
## Call:
## lm(formula = Heroism ~ Risk_dummy + Help_dummy, data = Nurses)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.5576 -0.6035 0.4424 1.3965 1.6376
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.48295 0.08773 62.500 <2e-16 ***
## Risk_dummy 0.19519 0.17546 1.112 0.267
## Help_dummy 0.04594 0.17546 0.262 0.794
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.444 on 268 degrees of freedom
## Multiple R-squared: 0.004874, Adjusted R-squared: -0.002552
## F-statistic: 0.6563 on 2 and 268 DF, p-value: 0.5196##
## Call:
## lm(formula = Heroism ~ Risk_dummy * Help_dummy, data = Nurses)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.6866 -0.5373 0.3134 1.3134 1.7647
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.48436 0.08755 62.643 <2e-16 ***
## Risk_dummy 0.19611 0.17510 1.120 0.264
## Help_dummy 0.04686 0.17510 0.268 0.789
## Risk_dummy:Help_dummy -0.51033 0.35020 -1.457 0.146
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.441 on 267 degrees of freedom
## Multiple R-squared: 0.01273, Adjusted R-squared: 0.001633
## F-statistic: 1.147 on 3 and 267 DF, p-value: 0.3305## Analysis of Variance Table
##
## Model 1: Heroism ~ Risk_dummy + Help_dummy
## Model 2: Heroism ~ Risk_dummy * Help_dummy
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 268 558.94
## 2 267 554.53 1 4.4104 2.1236 0.1462paste0("Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive")## [1] "Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive"##
## Linear hypothesis test:
## Risk_dummy - Help_dummy = 0
##
## Model 1: restricted model
## Model 2: Heroism ~ Risk_dummy + Help_dummy
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 269 559.68
## 2 268 558.94 1 0.74627 0.3578 0.5502In nurses: No real difference here in fit between additive and interactive. risk and motiv provide equal contributions to the model.
Police
##
## Call:
## lm(formula = Heroism ~ Risk_dummy + Help_dummy, data = Pol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7074 -0.6137 0.2926 0.6595 2.6595
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.5240 0.0809 55.920 <2e-16 ***
## Risk_dummy 0.2419 0.1618 1.495 0.136
## Help_dummy 0.1250 0.1618 0.773 0.440
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.334 on 269 degrees of freedom
## Multiple R-squared: 0.01042, Adjusted R-squared: 0.003064
## F-statistic: 1.416 on 2 and 269 DF, p-value: 0.2444##
## Call:
## lm(formula = Heroism ~ Risk_dummy * Help_dummy, data = Pol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7101 -0.6123 0.2899 0.6567 2.6567
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.52396 0.08105 55.816 <2e-16 ***
## Risk_dummy 0.24194 0.16210 1.493 0.137
## Help_dummy 0.12492 0.16210 0.771 0.442
## Risk_dummy:Help_dummy 0.01103 0.32421 0.034 0.973
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.337 on 268 degrees of freedom
## Multiple R-squared: 0.01043, Adjusted R-squared: -0.0006516
## F-statistic: 0.9412 on 3 and 268 DF, p-value: 0.4212## Analysis of Variance Table
##
## Model 1: Heroism ~ Risk_dummy + Help_dummy
## Model 2: Heroism ~ Risk_dummy * Help_dummy
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 269 478.78
## 2 268 478.78 1 0.0020685 0.0012 0.9729paste0("Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive")## [1] "Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive"##
## Linear hypothesis test:
## Risk_dummy - Help_dummy = 0
##
## Model 1: restricted model
## Model 2: Heroism ~ Risk_dummy + Help_dummy
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 270 479.24
## 2 269 478.78 1 0.46492 0.2612 0.6097For police officers, again, the interactive model does not provide any advantage over an additive model.
Risk and motivation provide equal contribution to the model
Psychiatrists
##
## Call:
## lm(formula = Heroism ~ Risk_dummy + Help_dummy, data = Psych)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9110 -0.9110 0.0890 0.9705 2.9705
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.47021 0.08546 52.307 < 2e-16 ***
## Risk_dummy 0.52206 0.17093 3.054 0.00248 **
## Help_dummy 0.35942 0.17091 2.103 0.03640 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.404 on 267 degrees of freedom
## Multiple R-squared: 0.04866, Adjusted R-squared: 0.04154
## F-statistic: 6.829 on 2 and 267 DF, p-value: 0.001281##
## Call:
## lm(formula = Heroism ~ Risk_dummy * Help_dummy, data = Psych)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.8382 -0.8382 0.1618 1.0455 3.0455
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.46966 0.08551 52.273 <2e-16 ***
## Risk_dummy 0.52210 0.17101 3.053 0.0025 **
## Help_dummy 0.36159 0.17101 2.114 0.0354 *
## Risk_dummy:Help_dummy -0.29309 0.34202 -0.857 0.3922
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.405 on 266 degrees of freedom
## Multiple R-squared: 0.05128, Adjusted R-squared: 0.04058
## F-statistic: 4.793 on 3 and 266 DF, p-value: 0.002866## Analysis of Variance Table
##
## Model 1: Heroism ~ Risk_dummy + Help_dummy
## Model 2: Heroism ~ Risk_dummy * Help_dummy
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 267 526.39
## 2 266 524.94 1 1.4492 0.7344 0.3922paste0("Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive")## [1] "Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive"##
## Linear hypothesis test:
## Risk_dummy - Help_dummy = 0
##
## Model 1: restricted model
## Model 2: Heroism ~ Risk_dummy + Help_dummy
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 268 527.29
## 2 267 526.39 1 0.89927 0.4561 0.5For psychiatrists: here also, interactive and additive are not distinguished. Risk and motivation provide equal contribution to the model
Welders
##
## Call:
## lm(formula = Heroism ~ Risk_dummy + Help_dummy, data = Weld)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.0738 -0.7891 0.1043 0.9262 3.1043
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.68248 0.07888 59.359 < 2e-16 ***
## Risk_dummy 1.17807 0.15777 7.467 1.13e-12 ***
## Help_dummy 0.39546 0.15777 2.507 0.0128 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.306 on 271 degrees of freedom
## Multiple R-squared: 0.1856, Adjusted R-squared: 0.1796
## F-statistic: 30.88 on 2 and 271 DF, p-value: 8.267e-13##
## Call:
## lm(formula = Heroism ~ Risk_dummy * Help_dummy, data = Weld)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.0290 -0.8346 0.0588 0.9710 3.0588
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.68281 0.07898 59.288 < 2e-16 ***
## Risk_dummy 1.17807 0.15797 7.458 1.21e-12 ***
## Help_dummy 0.39546 0.15797 2.503 0.0129 *
## Risk_dummy:Help_dummy 0.18052 0.31594 0.571 0.5682
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.307 on 270 degrees of freedom
## Multiple R-squared: 0.1866, Adjusted R-squared: 0.1776
## F-statistic: 20.65 on 3 and 270 DF, p-value: 4.489e-12## Analysis of Variance Table
##
## Model 1: Heroism ~ Risk_dummy + Help_dummy
## Model 2: Heroism ~ Risk_dummy * Help_dummy
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 271 462.06
## 2 270 461.50 1 0.55803 0.3265 0.5682paste0("Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive")## [1] "Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive"##
## Linear hypothesis test:
## Risk_dummy - Help_dummy = 0
##
## Model 1: restricted model
## Model 2: Heroism ~ Risk_dummy + Help_dummy
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 272 483.19
## 2 271 462.06 1 21.13 12.393 0.0005054 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1For welders: No advantage for an interactive model. Risk contributes significantly more to the model than the motivation part – note that controlling for credibility does not influence this result.
Job Analysis and Character attribution : Interactive vs Additive components of heroism?
Having established that the Personality attributes (Bravery/Selflessness) are vaguely interactive and the model of Situational evaluation (Risk/Helpfulness) is clearly additive, we now want to assess the relative contribution of each Heroism elements (Brave vs Selfless and Danger vs Helpful) in predicting heroism.
In the next section, for each occupation, I systematically 1) Compare the fit of an interactive vs additive model in each occupation, and 2) compare the betas of the two predictors in the best model.
Regarding (1), I fit an interactive
(Heroism ~ FeatureA * FeatureB) and an additive
(Heroism ~ FeatureA + FeatureB) model. I then compare their
RSS in an ANOVA to decide which model provides the best fit.
Regarding (2), I use the best model (see Point 1 just above). Then,
to test that one feature of heroism contribute significantly more than
the other, I use car::linearHypothesis: I force the model
betas of the two predictors to be equivalent (e.g.,
Brave = Selfless) and see if this constrained model
provides a better fit than the model where the betas are let loose. If
the non-constrained model provides a better fit, it points to the
relative superiority of one beta over the other in explaining the
outcome.
Firefighters
##
## Call:
## lm(formula = Heroism ~ Brave_scale + Selfless_scale, data = Firef)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9551 -0.4150 0.2968 0.5850 2.8556
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.42227 0.07127 76.077 < 2e-16 ***
## Brave_scale 0.32257 0.11490 2.807 0.00536 **
## Selfless_scale 0.61293 0.09898 6.193 2.19e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.925 on 270 degrees of freedom
## Multiple R-squared: 0.3652, Adjusted R-squared: 0.3605
## F-statistic: 77.66 on 2 and 270 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ Brave_scale * Selfless_scale, data = Firef)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.0064 -0.5562 0.4438 0.4438 2.0932
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.12141 0.08912 57.464 < 2e-16 ***
## Brave_scale 0.65106 0.12642 5.150 5.04e-07 ***
## Selfless_scale 0.52142 0.09609 5.426 1.28e-07 ***
## Brave_scale:Selfless_scale 0.22611 0.04327 5.226 3.48e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.883 on 269 degrees of freedom
## Multiple R-squared: 0.4237, Adjusted R-squared: 0.4173
## F-statistic: 65.92 on 3 and 269 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Model 1: Heroism ~ Brave_scale + Selfless_scale
## Model 2: Heroism ~ Brave_scale * Selfless_scale
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 270 231.04
## 2 269 209.74 1 21.296 27.312 3.477e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## [1] "The interactive model (smaller RSS, significant F-statistic) is the best fit."##
## Linear hypothesis test:
## Brave_scale - Selfless_scale = 0
##
## Model 1: restricted model
## Model 2: Heroism ~ Brave_scale * Selfless_scale
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 270 210.05
## 2 269 209.74 1 0.30747 0.3943 0.5306In firefighters, 1) Interactive model is a better fit than additive model. 2) In the interactive model (note: and in the additive one), Bravery and Selflessness provide similar contributions to heroism.
Nurses
##
## Call:
## lm(formula = Heroism ~ scale(Brave) + scale(Selfless), data = Nurses)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.3011 -0.6296 0.1016 0.6989 4.7280
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.48339 0.07225 75.898 < 2e-16 ***
## scale(Brave) 0.33159 0.11337 2.925 0.00374 **
## scale(Selfless) 0.53942 0.11337 4.758 3.2e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.189 on 268 degrees of freedom
## Multiple R-squared: 0.3251, Adjusted R-squared: 0.32
## F-statistic: 64.54 on 2 and 268 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ scale(Brave) * scale(Selfless), data = Nurses)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.5977 -0.4969 0.4023 0.5031 2.9977
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.30036 0.07737 68.510 < 2e-16 ***
## scale(Brave) 0.52032 0.11409 4.560 7.78e-06 ***
## scale(Selfless) 0.63472 0.10974 5.784 2.04e-08 ***
## scale(Brave):scale(Selfless) 0.23868 0.04575 5.217 3.66e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.135 on 267 degrees of freedom
## Multiple R-squared: 0.3875, Adjusted R-squared: 0.3806
## F-statistic: 56.31 on 3 and 267 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Model 1: Heroism ~ scale(Brave) + scale(Selfless)
## Model 2: Heroism ~ scale(Brave) * scale(Selfless)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 268 379.09
## 2 267 344.02 1 35.062 27.212 3.662e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## [1] "The interactive model (smaller RSS, significant F-statistic) is the best fit."##
## Linear hypothesis test:
## scale(Brave) - scale(Selfless) = 0
##
## Model 1: restricted model
## Model 2: Heroism ~ scale(Brave) * scale(Selfless)
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 268 344.43
## 2 267 344.02 1 0.4038 0.3134 0.5761For nurses: 1) Interactive model (RSS = 344.02) is a better fit than additive model (RSS = 379.09), F (2, 267) = 27.21, p < .00001. 2) Linear hypothesis model indicates that not restricting the beta provides a better fit. It can be concluded that Selflessness and Bravery contributes equally to heroism for nurses.
Police
##
## Call:
## lm(formula = Heroism ~ scale(Brave) + scale(Selfless), data = Pol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.8167 -0.4534 0.1833 0.5759 3.6647
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.52574 0.06587 68.704 < 2e-16 ***
## scale(Brave) 0.41133 0.08430 4.879 1.83e-06 ***
## scale(Selfless) 0.45824 0.08430 5.436 1.23e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.086 on 269 degrees of freedom
## Multiple R-squared: 0.3438, Adjusted R-squared: 0.3389
## F-statistic: 70.46 on 2 and 269 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ scale(Brave) * scale(Selfless), data = Pol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.7383 -0.4540 0.1713 0.5759 3.8594
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.55066 0.07291 62.416 < 2e-16 ***
## scale(Brave) 0.39739 0.08614 4.613 6.15e-06 ***
## scale(Selfless) 0.45904 0.08437 5.441 1.20e-07 ***
## scale(Brave):scale(Selfless) -0.04020 0.05025 -0.800 0.424
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.087 on 268 degrees of freedom
## Multiple R-squared: 0.3453, Adjusted R-squared: 0.338
## F-statistic: 47.12 on 3 and 268 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Model 1: Heroism ~ scale(Brave) + scale(Selfless)
## Model 2: Heroism ~ scale(Brave) * scale(Selfless)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 269 317.49
## 2 268 316.74 1 0.75653 0.6401 0.4244paste0("The interactive model (smaller RSS, significant F-statistic) is the best fit. But it's really slim")## [1] "The interactive model (smaller RSS, significant F-statistic) is the best fit. But it's really slim"##
## Linear hypothesis test:
## scale(Brave) - scale(Selfless) = 0
##
## Model 1: restricted model
## Model 2: Heroism ~ scale(Brave) * scale(Selfless)
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 269 316.93
## 2 268 316.74 1 0.19168 0.1622 0.6875For police officers: there is no model that stands out as better, but a small advantage for interactive model (p = .42). In this interactive model, it appears that Selflessness and bravery provide equal contribution to heroism.
Psychiatrists
##
## Call:
## lm(formula = Heroism ~ scale(Brave) + scale(Selfless), data = Psych)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.3660 -0.6487 0.1919 0.7935 4.1995
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.47407 0.07313 61.180 < 2e-16 ***
## scale(Brave) 0.59979 0.09072 6.611 2.06e-10 ***
## scale(Selfless) 0.27008 0.09072 2.977 0.00318 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.202 on 267 degrees of freedom
## Multiple R-squared: 0.3032, Adjusted R-squared: 0.298
## F-statistic: 58.1 on 2 and 267 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ scale(Brave) * scale(Selfless), data = Psych)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2357 -0.6637 0.2474 0.7643 3.2342
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.35846 0.07809 55.813 < 2e-16 ***
## scale(Brave) 0.71198 0.09378 7.592 5.33e-13 ***
## scale(Selfless) 0.25024 0.08883 2.817 0.005212 **
## scale(Brave):scale(Selfless) 0.19676 0.05354 3.675 0.000287 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.174 on 266 degrees of freedom
## Multiple R-squared: 0.3369, Adjusted R-squared: 0.3294
## F-statistic: 45.05 on 3 and 266 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Model 1: Heroism ~ scale(Brave) + scale(Selfless)
## Model 2: Heroism ~ scale(Brave) * scale(Selfless)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 267 385.53
## 2 266 366.90 1 18.63 13.507 0.0002875 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## [1] "The interactive model (smaller RSS, significant F-statistic) is the best fit."##
## Linear hypothesis test:
## scale(Brave) - scale(Selfless) = 0
##
## Model 1: restricted model
## Model 2: Heroism ~ scale(Brave) * scale(Selfless)
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 267 378.08
## 2 266 366.90 1 11.187 8.1104 0.004745 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1For psychiatrists, the interactive model (RSS = 366.9) provides a better fit than the additive model (RSS= 383.53), p = .0003. Bravery contributes significantly more to heroism than Selflessness, p = .005.
Welders
##
## Call:
## lm(formula = Heroism ~ scale(Brave) + scale(Selfless), data = Weld)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.6541 -0.6731 0.1077 0.8034 4.0906
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.68248 0.07409 63.196 < 2e-16 ***
## scale(Brave) 0.35643 0.08326 4.281 2.58e-05 ***
## scale(Selfless) 0.53434 0.08326 6.418 6.14e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.226 on 271 degrees of freedom
## Multiple R-squared: 0.2815, Adjusted R-squared: 0.2762
## F-statistic: 53.09 on 2 and 271 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ scale(Brave) * scale(Selfless), data = Weld)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.8247 -0.7899 0.1753 0.7481 4.6123
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.59765 0.07732 59.465 < 2e-16 ***
## scale(Brave) 0.45945 0.08770 5.239 3.26e-07 ***
## scale(Selfless) 0.52031 0.08193 6.351 9.03e-10 ***
## scale(Brave):scale(Selfless) 0.18801 0.05764 3.262 0.00125 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.205 on 270 degrees of freedom
## Multiple R-squared: 0.3087, Adjusted R-squared: 0.3011
## F-statistic: 40.2 on 3 and 270 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Model 1: Heroism ~ scale(Brave) + scale(Selfless)
## Model 2: Heroism ~ scale(Brave) * scale(Selfless)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 271 407.66
## 2 270 392.20 1 15.453 10.638 0.00125 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## [1] "The interactive model (smaller RSS, significant F-statistic) is the best fit."##
## Linear hypothesis test:
## scale(Brave) - scale(Selfless) = 0
##
## Model 1: restricted model
## Model 2: Heroism ~ scale(Brave) * scale(Selfless)
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 271 392.46
## 2 270 392.20 1 0.25945 0.1786 0.6729For welders, interactive model provides a better fit than additive model (RSS = 392.2 vs RSS = 407.66), p = .00125. In the interactive model, Selflessness and bravery provides equal contribution to heroism.
Job Analysis and Situation attribution : Interactive vs Additive components of heroism?
We repeat the same analyses but using our second manipulation check: Situation attribution (Physical danger & Helpfulness of the occupation).
Firefighters
##
## Call:
## lm(formula = Heroism ~ scale(Danger) + scale(Helpfulness), data = Firef)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.3375 -0.3375 0.2788 0.6625 1.8097
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.93773 0.05913 100.426 < 2e-16 ***
## scale(Danger) 0.25907 0.07917 3.272 0.00121 **
## scale(Helpfulness) 0.42234 0.07917 5.335 2.03e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9769 on 270 degrees of freedom
## Multiple R-squared: 0.292, Adjusted R-squared: 0.2867
## F-statistic: 55.67 on 2 and 270 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ scale(Danger) * scale(Helpfulness), data = Firef)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.3549 -0.3549 0.3133 0.6451 1.7724
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.92377 0.06204 95.482 < 2e-16 ***
## scale(Danger) 0.26680 0.07990 3.339 0.00096 ***
## scale(Helpfulness) 0.45664 0.09152 4.990 1.09e-06 ***
## scale(Danger):scale(Helpfulness) 0.02112 0.02820 0.749 0.45454
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9777 on 269 degrees of freedom
## Multiple R-squared: 0.2935, Adjusted R-squared: 0.2856
## F-statistic: 37.24 on 3 and 269 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Model 1: Heroism ~ scale(Danger) + scale(Helpfulness)
## Model 2: Heroism ~ scale(Danger) * scale(Helpfulness)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 270 257.68
## 2 269 257.14 1 0.5362 0.5609 0.4545paste0("Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive")## [1] "Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive"##
## Linear hypothesis test:
## scale(Danger) - scale(Helpfulness) = 0
##
## Model 1: restricted model
## Model 2: Heroism ~ scale(Danger) + scale(Helpfulness)
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 271 258.90
## 2 270 257.68 1 1.2201 1.2784 0.2592In firefighters, No model stands out as a better fit. In the interactive fit (chosen for parsimony reasons), Danger and helpfulness provide equal contributions to heroism.
Nurses
##
## Call:
## lm(formula = Heroism ~ scale(Danger) + scale(Helpfulness), data = Nurses)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.0613 -0.5000 0.1621 0.6580 2.9932
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.48339 0.06990 78.444 < 2e-16 ***
## scale(Danger) 0.34514 0.07893 4.373 1.76e-05 ***
## scale(Helpfulness) 0.66065 0.07893 8.371 3.21e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.151 on 268 degrees of freedom
## Multiple R-squared: 0.3682, Adjusted R-squared: 0.3635
## F-statistic: 78.08 on 2 and 268 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ scale(Danger) * scale(Helpfulness), data = Nurses)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.0583 -0.5187 0.1772 0.6729 3.0262
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.49175 0.07663 71.667 < 2e-16 ***
## scale(Danger) 0.34346 0.07931 4.331 2.10e-05 ***
## scale(Helpfulness) 0.65103 0.08681 7.499 9.52e-13 ***
## scale(Danger):scale(Helpfulness) -0.01819 0.06774 -0.268 0.789
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.153 on 267 degrees of freedom
## Multiple R-squared: 0.3683, Adjusted R-squared: 0.3612
## F-statistic: 51.9 on 3 and 267 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Model 1: Heroism ~ scale(Danger) + scale(Helpfulness)
## Model 2: Heroism ~ scale(Danger) * scale(Helpfulness)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 268 354.89
## 2 267 354.79 1 0.095766 0.0721 0.7886paste0("Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive")## [1] "Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive"##
## Linear hypothesis test:
## scale(Danger) - scale(Helpfulness) = 0
##
## Model 1: restricted model
## Model 2: Heroism ~ scale(Danger) + scale(Helpfulness)
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 269 362.13
## 2 268 354.89 1 7.2413 5.4684 0.0201 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1In nurses: No real difference here in fit between additive and interactive. We observe a barely significant superior contribution of Helpfulness in comparison to Danger, p = .02.
Police
##
## Call:
## lm(formula = Heroism ~ scale(Danger) + scale(Helpfulness), data = Pol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.7606 -0.5506 0.0884 0.7790 2.9778
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.52574 0.06390 70.824 <2e-16 ***
## scale(Danger) 0.12546 0.07922 1.584 0.114
## scale(Helpfulness) 0.74619 0.07922 9.419 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.054 on 269 degrees of freedom
## Multiple R-squared: 0.3825, Adjusted R-squared: 0.3779
## F-statistic: 83.3 on 2 and 269 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ scale(Danger) * scale(Helpfulness), data = Pol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.8871 -0.5108 0.0161 0.8233 3.0095
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.48612 0.07166 62.599 <2e-16 ***
## scale(Danger) 0.14025 0.08008 1.751 0.081 .
## scale(Helpfulness) 0.76996 0.08153 9.444 <2e-16 ***
## scale(Danger):scale(Helpfulness) 0.06749 0.05547 1.217 0.225
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.053 on 268 degrees of freedom
## Multiple R-squared: 0.3859, Adjusted R-squared: 0.379
## F-statistic: 56.13 on 3 and 268 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Model 1: Heroism ~ scale(Danger) + scale(Helpfulness)
## Model 2: Heroism ~ scale(Danger) * scale(Helpfulness)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 269 298.77
## 2 268 297.13 1 1.6416 1.4806 0.2247paste0("Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive")## [1] "Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive"##
## Linear hypothesis test:
## scale(Danger) - scale(Helpfulness) = 0
##
## Model 1: restricted model
## Model 2: Heroism ~ scale(Danger) + scale(Helpfulness)
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 270 320.23
## 2 269 298.77 1 21.454 19.316 1.596e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1For police officers, again, the interactive model does not provide any advantage over an additive model.
Helpfulness contributes significantly more than Danger to heroism of police officers.
Psychiatrists
##
## Call:
## lm(formula = Heroism ~ scale(Danger) + scale(Helpfulness), data = Psych)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4245 -0.6204 0.1836 0.7033 2.3796
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.47407 0.07219 61.975 <2e-16 ***
## scale(Danger) 0.18109 0.07909 2.290 0.0228 *
## scale(Helpfulness) 0.72224 0.07909 9.132 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.186 on 267 degrees of freedom
## Multiple R-squared: 0.321, Adjusted R-squared: 0.3159
## F-statistic: 63.11 on 2 and 267 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ scale(Danger) * scale(Helpfulness), data = Psych)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4511 -0.6129 0.1978 0.6907 2.3997
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.46569 0.07640 58.454 < 2e-16 ***
## scale(Danger) 0.18022 0.07926 2.274 0.0238 *
## scale(Helpfulness) 0.73211 0.08436 8.678 4.1e-16 ***
## scale(Danger):scale(Helpfulness) 0.02080 0.06115 0.340 0.7340
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.188 on 266 degrees of freedom
## Multiple R-squared: 0.3213, Adjusted R-squared: 0.3136
## F-statistic: 41.97 on 3 and 266 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Model 1: Heroism ~ scale(Danger) + scale(Helpfulness)
## Model 2: Heroism ~ scale(Danger) * scale(Helpfulness)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 267 375.71
## 2 266 375.54 1 0.16333 0.1157 0.734paste0("Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive")## [1] "Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive"##
## Linear hypothesis test:
## scale(Danger) - scale(Helpfulness) = 0
##
## Model 1: restricted model
## Model 2: Heroism ~ scale(Danger) + scale(Helpfulness)
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 268 399.16
## 2 267 375.71 1 23.452 16.667 5.892e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1For psychiatrists: here also, interactive and additive are not distinguished. Helpfulness contributes more to heroism than Danger.
Welders
##
## Call:
## lm(formula = Heroism ~ scale(Danger) + scale(Helpfulness), data = Weld)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.7382 -0.7222 0.0124 0.7630 3.0146
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.68248 0.07322 63.948 < 2e-16 ***
## scale(Danger) 0.43648 0.07606 5.738 2.56e-08 ***
## scale(Helpfulness) 0.55001 0.07606 7.231 4.91e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.212 on 271 degrees of freedom
## Multiple R-squared: 0.2983, Adjusted R-squared: 0.2931
## F-statistic: 57.61 on 2 and 271 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ scale(Danger) * scale(Helpfulness), data = Weld)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.6892 -0.6892 0.0038 0.7559 2.9158
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.69611 0.07579 61.961 < 2e-16 ***
## scale(Danger) 0.42995 0.07669 5.606 5.11e-08 ***
## scale(Helpfulness) 0.54876 0.07616 7.206 5.78e-12 ***
## scale(Danger):scale(Helpfulness) -0.05174 0.07329 -0.706 0.481
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.213 on 270 degrees of freedom
## Multiple R-squared: 0.2996, Adjusted R-squared: 0.2918
## F-statistic: 38.5 on 3 and 270 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Model 1: Heroism ~ scale(Danger) + scale(Helpfulness)
## Model 2: Heroism ~ scale(Danger) * scale(Helpfulness)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 271 398.12
## 2 270 397.39 1 0.73357 0.4984 0.4808paste0("Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive")## [1] "Model do not significantly differ. Consistency motive: we keep interaction; or Parsimony motive: we go with additive"##
## Linear hypothesis test:
## scale(Danger) - scale(Helpfulness) = 0
##
## Model 1: restricted model
## Model 2: Heroism ~ scale(Danger) + scale(Helpfulness)
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 272 399.41
## 2 271 398.12 1 1.2942 0.881 0.3488For welders: No advantage for an interactive model. Helpfulness and danger provide equal contribution to heroism.
Final Conclusion
Hurray, this second attempt was quite a success. The manipulation checks indicate that the manipulations worked, and we observed all the principal registered effects.
However, looking in details, the manipulation worked in psychiatrists and welders, but not the other occupations – indicating that heroism ratings might be mainly driven by strongly held opinions of the heroism of an occupation. Because we have strong views of how heroic firefighters, nurses, and police officers are, our manipulation was unsuccessful.
Moreover, while we did observe a significant effect of motivation, it was close to non-significance In contrast, the effect of risk exposure was quite large – perhaps reflecting an effect stemming from the contrast with boredom: Can we really imagine a hero being bored?
Replicating the previous findings: both the character evaluation (selflessness and bravery) and the situation evaluation (Danger and helpfulness) predicted heroism. However, in contrast to the previous findings, the contributions were more balanced with the exception of psychiatrists’ heroism being mainly predicted by bravery, rather than selflessness (H2). Welders also showed a strong effect of the risk manipulation relative to the motivation condition (H1). Replicating the previous study: Helpfulness is a stronger predictor of heroism compared to physical danger – we can have a dangerous profession without necessarily being typecasted as a hero. This is further emphasised by Danger being the least correlated variable of the set with heroism (see correlation matrix).
The plots below describe the Beta comparisons reported in the exploratory analyses:
# Right, so we're going to plot the betas difference for each occupation
# We create a list of df
datasets <- list(
Firefighters = Firef,
Nurses = Nurses,
Police = Pol,
Psychiatrists = Psych,
Welders = Weld
)
# Storing the results of the models
results <- list()
# for loop: in each dataset, fit the model, and extract the betas to substract them
for(model_name in names(datasets)) {
data_ <- datasets[[model_name]]
# Fitting mod
mod <- lm(Heroism ~ Brave * Selfless, data = data_)
# Extract coefficients and the variance-covariance matrix (used for 95%CI)
coefs <- coef(mod)
vc <- vcov(mod)
# Compute the difference between coefficients "Brave" and "Selfless"
diff_coef <- coefs["Brave"] - coefs["Selfless"]
# Compute standard error of the difference:
# Var(Brave - Selfless) = Var(Brave) + Var(Selfless) - 2*Cov(Brave,Selfless)
se_diff <- sqrt(vc["Brave", "Brave"] + vc["Selfless", "Selfless"] - 2 * vc["Brave", "Selfless"])
# Compute the 95% confidence interval using a normal approximation (z = 1.96)
crit <- qnorm(0.975)
lower <- diff_coef - crit * se_diff
upper <- diff_coef + crit * se_diff
# Store the results in a data frame
results[[model_name]] <- data.frame(
Model = model_name,
diff = diff_coef,
lower = lower,
upper = upper
)
}
# Combine the list of data frames into one
df_results <- do.call(rbind, results)
df_results$Model <- factor(df_results$Model, levels = names(datasets))
ggplot(df_results, aes(x = Model, y = diff)) +
geom_point(size = 3) +
geom_errorbar(aes(ymin = lower, ymax = upper), width = 0.2) +
geom_hline(yintercept = 0, linetype = "dashed", color = "red") +
labs(
title = "Relative contribution of Bravery vs Selflessness in predicting Heroism",
y = "Coefficient Difference (Brave - Selfless)",
x = "Occupation"
) +
theme_minimal()
# Right, so we're going to plot the betas difference for each occupation
# We create a list of df
datasets <- list(
Firefighters = Firef,
Nurses = Nurses,
Police = Pol,
Psychiatrists = Psych,
Welders = Weld
)
# Storing the results of the models
results <- list()
Firef$Danger <- scale(Firef$Danger)
Firef$Helpfulness <- scale(Firef$Helpfulness)
Nurses$Danger <- scale(Nurses$Danger)
Nurses$Helpfulness <- scale(Nurses$Helpfulness)
Weld$Danger <- scale(Weld$Danger)
Weld$Helpfulness <- scale(Weld$Helpfulness)
Pol$Danger <- scale(Pol$Danger)
Pol$Helpfulness <- scale(Pol$Helpfulness)
Psych$Danger <- scale(Psych$Danger)
Psych$Helpful <- scale(Psych$Helpfulness)
# for loop: in each dataset, fit the model, and extract the betas to substract them
for(model_name in names(datasets)) {
data_ <- datasets[[model_name]]
# Fitting mod
mod <- lm(Heroism ~ Danger + Helpfulness, data = data_)
# Extract coefficients and the variance-covariance matrix (used for 95%CI)
coefs <- coef(mod)
vc <- vcov(mod)
# Compute the difference between coefficients "Brave" and "Selfless"
diff_coef <- coefs["Danger"] - coefs["Helpfulness"]
# Compute standard error of the difference:
se_diff <- sqrt(vc["Danger", "Danger"] + vc["Helpfulness", "Helpfulness"] - 2 * vc["Danger", "Helpfulness"])
# Compute the 95% confidence interval using a normal approximation (z = 1.96)
crit <- qnorm(0.975)
lower <- diff_coef - crit * se_diff
upper <- diff_coef + crit * se_diff
# Store the results in a data frame
results[[model_name]] <- data.frame(
Model = model_name,
diff = diff_coef,
lower = lower,
upper = upper
)
}
# Combine the list of data frames into one
df_results <- do.call(rbind, results)
df_results$Model <- factor(df_results$Model, levels = names(datasets))
ggplot(df_results, aes(x = Model, y = diff)) +
geom_point(size = 3) +
geom_errorbar(aes(ymin = lower, ymax = upper), width = 0.2) +
geom_hline(yintercept = 0, linetype = "dashed", color = "red") +
labs(
title = "Relative contribution of Risk vs Helpfulness in predicting Heroism",
y = "Coefficient Difference (Risk - Helpfulness)",
x = "Occupation"
) +
theme_minimal()
# Storing the results of the models
results <- list()
# for loop: in each dataset, fit the model, and extract the betas to substract them
for(model_name in names(datasets)) {
data_ <- datasets[[model_name]]
# Fitting mod
mod <- lm(Heroism ~ Risk_dummy * Help_dummy, data = data_)
# Extract coefficients and the variance-covariance matrix (used for 95%CI)
coefs <- coef(mod)
vc <- vcov(mod)
# Compute the difference between coefficients "Brave" and "Selfless"
diff_coef <- coefs["Risk_dummy"] - coefs["Help_dummy"]
# Compute standard error of the difference:
# Var(Brave - Selfless) = Var(Brave) + Var(Help_dummy) - 2*Cov(Brave,Help_dummy)
se_diff <- sqrt(vc["Risk_dummy", "Risk_dummy"] + vc["Help_dummy", "Help_dummy"] - 2 * vc["Risk_dummy", "Help_dummy"])
# Compute the 95% confidence interval using a normal approximation (z = 1.96)
crit <- qnorm(0.975)
lower <- diff_coef - crit * se_diff
upper <- diff_coef + crit * se_diff
# Store the results in a data frame
results[[model_name]] <- data.frame(
Model = model_name,
diff = diff_coef,
lower = lower,
upper = upper
)
}
# Combine the list of data frames into one
df_results <- do.call(rbind, results)
df_results$Model <- factor(df_results$Model, levels = names(datasets))
ggplot(df_results, aes(x = Model, y = diff)) +
geom_point(size = 3) +
geom_errorbar(aes(ymin = lower, ymax = upper), width = 0.2) +
geom_hline(yintercept = 0, linetype = "dashed", color = "red") +
labs(
title = "Relative contribution of Risk condition vs Motivation condition in predicting Heroism",
y = "Coefficient Difference (Risk cond - Motivation)",
x = "Occupation"
) +
theme_minimal()
Any question can be addressed to Jean Monéger (My contact can be easily found using Google).
Our manipulation globally worked - although the Motivation variable barely worked
Appendix
Data wrangling
Below is the code for organising the dataset from the Qualtrics output to the neat dataframe used to run this document:
- isolating Demographics
- putting the reported participants’ occupation in a single column (Part_job)
- Changing the response labels from characters to numeric: Very negative –> 1, etc.
- Recoding condition in two different ways to enable verification that there was no bug (there were none of course)
- ‘Aligning columns’: different columns code for the same variables depending on the experimental conditions. So, we recode things to have, all the heroism rating in the same columns, etc.
- Conditions are dummy coded: Boredom -> -0.5, Risk -> 0.5 / Self-improvement -> -0.5, Selflessness -> 0.5
The wrangling process requires that you download the datafile
Raw_Qualtrics_Data_HeroFactory_April2025.csv available from
our OSF webpage.
Set <- read.csv("Raw_Qualtrics_Data_HeroFactory_April2025.csv", comment.char="#")
Set <- subset(Set, Set$Q233 != "No, I won't")
Set <- Set[-c(1:2),]
Set <- subset(Set, Set$FailedComp == "No") # Keep only participants who succeeded the completion checks
# Two participants timed out but completed the survey. Let's remove them to not threaten representativity and stick closely to registration:
Set <- subset(Set, !(Set$Prol_ID %in% c("5cb6f38ffdc7fa0013f809a3", "5cf84c0f4b639a0016a45a54")))
QualCheck <- Set[, c(21:26)] # Quality evaluation is Good. There are 8 participant flagged as duplicatated, but I do not trust this opaque quality check
Demographics <- Set[, 38:48] # Keeping demographics aside
# First, add a unique row identifier if one does not exist already:
job_cols <- c("Job_match_1", "Job_match_2", "Job_match_3",
"Job_match_4", "Job_match_5", "Job_match_7", "Job_match_6")
Demographics$JOB <- apply(Demographics[, job_cols], 1, function(x) {
# Remove empty strings
reported_jobs <- x[x != ""]
# If no jobs reported, assign NA; else paste the jobs together
if (length(reported_jobs) == 0) NA else paste(reported_jobs, collapse = ", ")
})
Set$Credibility[Set$Credibility == "Very unbelievable"] <- 1
Set$Credibility[Set$Credibility == "Quite unbelievable"] <- 2
Set$Credibility[Set$Credibility == "Somewhat unbelievable"] <- 3
Set$Credibility[Set$Credibility == "Neutral"] <- 4
Set$Credibility[Set$Credibility == "Somewhat believable"] <- 5
Set$Credibility[Set$Credibility == "Quite believable"] <- 6
Set$Credibility[Set$Credibility == "Very believable"] <- 7
Set <- Set %>%
dplyr::mutate(across(
where(is.character),
~ dplyr::case_match(.,
"83% of the workers reported feeling bored most of the time" ~ "Bored",
"83% of the workers reported that their life was at risk in the past 12 months" ~ "Risk",
"74% of the workers identified \"helping people\" as their primary motivation" ~ "Help",
"74% of the workers identified \"self-improvement\" as their primary motivation" ~ "Self",
.default = .
)
))
# I need to code the condition. It can be retrieved using non-empty heroism ratings. e.g., NRH is Nurses, Risk, Help. Note that it can also be re-computed from succeeded Comprehension checks (AC___1, AC____2, and AC_____3)
# I concatenate Comprehension checks (AC1, AC2, and AC3)
Set_long <- Set %>%
# Gather all columns matching the pattern
pivot_longer(
cols = matches("^AC.*[123]$"),
names_to = c("base", "suffix"),
names_pattern = "^(AC.*?)([123])$",
values_to = "value"
) %>%
# Now spread the suffix into separate columns.
pivot_wider(
names_from = suffix,
values_from = value,
names_prefix = "AC"
)
# Identify all columns ending with "h_1" and use it to fill the column "CONDITION"
h1_cols <- grep("_h_1$", names(Set_long), value = TRUE)
# Creating the condition
Set_long_filtered <- Set_long %>%
rowwise() %>% # process each row individually
mutate(
# Count how many of the h1_cols are non-empty ("")
non_empty_count = sum(c_across(all_of(h1_cols)) != ""),
# Determine the Condition based on non-empty count
Condition_2 = if (non_empty_count == 1) {
# Get the name of the column that is non-empty
selected_col <- h1_cols[which(c_across(all_of(h1_cols)) != "")]
# Remove the "_h_1" suffix to get the condition (e.g., "NRS" from "NRS_h_1")
str_remove(selected_col, "_h_1")
} else {
"Error"
}
) %>%
ungroup() %>% # exit rowwise mode
select(-non_empty_count) %>% distinct(ResponseId, .keep_all=T) # remove the helper column if no longer needed
# Now I'll neatly create the main data frame. I create a helper function that extract all non empty values and apply it on all rows ending with our codes:
# - _h_1 is heroism rating, _m_1_1 is first item of MC1, m_1_2, is second item of mc2, _at is attitude etc.
# Helper function: Given a vector, return the only non-empty element (or NA if none/few found)
extract_value <- function(x) {
non_empty <- x[x != ""]
if(length(non_empty) == 1) return(non_empty)
else return(NA)
}
# Create the final data frame
final_df <- Set_long_filtered %>%
mutate(
# Extract the non-empty value from each group of columns:
Heroism = apply(select(., ends_with("_h_1")), 1, extract_value),
Danger = apply(select(., ends_with("m1_1")), 1, extract_value),
Helpfulness = apply(select(., ends_with("m1_2")), 1, extract_value),
Selfless = apply(select(., ends_with("m2_1")), 1, extract_value),
Brave = apply(select(., ends_with("m2_2")), 1, extract_value),
Attitude = apply(select(., matches("(_at)$")), 1, extract_value)
) %>%
# Select only the required columns in the final data frame
select(ResponseId, Condition, Condition_2, Heroism, Danger, Helpfulness, Selfless, Brave, Attitude, Credibility, Gender, Age)
# Recoding values:
final_df <- final_df %>%
# 1. Split Condition into Job, Risk, and Help
mutate(
Job = if_else(str_sub(Condition_2, 1, 2) == "Ps", "Ps", str_sub(Condition_2, 1, 1)),
Risk = if_else(str_sub(Condition_2, 1, 2) == "Ps", str_sub(Condition_2, 3, 3), str_sub(Condition_2, 2, 2)),
Help = if_else(str_sub(Condition_2, 1, 2) == "Ps", str_sub(Condition_2, 4, 4), str_sub(Condition_2, 3, 3))
) %>%
# 2. Dummy code Risk and Help: R -> 0.5, B -> -0.5; H -> 0.5, S -> -0.5
mutate(
Risk_dummy = case_when(
Risk == "R" ~ 0.5,
Risk == "B" ~ -0.5,
TRUE ~ NA_real_
),
Help_dummy = case_when(
Help == "H" ~ 0.5,
Help == "S" ~ -0.5,
TRUE ~ NA_real_
)
) %>%
# 3. Recode rating items (HeroismScore, MC1_1, MC1_2, MC2_1, MC2_2)
mutate_at(vars(Heroism, Danger, Helpfulness, Selfless, Brave),
~ case_when(
. == "1 - Strongly disagree" ~ "1",
. == "7 - Strongly agree" ~ "7",
TRUE ~ .
)) %>%
# Optionally convert these recoded columns to numeric
mutate_at(vars(Heroism, Danger, Helpfulness, Selfless, Brave), as.numeric) %>%
# 4. Recode Attitude values
mutate(
Attitude = case_when(
Attitude == "Very negative" ~ 1,
Attitude == "Quite negative" ~ 2,
Attitude == "Somewhat negative" ~ 3,
Attitude == "Neutral" ~ 4,
Attitude == "Somewhat positive" ~ 5,
Attitude == "Quite positive" ~ 6,
Attitude == "Very positive" ~ 7,
TRUE ~ NA_real_
)
)
final_df$Part_Job <- Demographics$JOB
Set<-final_df
#write.csv(Set, "DF_HeroFactory_April2025.csv", row.names = F)Credibility test
Below are some additional insights into credibility of the manipulation and how it 1) is influenced by the conclusion, and 2) how it influences our results. There is solid ground to consider that the manipulation was:
- Credible
- Weaker for nurses and firefighters
- The more credible, the better the effect of our manipulation.
##
## Call:
## lm(formula = Credibility ~ Job, data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.2747 -0.9926 0.0996 1.0074 2.0996
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.27473 0.09188 57.407 <2e-16 ***
## JobN -0.37436 0.13018 -2.876 0.0041 **
## JobP -0.19384 0.13006 -1.490 0.1364
## JobPs -0.28213 0.13030 -2.165 0.0305 *
## JobW -0.03385 0.12982 -0.261 0.7943
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.518 on 1355 degrees of freedom
## Multiple R-squared: 0.008818, Adjusted R-squared: 0.005892
## F-statistic: 3.014 on 4 and 1355 DF, p-value: 0.01728##
## Call:
## lm(formula = Credibility ~ Risk_dummy * Help_dummy, data = Firef)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.3235 -0.3235 0.6765 0.7794 2.6812
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.27824 0.08766 60.211 < 2e-16 ***
## Risk_dummy 1.01705 0.17532 5.801 1.85e-08 ***
## Help_dummy 0.91411 0.17532 5.214 3.69e-07 ***
## Risk_dummy:Help_dummy 0.02472 0.35065 0.071 0.944
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.448 on 269 degrees of freedom
## Multiple R-squared: 0.185, Adjusted R-squared: 0.1759
## F-statistic: 20.35 on 3 and 269 DF, p-value: 6.455e-12## Firef$Risk_dummy: -0.5
## [1] 4.766423
## ------------------------------------------------------------
## Firef$Risk_dummy: 0.5
## [1] 5.786765## Firef$Risk_dummy: -0.5
## [1] 1.60084
## ------------------------------------------------------------
## Firef$Risk_dummy: 0.5
## [1] 1.42157## Firef$Help_dummy: -0.5
## [1] 4.817518
## ------------------------------------------------------------
## Firef$Help_dummy: 0.5
## [1] 5.735294## Firef$Help_dummy: -0.5
## [1] 1.737218
## ------------------------------------------------------------
## Firef$Help_dummy: 0.5
## [1] 1.289475ggplot(Firef, aes(x = interaction(Risk, Help, sep = " & "), y = Credibility)) +
geom_boxplot() +
labs(x = "Condition (Risk_dummy & Help_dummy)",
y = "Credibility",
title = "FIREFIGHTERS: Credibility by Risk and Help Conditions") +
theme_minimal()
##
## Call:
## lm(formula = Credibility ~ Risk_dummy * Help_dummy, data = Psych)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7794 -1.0211 0.2206 1.0896 2.8030
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.986200 0.087312 57.108 < 2e-16 ***
## Risk_dummy 0.864983 0.174624 4.953 1.3e-06 ***
## Help_dummy 0.717459 0.174624 4.109 5.3e-05 ***
## Risk_dummy:Help_dummy 0.007963 0.349248 0.023 0.982
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.434 on 266 degrees of freedom
## Multiple R-squared: 0.1339, Adjusted R-squared: 0.1241
## F-statistic: 13.71 on 3 and 266 DF, p-value: 2.43e-08## Psych$Risk_dummy: -0.5
## [1] 4.556391
## ------------------------------------------------------------
## Psych$Risk_dummy: 0.5
## [1] 5.416058## Psych$Risk_dummy: -0.5
## [1] 1.611575
## ------------------------------------------------------------
## Psych$Risk_dummy: 0.5
## [1] 1.326441## Psych$Help_dummy: -0.5
## [1] 4.637037
## ------------------------------------------------------------
## Psych$Help_dummy: 0.5
## [1] 5.348148## Psych$Help_dummy: -0.5
## [1] 1.637287
## ------------------------------------------------------------
## Psych$Help_dummy: 0.5
## [1] 1.334494ggplot(Psych, aes(x = interaction(Risk, Help, sep = " & "), y = Credibility)) +
geom_boxplot() +
labs(x = "Condition (Risk_dummy & Help_dummy)",
y = "Credibility",
title = "PSYCH: Credibility by Risk and Help Conditions") +
theme_minimal()
##
## Call:
## lm(formula = Credibility ~ Risk_dummy * Help_dummy, data = Nurses)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.9565 -0.9565 0.0435 1.0435 3.2206
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.8967 0.0906 54.046 < 2e-16 ***
## Risk_dummy 1.3871 0.1812 7.655 3.55e-13 ***
## Help_dummy 0.7901 0.1812 4.360 1.86e-05 ***
## Risk_dummy:Help_dummy -0.1148 0.3624 -0.317 0.752
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.491 on 267 degrees of freedom
## Multiple R-squared: 0.227, Adjusted R-squared: 0.2184
## F-statistic: 26.14 on 3 and 267 DF, p-value: 7.395e-15ggplot(Nurses, aes(x = interaction(Risk, Help, sep = " & "), y = Credibility)) +
geom_boxplot() +
labs(x = "Condition (Risk_dummy & Help_dummy)",
y = "Credibility",
title = "NURSES: Credibility by Risk and Help Conditions") +
theme_minimal()
##
## Call:
## lm(formula = Credibility ~ Risk_dummy * Help_dummy, data = Weld)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.8971 -0.7794 0.2206 1.1029 2.2029
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.24158 0.08274 63.354 < 2e-16 ***
## Risk_dummy 0.78900 0.16547 4.768 3.04e-06 ***
## Help_dummy 0.09335 0.16547 0.564 0.573
## Risk_dummy:Help_dummy 0.38662 0.33094 1.168 0.244
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.369 on 270 degrees of freedom
## Multiple R-squared: 0.08282, Adjusted R-squared: 0.07263
## F-statistic: 8.127 on 3 and 270 DF, p-value: 3.357e-05## Weld$Risk_dummy: -0.5
## [1] 4.846715
## ------------------------------------------------------------
## Weld$Risk_dummy: 0.5
## [1] 5.635036## Weld$Risk_dummy: -0.5
## [1] 1.439416
## ------------------------------------------------------------
## Weld$Risk_dummy: 0.5
## [1] 1.294081## Weld$Help_dummy: -0.5
## [1] 5.19708
## ------------------------------------------------------------
## Weld$Help_dummy: 0.5
## [1] 5.284672## Weld$Help_dummy: -0.5
## [1] 1.418571
## ------------------------------------------------------------
## Weld$Help_dummy: 0.5
## [1] 1.429464ggplot(Weld, aes(x = interaction(Risk, Help, sep = " & "), y = Credibility)) +
geom_boxplot() +
labs(x = "Condition (Risk_dummy & Help_dummy)",
y = "Credibility",
title = "WELDERS: Credibility by Risk and Help Conditions") +
theme_minimal()
##
## Call:
## lm(formula = Credibility ~ Risk_dummy * Help_dummy, data = Pol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7761 -0.7761 0.2239 1.0746 2.2239
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.07755 0.07893 64.326 < 2e-16 ***
## Risk_dummy 0.45360 0.15787 2.873 0.00439 **
## Help_dummy 0.33550 0.15787 2.125 0.03449 *
## Risk_dummy:Help_dummy 0.37249 0.31574 1.180 0.23916
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.302 on 268 degrees of freedom
## Multiple R-squared: 0.05045, Adjusted R-squared: 0.03982
## F-statistic: 4.746 on 3 and 268 DF, p-value: 0.003046ggplot(Pol, aes(x = interaction(Risk, Help, sep = " & "), y = Credibility)) +
geom_boxplot() +
labs(x = "Condition (Risk_dummy & Help_dummy)",
y = "Credibility",
title = "POLICE: Credibility by Risk and Help Conditions") +
theme_minimal()
## Pol$Risk_dummy: -0.5
## [1] 4.850746
## ------------------------------------------------------------
## Pol$Risk_dummy: 0.5
## [1] 5.304348## Pol$Risk_dummy: -0.5
## [1] 1.422206
## ------------------------------------------------------------
## Pol$Risk_dummy: 0.5
## [1] 1.19371## Pol$Help_dummy: -0.5
## [1] 4.911765
## ------------------------------------------------------------
## Pol$Help_dummy: 0.5
## [1] 5.25## Pol$Help_dummy: -0.5
## [1] 1.395605
## ------------------------------------------------------------
## Pol$Help_dummy: 0.5
## [1] 1.239773Using credibility as a covariate in our analyses:
summary(lm(as.numeric(Heroism) ~ Risk_dummy * Help_dummy * scale(as.numeric(Credibility)), data = Set))##
## Call:
## lm(formula = as.numeric(Heroism) ~ Risk_dummy * Help_dummy *
## scale(as.numeric(Credibility)), data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.9967 -0.8037 0.1086 1.0033 3.3730
##
## Coefficients:
## Estimate Std. Error
## (Intercept) 4.91688 0.04096
## Risk_dummy 0.17465 0.08192
## Help_dummy -0.02904 0.08192
## scale(as.numeric(Credibility)) 0.48601 0.04229
## Risk_dummy:Help_dummy -0.47792 0.16384
## Risk_dummy:scale(as.numeric(Credibility)) 0.57391 0.08458
## Help_dummy:scale(as.numeric(Credibility)) 0.19451 0.08458
## Risk_dummy:Help_dummy:scale(as.numeric(Credibility)) 0.12725 0.16915
## t value Pr(>|t|)
## (Intercept) 120.043 < 2e-16 ***
## Risk_dummy 2.132 0.03319 *
## Help_dummy -0.354 0.72303
## scale(as.numeric(Credibility)) 11.493 < 2e-16 ***
## Risk_dummy:Help_dummy -2.917 0.00359 **
## Risk_dummy:scale(as.numeric(Credibility)) 6.786 1.72e-11 ***
## Help_dummy:scale(as.numeric(Credibility)) 2.300 0.02161 *
## Risk_dummy:Help_dummy:scale(as.numeric(Credibility)) 0.752 0.45202
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.389 on 1352 degrees of freedom
## Multiple R-squared: 0.129, Adjusted R-squared: 0.1245
## F-statistic: 28.6 on 7 and 1352 DF, p-value: < 2.2e-16Controlling for Credibility nullifies the effect of the Help condition. Furthermore, when using Credibility as a moderator:
summary(lm(as.numeric(Heroism) ~ Risk_dummy * Help_dummy + scale(as.numeric(Credibility)), data = Set))##
## Call:
## lm(formula = as.numeric(Heroism) ~ Risk_dummy * Help_dummy +
## scale(as.numeric(Credibility)), data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.6315 -0.8353 0.0726 0.9848 3.2553
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.02064 0.03831 131.059 < 2e-16 ***
## Risk_dummy 0.23374 0.08036 2.909 0.00369 **
## Help_dummy 0.02988 0.07813 0.382 0.70221
## scale(as.numeric(Credibility)) 0.41192 0.04093 10.064 < 2e-16 ***
## Risk_dummy:Help_dummy -0.14148 0.15327 -0.923 0.35613
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.413 on 1355 degrees of freedom
## Multiple R-squared: 0.0975, Adjusted R-squared: 0.09484
## F-statistic: 36.6 on 4 and 1355 DF, p-value: < 2.2e-16the more credible, the more effective the boredom condition. Same conclusions for the Help condition, but it is smaller.
Details for Job Decomposition (H1)
NURSES
IN THE NURSE CONDITION:
- The effect of Risk dummy is statistically non-significant (beta = 0.20, 95% CI [-0.15, 0.54], t(267) = 1.12, p = 0.264; Std. beta = 0.07, 95% CI [-0.05, 0.19])
- The effect of Help dummy is statistically non-significant (beta = 0.05, 95% CI [-0.30, 0.39], t(267) = 0.27, p = 0.789; Std. beta = 0.02, 95% CI [-0.10, 0.14])
- The effect of Risk dummy × Help dummy is statistically non-significant (beta = -0.51, 95% CI [-1.20, 0.18], t(267) = -1.46, p = 0.146; Std. beta = -0.09, 95% CI [-0.21, 0.03])
==> our manipulations (both physical risks and motivation type) did not work in the Nurses condition
For Nurses, the effects sizes are:
## [1] "Nurses: Cohen's d for the effect of risk is:"## Cohen's d | 95% CI
## -------------------------
## 0.14 | [-0.10, 0.37]
##
## - Estimated using pooled SD.## [1] "Nurses: Cohen's d for the effect of Motivation is:"## Cohen's d | 95% CI
## -------------------------
## 0.03 | [-0.20, 0.27]
##
## - Estimated using pooled SD.POLICE OFFICERS
IN THE POLICE CONDITION:
- The effect of Risk dummy is statistically non-significant (beta = 0.24, 95% CI [-0.08, 0.56], t(268) = 1.49, p = 0.137; Std. beta = 0.09, 95% CI [-0.03, 0.21])
- The effect of Help dummy is statistically non-significant (beta = 0.12, 95% CI [-0.19, 0.44], t(268) = 0.77, p = 0.442; Std. beta = 0.05, 95% CI [-0.07, 0.17])
- The effect of Risk dummy × Help dummy is statistically non-significant (beta = 0.01, 95% CI [-0.63, 0.65], t(268) = 0.03, p = 0.973; Std. beta = 2.07e-03, 95% CI [-0.12, 0.12])
==> our manipulations (both physical risks and motivation type) did not work in the Police Officers condition
For Police officers, the effects sizes are:
## [1] "Police: Cohen's d for the effect of risk is:"## Cohen's d | 95% CI
## -------------------------
## 0.18 | [-0.06, 0.42]
##
## - Estimated using pooled SD.## [1] "Police: Cohen's d for the effect of Motivation is:"## Cohen's d | 95% CI
## -------------------------
## 0.09 | [-0.14, 0.33]
##
## - Estimated using pooled SD.FIREFIGHTERS
IN THE FIREFIGHTER CONDITION:
- The effect of Risk dummy is statistically significant and positive (beta = 0.29, 95% CI [0.01, 0.56], t(269) = 2.04, p = 0.042; Std. beta = 0.12, 95% CI [4.40e-03, 0.24])
- The effect of Help dummy is statistically non-significant (beta = 5.86e-03, 95% CI [-0.27, 0.28], t(269) = 0.04, p = 0.967; Std. beta = 2.52e-03, 95% CI [-0.12, 0.12])
- The effect of Risk dummy × Help dummy is statistically non-significant (beta = 0.02, 95% CI [-0.53, 0.57], t(269) = 0.06, p = 0.950; Std. beta = 3.84e-03, 95% CI [-0.12, 0.12])
==> The manipulation of Risk kinda worked, but not the manipulation of Motivation in the firefighters condition.
For Firefighters, the effects sizes are:
## [1] "Fire: Cohen's d for the effect of risk is:"## Cohen's d | 95% CI
## ------------------------
## 0.25 | [0.01, 0.49]
##
## - Estimated using pooled SD.## [1] "Fire: Cohen's d for the effect of Motivation is:"## Cohen's d | 95% CI
## -------------------------
## 5.93e-03 | [-0.23, 0.24]
##
## - Estimated using pooled SD.PSYCHIATRISTS
IN THE Psychiatrists CONDITION:
- The effect of Risk dummy is statistically significant and positive (beta = 0.52, 95% CI [0.19, 0.86], t(266) = 3.05, p = 0.002; Std. beta = 0.18, 95% CI [0.06, 0.30])
- The effect of Help dummy is statistically significant and positive (beta = 0.36, 95% CI [0.02, 0.70], t(266) = 2.11, p = 0.035; Std. beta = 0.13, 95% CI [7.95e-03, 0.24])
- The effect of Risk dummy × Help dummy is statistically non-significant (beta = -0.29, 95% CI [-0.97, 0.38], t(266) = -0.86, p = 0.392; Std. beta = -0.05, 95% CI [-0.17, 0.07])
==> The manipulations of Risk and Motivation worked, in the Psychiatrists condition. For Psychiatrists, the effects sizes are:
## [1] "PSYCH: Cohen's d for the effect of risk is:"## Cohen's d | 95% CI
## ------------------------
## 0.37 | [0.13, 0.61]
##
## - Estimated using pooled SD.## [1] "PSYCH: Cohen's d for the effect of Motivation is:"## Cohen's d | 95% CI
## ------------------------
## 0.25 | [0.01, 0.49]
##
## - Estimated using pooled SD.WELDERS
## We fitted a linear model (estimated using OLS) to predict Heroism with
## Risk_dummy and Help_dummy (formula: Heroism ~ Risk_dummy * Help_dummy). The
## model explains a statistically significant and moderate proportion of variance
## (R2 = 0.19, F(3, 270) = 20.65, p < .001, adj. R2 = 0.18). The model's
## intercept, corresponding to Risk_dummy = 0 and Help_dummy = 0, is at 4.68 (95%
## CI [4.53, 4.84], t(270) = 59.29, p < .001). Within this model:
##
## - The effect of Risk dummy is statistically significant and positive (beta =
## 1.18, 95% CI [0.87, 1.49], t(270) = 7.46, p < .001; Std. beta = 0.41, 95% CI
## [0.30, 0.52])
## - The effect of Help dummy is statistically significant and positive (beta =
## 0.40, 95% CI [0.08, 0.71], t(270) = 2.50, p = 0.013; Std. beta = 0.14, 95% CI
## [0.03, 0.25])
## - The effect of Risk dummy × Help dummy is statistically non-significant and
## positive (beta = 0.18, 95% CI [-0.44, 0.80], t(270) = 0.57, p = 0.568; Std.
## beta = 0.03, 95% CI [-0.08, 0.14])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.IN THE WELDERS CONDITION:
- The effect of Risk dummy is statistically significant and
positive (beta = 1.18, 95% CI [0.87, 1.49], t(270) = 7.46, p
< .001; Std. beta = 0.41, 95% CI [0.30, 0.52])
- The effect of Help dummy is statistically significant and positive (beta = 0.40, 95% CI [0.08, 0.71], t(270) = 2.50, p = 0.013; Std. beta = 0.14, 95% CI [0.03, 0.25])
- The effect of Risk dummy × Help dummy is statistically non-significant and positive (beta = 0.18, 95% CI [-0.44, 0.80], t(270) = 0.57, p = 0.568; Std. beta = 0.03, 95% CI [-0.08, 0.14])
==> The manipulations of Risk and Motivation worked, in the Underwater Welders condition. For welders, the effects sizes are:
## [1] "WELDERS: Cohen's d for the effect of risk is:"## Cohen's d | 95% CI
## ------------------------
## 0.89 | [0.64, 1.14]
##
## - Estimated using pooled SD.## [1] "WELDERS: Cohen's d for the effect of Motivation is:"## Cohen's d | 95% CI
## ------------------------
## 0.27 | [0.03, 0.51]
##
## - Estimated using pooled SD.Additional robustness checks
Robust models
Robust models are less sensitive to deviations from assumptions (linearity, normality, homoscedasticity) and account for outliers by weighting residuals based on their distance to the bulk of the data. To re-weight residuals, we use a Huber-function that iteratively re-weight residuals until convergence – the aim if an efficient analysis coupled with a more robust breakdown point.
##
## Call:
## lmrob(formula = Set$Heroism ~ Set$Risk_dummy * Set$Help_dummy)
## \--> method = "MM"
## Residuals:
## Min 1Q Median 3Q Max
## -4.40872 -0.96122 0.03878 1.03878 2.25711
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.10065 0.04178 122.071 < 2e-16 ***
## Set$Risk_dummy 0.49720 0.08155 6.097 1.41e-09 ***
## Set$Help_dummy 0.16863 0.08137 2.072 0.0384 *
## Set$Risk_dummy:Set$Help_dummy -0.09939 0.16268 -0.611 0.5413
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Robust residual standard error: 1.462
## Multiple R-squared: 0.03149, Adjusted R-squared: 0.02935
## Convergence in 10 IRWLS iterations
##
## Robustness weights:
## 93 weights are ~= 1. The remaining 1267 ones are summarized as
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3432 0.8792 0.9545 0.9088 0.9852 0.9972
## Algorithmic parameters:
## tuning.chi bb tuning.psi refine.tol
## 1.548e+00 5.000e-01 4.685e+00 1.000e-07
## rel.tol scale.tol solve.tol zero.tol
## 1.000e-07 1.000e-10 1.000e-07 1.000e-10
## eps.outlier eps.x warn.limit.reject warn.limit.meanrw
## 7.353e-05 1.819e-12 5.000e-01 5.000e-01
## nResample max.it best.r.s k.fast.s k.max
## 500 50 2 1 200
## maxit.scale trace.lev mts compute.rd fast.s.large.n
## 200 0 1000 0 2000
## psi subsampling cov
## "bisquare" "nonsingular" ".vcov.avar1"
## compute.outlier.stats
## "SM"
## seed : int(0)##
## Call:
## lmrob(formula = Heroism ~ Selfless_scale * Brave_scale, data = Set)
## \--> method = "MM"
## Residuals:
## Min 1Q Median 3Q Max
## -5.5042 -0.5042 0.1853 0.5754 4.6326
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.97647 0.05490 90.653 < 2e-16 ***
## Selfless_scale 0.72545 0.06639 10.927 < 2e-16 ***
## Brave_scale 0.52584 0.06403 8.212 5.03e-16 ***
## Selfless_scale:Brave_scale 0.20698 0.09187 2.253 0.0244 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Robust residual standard error: 0.8809
## Multiple R-squared: 0.5328, Adjusted R-squared: 0.5318
## Convergence in 41 IRWLS iterations
##
## Robustness weights:
## 8 observations c(289,471,487,512,626,798,1095,1150)
## are outliers with |weight| = 0 ( < 7.4e-05);
## 57 weights are ~= 1. The remaining 1295 ones are summarized as
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.01441 0.84180 0.96150 0.87600 0.97890 0.99890
## Algorithmic parameters:
## tuning.chi bb tuning.psi refine.tol
## 1.548e+00 5.000e-01 4.685e+00 1.000e-07
## rel.tol scale.tol solve.tol zero.tol
## 1.000e-07 1.000e-10 1.000e-07 1.000e-10
## eps.outlier eps.x warn.limit.reject warn.limit.meanrw
## 7.353e-05 2.302e-11 5.000e-01 5.000e-01
## nResample max.it best.r.s k.fast.s k.max
## 500 50 2 1 200
## maxit.scale trace.lev mts compute.rd fast.s.large.n
## 200 0 1000 0 2000
## psi subsampling cov
## "bisquare" "nonsingular" ".vcov.avar1"
## compute.outlier.stats
## "SM"
## seed : int(0)##
## Call:
## lmrob(formula = Heroism ~ Danger_scale * Helpfulness_scale, data = Set)
## \--> method = "MM"
## Residuals:
## Min 1Q Median 3Q Max
## -5.35359 -0.61788 0.01426 0.64641 3.96659
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.10176 0.03226 158.125 < 2e-16 ***
## Danger_scale 0.39099 0.04168 9.380 < 2e-16 ***
## Helpfulness_scale 0.83700 0.03579 23.385 < 2e-16 ***
## Danger_scale:Helpfulness_scale 0.10235 0.02523 4.056 5.27e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Robust residual standard error: 0.9275
## Multiple R-squared: 0.5241, Adjusted R-squared: 0.523
## Convergence in 11 IRWLS iterations
##
## Robustness weights:
## 14 observations c(128,306,363,379,471,626,689,798,936,1036,1150,1230,1305,1309)
## are outliers with |weight| = 0 ( < 7.4e-05);
## 113 weights are ~= 1. The remaining 1233 ones are summarized as
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.02519 0.84750 0.95620 0.88450 0.97740 0.99800
## Algorithmic parameters:
## tuning.chi bb tuning.psi refine.tol
## 1.548e+00 5.000e-01 4.685e+00 1.000e-07
## rel.tol scale.tol solve.tol zero.tol
## 1.000e-07 1.000e-10 1.000e-07 1.000e-10
## eps.outlier eps.x warn.limit.reject warn.limit.meanrw
## 7.353e-05 2.841e-11 5.000e-01 5.000e-01
## nResample max.it best.r.s k.fast.s k.max
## 500 50 2 1 200
## maxit.scale trace.lev mts compute.rd fast.s.large.n
## 200 0 1000 0 2000
## psi subsampling cov
## "bisquare" "nonsingular" ".vcov.avar1"
## compute.outlier.stats
## "SM"
## seed : int(0)##
## Call:
## lmrob(formula = Psych$Heroism ~ Psych$Risk_dummy * Psych$Help_dummy)
## \--> method = "MM"
## Residuals:
## Min 1Q Median 3Q Max
## -3.90584 -0.90584 0.09416 0.97848 2.97848
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.5334 0.0884 51.284 < 2e-16 ***
## Psych$Risk_dummy 0.5094 0.1736 2.934 0.00364 **
## Psych$Help_dummy 0.3749 0.1734 2.163 0.03144 *
## Psych$Risk_dummy:Psych$Help_dummy -0.2787 0.3473 -0.803 0.42292
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Robust residual standard error: 1.311
## Multiple R-squared: 0.0522, Adjusted R-squared: 0.04151
## Convergence in 9 IRWLS iterations
##
## Robustness weights:
## 40 weights are ~= 1. The remaining 230 ones are summarized as
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3550 0.8168 0.9477 0.8882 0.9848 0.9942
## Algorithmic parameters:
## tuning.chi bb tuning.psi refine.tol
## 1.548e+00 5.000e-01 4.685e+00 1.000e-07
## rel.tol scale.tol solve.tol zero.tol
## 1.000e-07 1.000e-10 1.000e-07 1.000e-10
## eps.outlier eps.x warn.limit.reject warn.limit.meanrw
## 3.704e-04 1.819e-12 5.000e-01 5.000e-01
## nResample max.it best.r.s k.fast.s k.max
## 500 50 2 1 200
## maxit.scale trace.lev mts compute.rd fast.s.large.n
## 200 0 1000 0 2000
## psi subsampling cov
## "bisquare" "nonsingular" ".vcov.avar1"
## compute.outlier.stats
## "SM"
## seed : int(0)##
## Call:
## lmrob(formula = Heroism ~ Selfless_scale * Brave_scale, data = Psych)
## \--> method = "MM"
## Residuals:
## Min 1Q Median 3Q Max
## -3.4974 -0.7255 0.2356 0.5895 5.0017
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.83271 0.08928 54.128 < 2e-16 ***
## Selfless_scale 0.69814 0.12356 5.650 4.12e-08 ***
## Brave_scale 0.57529 0.10354 5.556 6.69e-08 ***
## Selfless_scale:Brave_scale 0.32230 0.14320 2.251 0.0252 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Robust residual standard error: 0.8669
## Multiple R-squared: 0.4666, Adjusted R-squared: 0.4606
## Convergence in 30 IRWLS iterations
##
## Robustness weights:
## 2 observations c(59,217) are outliers with |weight| = 0 ( < 0.00037);
## 13 weights are ~= 1. The remaining 255 ones are summarized as
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0008491 0.8256000 0.9393000 0.8608000 0.9900000 0.9984000
## Algorithmic parameters:
## tuning.chi bb tuning.psi refine.tol
## 1.548e+00 5.000e-01 4.685e+00 1.000e-07
## rel.tol scale.tol solve.tol zero.tol
## 1.000e-07 1.000e-10 1.000e-07 1.000e-10
## eps.outlier eps.x warn.limit.reject warn.limit.meanrw
## 3.704e-04 2.302e-11 5.000e-01 5.000e-01
## nResample max.it best.r.s k.fast.s k.max
## 500 50 2 1 200
## maxit.scale trace.lev mts compute.rd fast.s.large.n
## 200 0 1000 0 2000
## psi subsampling cov
## "bisquare" "nonsingular" ".vcov.avar1"
## compute.outlier.stats
## "SM"
## seed : int(0)##
## Call:
## lmrob(formula = Heroism ~ Danger_scale * Helpfulness_scale, data = Psych)
## \--> method = "MM"
## Residuals:
## Min 1Q Median 3Q Max
## -4.6713 -0.7236 0.1489 0.6068 2.5455
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.64138 0.07844 59.168 <2e-16 ***
## Danger_scale 0.21585 0.08465 2.550 0.0113 *
## Helpfulness_scale 0.82881 0.08958 9.253 <2e-16 ***
## Danger_scale:Helpfulness_scale 0.05611 0.04256 1.318 0.1885
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Robust residual standard error: 1.088
## Multiple R-squared: 0.3782, Adjusted R-squared: 0.3712
## Convergence in 10 IRWLS iterations
##
## Robustness weights:
## 18 weights are ~= 1. The remaining 252 ones are summarized as
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.02566 0.86870 0.96010 0.89720 0.98510 0.99880
## Algorithmic parameters:
## tuning.chi bb tuning.psi refine.tol
## 1.548e+00 5.000e-01 4.685e+00 1.000e-07
## rel.tol scale.tol solve.tol zero.tol
## 1.000e-07 1.000e-10 1.000e-07 1.000e-10
## eps.outlier eps.x warn.limit.reject warn.limit.meanrw
## 3.704e-04 2.841e-11 5.000e-01 5.000e-01
## nResample max.it best.r.s k.fast.s k.max
## 500 50 2 1 200
## maxit.scale trace.lev mts compute.rd fast.s.large.n
## 200 0 1000 0 2000
## psi subsampling cov
## "bisquare" "nonsingular" ".vcov.avar1"
## compute.outlier.stats
## "SM"
## seed : int(0)##
## Call:
## lmrob(formula = Weld$Heroism ~ Weld$Risk_dummy * Weld$Help_dummy)
## \--> method = "MM"
## Residuals:
## Min 1Q Median 3Q Max
## -4.13058 -0.91152 -0.01771 0.86942 2.98229
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.74029 0.07967 59.500 < 2e-16 ***
## Weld$Risk_dummy 1.24293 0.15786 7.874 8.41e-14 ***
## Weld$Help_dummy 0.33229 0.15982 2.079 0.0386 *
## Weld$Risk_dummy:Weld$Help_dummy 0.26014 0.31956 0.814 0.4163
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Robust residual standard error: 1.232
## Multiple R-squared: 0.2081, Adjusted R-squared: 0.1993
## Convergence in 10 IRWLS iterations
##
## Robustness weights:
## 27 weights are ~= 1. The remaining 247 ones are summarized as
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.2384 0.8536 0.9430 0.8970 0.9846 0.9990
## Algorithmic parameters:
## tuning.chi bb tuning.psi refine.tol
## 1.548e+00 5.000e-01 4.685e+00 1.000e-07
## rel.tol scale.tol solve.tol zero.tol
## 1.000e-07 1.000e-10 1.000e-07 1.000e-10
## eps.outlier eps.x warn.limit.reject warn.limit.meanrw
## 3.650e-04 1.819e-12 5.000e-01 5.000e-01
## nResample max.it best.r.s k.fast.s k.max
## 500 50 2 1 200
## maxit.scale trace.lev mts compute.rd fast.s.large.n
## 200 0 1000 0 2000
## psi subsampling cov
## "bisquare" "nonsingular" ".vcov.avar1"
## compute.outlier.stats
## "SM"
## seed : int(0)##
## Call:
## lmrob(formula = Heroism ~ Selfless_scale * Brave_scale, data = Weld)
## \--> method = "MM"
## Residuals:
## Min 1Q Median 3Q Max
## -5.0740 -0.8428 0.1035 0.7110 5.4670
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.50143 0.08279 54.375 < 2e-16 ***
## Selfless_scale 0.71285 0.11941 5.970 7.45e-09 ***
## Brave_scale 0.46554 0.12411 3.751 0.000216 ***
## Selfless_scale:Brave_scale 0.31653 0.05177 6.115 3.38e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Robust residual standard error: 1.071
## Multiple R-squared: 0.4064, Adjusted R-squared: 0.3998
## Convergence in 13 IRWLS iterations
##
## Robustness weights:
## 2 observations c(92,97) are outliers with |weight| = 0 ( < 0.00036);
## 25 weights are ~= 1. The remaining 247 ones are summarized as
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1438 0.8669 0.9420 0.8990 0.9893 0.9985
## Algorithmic parameters:
## tuning.chi bb tuning.psi refine.tol
## 1.548e+00 5.000e-01 4.685e+00 1.000e-07
## rel.tol scale.tol solve.tol zero.tol
## 1.000e-07 1.000e-10 1.000e-07 1.000e-10
## eps.outlier eps.x warn.limit.reject warn.limit.meanrw
## 3.650e-04 2.302e-11 5.000e-01 5.000e-01
## nResample max.it best.r.s k.fast.s k.max
## 500 50 2 1 200
## maxit.scale trace.lev mts compute.rd fast.s.large.n
## 200 0 1000 0 2000
## psi subsampling cov
## "bisquare" "nonsingular" ".vcov.avar1"
## compute.outlier.stats
## "SM"
## seed : int(0)##
## Call:
## lmrob(formula = Heroism ~ Danger_scale * Helpfulness_scale, data = Weld)
## \--> method = "MM"
## Residuals:
## Min 1Q Median 3Q Max
## -5.0476 -0.7062 -0.0476 0.7441 3.2782
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.99155 0.08402 59.410 < 2e-16 ***
## Danger_scale 0.45602 0.09793 4.657 5.04e-06 ***
## Helpfulness_scale 0.60925 0.07965 7.649 3.59e-13 ***
## Danger_scale:Helpfulness_scale 0.04838 0.09267 0.522 0.602
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Robust residual standard error: 1.019
## Multiple R-squared: 0.4196, Adjusted R-squared: 0.4132
## Convergence in 14 IRWLS iterations
##
## Robustness weights:
## 2 observations c(26,92) are outliers with |weight| = 0 ( < 0.00036);
## 24 weights are ~= 1. The remaining 248 ones are summarized as
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.07906 0.87780 0.93280 0.88790 0.98100 0.99880
## Algorithmic parameters:
## tuning.chi bb tuning.psi refine.tol
## 1.548e+00 5.000e-01 4.685e+00 1.000e-07
## rel.tol scale.tol solve.tol zero.tol
## 1.000e-07 1.000e-10 1.000e-07 1.000e-10
## eps.outlier eps.x warn.limit.reject warn.limit.meanrw
## 3.650e-04 1.334e-11 5.000e-01 5.000e-01
## nResample max.it best.r.s k.fast.s k.max
## 500 50 2 1 200
## maxit.scale trace.lev mts compute.rd fast.s.large.n
## 200 0 1000 0 2000
## psi subsampling cov
## "bisquare" "nonsingular" ".vcov.avar1"
## compute.outlier.stats
## "SM"
## seed : int(0)CLM models
Cumulative Link models model the association between DV and IV at each level of the Ordinal DV. They are designed to account for non-numeric DV – in our case, an ordinal variable (Likert item).
## formula: ordered(Heroism) ~ Risk_dummy * Help_dummy
## data: Set
##
## link threshold nobs logLik AIC niter max.grad cond.H
## logit flexible 1360 -2328.78 4675.56 5(0) 5.44e-08 3.8e+01
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## Risk_dummy 0.59565 0.09725 6.125 9.07e-10 ***
## Help_dummy 0.20359 0.09628 2.115 0.0345 *
## Risk_dummy:Help_dummy -0.10979 0.19233 -0.571 0.5681
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Threshold coefficients:
## Estimate Std. Error z value
## 1|2 -3.83582 0.18501 -20.733
## 2|3 -2.66230 0.10855 -24.527
## 3|4 -1.84560 0.07873 -23.444
## 4|5 -0.71009 0.05811 -12.220
## 5|6 0.42414 0.05592 7.584
## 6|7 1.50898 0.07038 21.441## formula: ordered(Heroism) ~ Brave_scale * Selfless_scale
## data: Set
##
## link threshold nobs logLik AIC niter max.grad cond.H
## logit flexible 1360 -1939.75 3897.50 6(0) 3.94e-11 5.4e+01
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## Brave_scale 0.98821 0.07960 12.41 <2e-16 ***
## Selfless_scale 1.12946 0.07918 14.26 <2e-16 ***
## Brave_scale:Selfless_scale 0.45021 0.04471 10.07 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Threshold coefficients:
## Estimate Std. Error z value
## 1|2 -4.56671 0.19789 -23.08
## 2|3 -3.30968 0.12539 -26.39
## 3|4 -2.37036 0.09618 -24.64
## 4|5 -0.87703 0.07253 -12.09
## 5|6 0.88164 0.07410 11.90
## 6|7 2.55186 0.10281 24.82## formula: ordered(Heroism) ~ Danger_scale * Helpfulness_scale
## data: Set
##
## link threshold nobs logLik AIC niter max.grad cond.H
## logit flexible 1360 -1974.77 3967.55 6(0) 1.56e-11 5.8e+01
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## Danger_scale 0.64401 0.05983 10.764 < 2e-16 ***
## Helpfulness_scale 1.27886 0.06532 19.580 < 2e-16 ***
## Danger_scale:Helpfulness_scale 0.18919 0.04359 4.341 1.42e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Threshold coefficients:
## Estimate Std. Error z value
## 1|2 -5.00003 0.21767 -22.97
## 2|3 -3.60312 0.13650 -26.40
## 3|4 -2.55879 0.10059 -25.44
## 4|5 -0.98444 0.07063 -13.94
## 5|6 0.67737 0.06771 10.01
## 6|7 2.16274 0.08871 24.38## formula: ordered(Heroism) ~ Risk_dummy * Help_dummy
## data: Psych
##
## link threshold nobs logLik AIC niter max.grad cond.H
## logit flexible 270 -459.18 936.37 5(0) 5.42e-07 3.0e+01
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## Risk_dummy 0.6572 0.2204 2.982 0.00286 **
## Help_dummy 0.4650 0.2188 2.126 0.03354 *
## Risk_dummy:Help_dummy -0.3336 0.4355 -0.766 0.44370
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Threshold coefficients:
## Estimate Std. Error z value
## 1|2 -3.33007 0.32433 -10.268
## 2|3 -2.25915 0.20560 -10.988
## 3|4 -1.44064 0.15518 -9.284
## 4|5 -0.03374 0.12383 -0.272
## 5|6 1.26357 0.14750 8.566
## 6|7 2.48835 0.22454 11.082## formula: ordered(Heroism) ~ Risk_dummy * Help_dummy
## data: Weld
##
## link threshold nobs logLik AIC niter max.grad cond.H
## logit flexible 274 -444.69 907.38 6(0) 1.58e-14 2.7e+01
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## Risk_dummy 1.6868 0.2377 7.096 1.28e-12 ***
## Help_dummy 0.4837 0.2177 2.222 0.0263 *
## Risk_dummy:Help_dummy 0.3995 0.4337 0.921 0.3570
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Threshold coefficients:
## Estimate Std. Error z value
## 1|2 -4.1270 0.4186 -9.859
## 2|3 -2.7397 0.2320 -11.808
## 3|4 -1.7832 0.1693 -10.530
## 4|5 -0.3359 0.1316 -2.552
## 5|6 1.1065 0.1468 7.536
## 6|7 2.2814 0.1991 11.458Additional Covariant analyses
Attitude
To account for a possible Halo effect, it is important to use Attitude as a covariant.
##
## Call:
## lm(formula = Heroism ~ Risk_dummy * Help_dummy + Attitude_scale,
## data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.1585 -0.4928 -0.0421 0.8415 3.6071
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.020511 0.029503 170.171 < 2e-16 ***
## Risk_dummy 0.276350 0.059317 4.659 3.49e-06 ***
## Help_dummy -0.008258 0.059290 -0.139 0.889
## Attitude_scale 0.989244 0.029823 33.171 < 2e-16 ***
## Risk_dummy:Help_dummy 0.012139 0.118064 0.103 0.918
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.088 on 1355 degrees of freedom
## Multiple R-squared: 0.4647, Adjusted R-squared: 0.4631
## F-statistic: 294.1 on 4 and 1355 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ Brave_scale * Selfless_scale + Attitude_scale,
## data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.4204 -0.4442 0.1491 0.5796 2.8274
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.91561 0.03090 159.075 < 2e-16 ***
## Brave_scale 0.34209 0.04221 8.104 1.18e-15 ***
## Selfless_scale 0.29629 0.04015 7.379 2.76e-13 ***
## Attitude_scale 0.67719 0.03679 18.408 < 2e-16 ***
## Brave_scale:Selfless_scale 0.15862 0.02058 7.708 2.46e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.021 on 1355 degrees of freedom
## Multiple R-squared: 0.5284, Adjusted R-squared: 0.527
## F-statistic: 379.6 on 4 and 1355 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ Danger_scale * Helpfulness_scale + Attitude_scale,
## data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.3125 -0.4388 0.1466 0.6875 2.9213
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.98466 0.03007 165.753 < 2e-16 ***
## Danger_scale 0.22601 0.03256 6.941 6.03e-12 ***
## Helpfulness_scale 0.34542 0.03916 8.820 < 2e-16 ***
## Attitude_scale 0.70355 0.03910 17.993 < 2e-16 ***
## Danger_scale:Helpfulness_scale 0.08330 0.02389 3.487 0.000505 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.039 on 1355 degrees of freedom
## Multiple R-squared: 0.5118, Adjusted R-squared: 0.5104
## F-statistic: 355.1 on 4 and 1355 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ Risk_dummy * Help_dummy + Attitude_scale,
## data = Psych)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.0586 -0.6244 0.1249 0.7649 3.0070
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.70130 0.07066 66.531 <2e-16 ***
## Risk_dummy 0.33675 0.13712 2.456 0.0147 *
## Help_dummy 0.09748 0.13795 0.707 0.4804
## Attitude_scale 0.89116 0.07187 12.399 <2e-16 ***
## Risk_dummy:Help_dummy -0.04083 0.27335 -0.149 0.8814
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.12 on 265 degrees of freedom
## Multiple R-squared: 0.3996, Adjusted R-squared: 0.3905
## F-statistic: 44.09 on 4 and 265 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ Risk_dummy * Help_dummy + Attitude_scale,
## data = Weld)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.6889 -0.5874 0.2206 0.8196 2.7121
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.65480 0.06998 66.513 < 2e-16 ***
## Risk_dummy 0.70622 0.14997 4.709 3.99e-06 ***
## Help_dummy 0.19772 0.14166 1.396 0.164
## Attitude_scale 0.83309 0.09578 8.698 3.43e-16 ***
## Risk_dummy:Help_dummy 0.24516 0.27974 0.876 0.382
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.157 on 269 degrees of freedom
## Multiple R-squared: 0.3651, Adjusted R-squared: 0.3557
## F-statistic: 38.68 on 4 and 269 DF, p-value: < 2.2e-16The motivation manipulation is nullified when accounting for attitude – the effect of motivation might first and foremost influence attitude, and without this part of the variance, the effect on heroism is non existent.
If we designed a Motivation manipulation that did not influence attitude, we might not find the effects…
Credibility
Maybe our effects are conditionned by the credibility of our manipulation. We can model our effects using credibility as a covariant
##
## Call:
## lm(formula = Heroism ~ Risk_dummy * Help_dummy + scale(Credibility),
## data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.6315 -0.8353 0.0726 0.9848 3.2553
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.02064 0.03831 131.059 < 2e-16 ***
## Risk_dummy 0.23374 0.08036 2.909 0.00369 **
## Help_dummy 0.02988 0.07813 0.382 0.70221
## scale(Credibility) 0.41192 0.04093 10.064 < 2e-16 ***
## Risk_dummy:Help_dummy -0.14148 0.15327 -0.923 0.35613
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.413 on 1355 degrees of freedom
## Multiple R-squared: 0.0975, Adjusted R-squared: 0.09484
## F-statistic: 36.6 on 4 and 1355 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ Brave_scale * Selfless_scale + scale(Credibility),
## data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.3242 -0.4410 0.1551 0.6758 4.0543
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.89365 0.03419 143.117 < 2e-16 ***
## Brave_scale 0.54646 0.04495 12.158 < 2e-16 ***
## Selfless_scale 0.54633 0.04150 13.165 < 2e-16 ***
## scale(Credibility) 0.17203 0.03224 5.335 1.12e-07 ***
## Brave_scale:Selfless_scale 0.19157 0.02277 8.412 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.13 on 1355 degrees of freedom
## Multiple R-squared: 0.4226, Adjusted R-squared: 0.4209
## F-statistic: 248 on 4 and 1355 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ Danger_scale * Helpfulness_scale + scale(Credibility),
## data = Set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.1271 -0.5484 0.1199 0.7531 3.5143
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.00642 0.03290 152.172 < 2e-16 ***
## Danger_scale 0.30532 0.03553 8.592 < 2e-16 ***
## Helpfulness_scale 0.71268 0.03573 19.946 < 2e-16 ***
## scale(Credibility) 0.22028 0.03225 6.830 1.28e-11 ***
## Danger_scale:Helpfulness_scale 0.03386 0.02607 1.299 0.194
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.137 on 1355 degrees of freedom
## Multiple R-squared: 0.4153, Adjusted R-squared: 0.4136
## F-statistic: 240.6 on 4 and 1355 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Heroism ~ Risk_dummy * Help_dummy + scale(Credibility),
## data = Psych)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1603 -0.6325 0.1036 0.9199 2.8335
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.4714 0.0825 54.199 < 2e-16 ***
## Risk_dummy 0.2938 0.1724 1.704 0.0896 .
## Help_dummy 0.1723 0.1701 1.012 0.3123
## scale(Credibility) 0.4045 0.0888 4.555 7.99e-06 ***
## Risk_dummy:Help_dummy -0.2952 0.3300 -0.895 0.3718
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.355 on 265 degrees of freedom
## Multiple R-squared: 0.1202, Adjusted R-squared: 0.1069
## F-statistic: 9.049 on 4 and 265 DF, p-value: 7.262e-07##
## Call:
## lm(formula = Heroism ~ Risk_dummy * Help_dummy + scale(Credibility),
## data = Weld)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1640 -0.5734 0.0314 0.9641 2.7653
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.68262 0.07599 61.618 < 2e-16 ***
## Risk_dummy 0.96808 0.15826 6.117 3.35e-09 ***
## Help_dummy 0.37062 0.15208 2.437 0.0155 *
## scale(Credibility) 0.37849 0.07949 4.761 3.15e-06 ***
## Risk_dummy:Help_dummy 0.07762 0.30474 0.255 0.7991
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.258 on 269 degrees of freedom
## Multiple R-squared: 0.2498, Adjusted R-squared: 0.2387
## F-statistic: 22.4 on 4 and 269 DF, p-value: 5.608e-16The motivation manipulation is nullified when accounting for credibility – the effect of motivation might first and foremost influence credibility, and without this part of the variance, the effect on heroism is non existent.
If we designed a Motivation manipulation that did not influence credibility, we might not find the effects…
Mediation analyses
We just observed that using credibility or attitude as covariant in the models inferring the effects of our manipulations, resulted in null effects of Motivation manipulation.
Given that our Motivation -> Heroism effect is causal, this does not mean that there is a confounder effect with attitude (i.e, it’s not a halo effect) – rather it means that our effect of motivation might be mediated by attitude or credibility.
With all the caution we need to exercise about this approach (see Julia Rohrer’s multiple rants) - we can evaluate mediation in our models. I use a SEM approach here.
# 1. Specify the mediation model in lavaan syntax
med.model <- '
# a path
Attitude ~ a*Help_dummy
# b and c paths
Heroism ~ b*Attitude + cp*Help_dummy
# indirect and total effects
indirect := a*b
total := cp + (a*b)
'
# 2. Fit the model
fit <- sem(med.model, data = Set, se = "bootstrap", bootstrap = 1000)
# 3. Inspect results
summary(fit, standardized = TRUE, fit.measures = TRUE,
ci = TRUE, rsquare = TRUE)## lavaan 0.6-19 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 5
##
## Number of observations 1360
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 841.183
## Degrees of freedom 3
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4211.338
## Loglikelihood unrestricted model (H1) -4211.338
##
## Akaike (AIC) 8432.675
## Bayesian (BIC) 8458.751
## Sample-size adjusted Bayesian (SABIC) 8442.868
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Bootstrap
## Number of requested bootstrap draws 1000
## Number of successful bootstrap draws 957
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## Attitude ~
## Help_dmmy (a) 0.231 0.066 3.524 0.000 0.100 0.353
## Heroism ~
## Attitude (b) 0.844 0.024 35.378 0.000 0.797 0.889
## Help_dmmy (cp) -0.011 0.059 -0.187 0.852 -0.125 0.109
## Std.lv Std.all
##
## 0.231 0.097
##
## 0.844 0.676
## -0.011 -0.004
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .Attitude 1.400 0.065 21.503 0.000 1.277 1.534
## .Heroism 1.198 0.065 18.512 0.000 1.077 1.322
## Std.lv Std.all
## 1.400 0.991
## 1.198 0.544
##
## R-Square:
## Estimate
## Attitude 0.009
## Heroism 0.456
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## indirect 0.195 0.056 3.506 0.000 0.084 0.298
## total 0.184 0.080 2.311 0.021 0.032 0.351
## Std.lv Std.all
## 0.195 0.066
## 0.184 0.062In a bootstrapped SEM (1 000 draws), Motivation_dummy significantly predicted Attitude, b = 0.231, SE = 0.065, z = 3.56, p < .001, and Attitude predicted Heroism, b = 0.844, SE = 0.025, z = 34.04, p < .001. The direct effect of Motivation_dummy on Heroism was not significant, b = –0.011, SE = 0.061, p = .86. The indirect effect (a × b) was 0.195, 95% CI [0.091, 0.310], p < .001, indicating full mediation. R² for Heroism was 0.456.
# 1. Specify the mediation model in lavaan syntax
med.model <- '
# a path
Credibility ~ a*Help_dummy
# b and c paths
Heroism ~ b*Credibility + cp*Help_dummy
# indirect and total effects
indirect := a*b
total := cp + (a*b)
'
# 2. Fit the model
fit <- sem(med.model, data = Set, se = "bootstrap", bootstrap = 1000)
# 3. Inspect results
summary(fit, standardized = TRUE, fit.measures = TRUE,
ci = TRUE, rsquare = TRUE)## lavaan 0.6-19 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 5
##
## Number of observations 1360
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 178.808
## Degrees of freedom 3
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4878.571
## Loglikelihood unrestricted model (H1) -4878.571
##
## Akaike (AIC) 9767.142
## Bayesian (BIC) 9793.218
## Sample-size adjusted Bayesian (SABIC) 9777.335
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Bootstrap
## Number of requested bootstrap draws 1000
## Number of successful bootstrap draws 896
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## Credibility ~
## Help_dmmy (a) 0.571 0.082 6.936 0.000 0.409 0.724
## Heroism ~
## Crediblty (b) 0.294 0.028 10.608 0.000 0.239 0.346
## Help_dmmy (cp) 0.016 0.078 0.210 0.834 -0.135 0.173
## Std.lv Std.all
##
## 0.571 0.187
##
## 0.294 0.301
## 0.016 0.005
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .Credibility 2.235 0.078 28.802 0.000 2.072 2.395
## .Heroism 2.002 0.079 25.437 0.000 1.832 2.149
## Std.lv Std.all
## 2.235 0.965
## 2.002 0.909
##
## R-Square:
## Estimate
## Credibility 0.035
## Heroism 0.091
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## indirect 0.168 0.029 5.848 0.000 0.114 0.223
## total 0.184 0.080 2.300 0.021 0.037 0.356
## Std.lv Std.all
## 0.168 0.056
## 0.184 0.062In a bootstrapped SEM (1 000 draws), Motivation_dummy significantly predicted Credibility, b = 0.571, SE = 0.081, z = 7.068, p < .001, and Credibility predicted Heroism, b = 0.294, SE = 0.080, z = 27.802, p < .001. The direct effect of Motivation_dummy on Heroism was not significant, b = 0.016, SE = 0.078, p = 0.834. The indirect effect (a × b) was 0.168, 95% CI [0.021, 0.348], p < .001, indicating full mediation. R² for Heroism was 0.091.
# 1. Specify the mediation model in lavaan syntax
med.model <- '
# a path
Heroism ~ a*Help_dummy
# b and c paths
Attitude ~ b*Heroism + cp*Help_dummy
# indirect and total effects
indirect := a*b
total := cp + (a*b)
'
# 2. Fit the model
fit <- sem(med.model, data = Set, se = "bootstrap", bootstrap = 1000)
# 3. Inspect results
summary(fit, standardized = TRUE, fit.measures = TRUE,
ci = TRUE, rsquare = TRUE)## lavaan 0.6-19 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 5
##
## Number of observations 1360
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 841.183
## Degrees of freedom 3
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4211.338
## Loglikelihood unrestricted model (H1) -4211.338
##
## Akaike (AIC) 8432.675
## Bayesian (BIC) 8458.751
## Sample-size adjusted Bayesian (SABIC) 8442.868
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Bootstrap
## Number of requested bootstrap draws 1000
## Number of successful bootstrap draws 938
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## Heroism ~
## Help_dmmy (a) 0.184 0.080 2.306 0.021 0.033 0.351
## Attitude ~
## Heroism (b) 0.538 0.021 25.661 0.000 0.493 0.578
## Help_dmmy (cp) 0.132 0.047 2.778 0.005 0.034 0.221
## Std.lv Std.all
##
## 0.184 0.062
##
## 0.538 0.672
## 0.132 0.055
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .Heroism 2.195 0.079 27.686 0.000 2.033 2.341
## .Attitude 0.764 0.038 19.896 0.000 0.692 0.841
## Std.lv Std.all
## 2.195 0.996
## 0.764 0.541
##
## R-Square:
## Estimate
## Heroism 0.004
## Attitude 0.459
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## indirect 0.099 0.043 2.289 0.022 0.017 0.188
## total 0.231 0.065 3.558 0.000 0.098 0.352
## Std.lv Std.all
## 0.099 0.042
## 0.231 0.097library(lavaan)
med.model.cov <- '
# structural regressions
Attitude ~ a*Help + d*Credibility
Heroism ~ b*Attitude + cp*Help + e*Credibility
# indirect & total effects
indirect := a * b
total := cp + (a * b)
'
fit.cov <- sem(
med.model.cov,
data = Set,
se = "bootstrap",
bootstrap = 1000
)
summary(fit.cov, standardized=TRUE, fit.measures=TRUE, ci=TRUE)## lavaan 0.6-19 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 7
##
## Number of observations 1360
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 976.331
## Degrees of freedom 5
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4143.763
## Loglikelihood unrestricted model (H1) NA
##
## Akaike (AIC) 8301.527
## Bayesian (BIC) 8338.034
## Sample-size adjusted Bayesian (SABIC) 8315.797
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Bootstrap
## Number of requested bootstrap draws 1000
## Number of successful bootstrap draws 1000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## Attitude ~
## Help (a) -0.113 0.064 -1.780 0.075 -0.234 0.015
## Crediblty (d) 0.206 0.022 9.305 0.000 0.162 0.251
## Heroism ~
## Attitude (b) 0.801 0.026 31.364 0.000 0.751 0.848
## Help (cp) 0.074 0.059 1.266 0.206 -0.045 0.188
## Crediblty (e) 0.128 0.022 5.722 0.000 0.084 0.172
## Std.lv Std.all
##
## -0.113 -0.048
## 0.206 0.264
##
## 0.801 0.642
## 0.074 0.025
## 0.128 0.132
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .Attitude 1.305 0.062 21.124 0.000 1.188 1.425
## .Heroism 1.164 0.062 18.671 0.000 1.044 1.286
## Std.lv Std.all
## 1.305 0.923
## 1.164 0.528
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## indirect -0.091 0.051 -1.774 0.076 -0.189 0.011
## total -0.016 0.078 -0.210 0.834 -0.172 0.136
## Std.lv Std.all
## -0.091 -0.031
## -0.016 -0.005## [1] 8301.527## [1] 8338.034library(lavaan)
med.model.cov <- '
# structural regressions
Heroism ~ a*Help + d*Credibility
Attitude ~ b*Heroism + cp*Help + e*Credibility
# indirect & total effects
indirect := a * b
total := cp + (a * b)
'
fit.reverse.cov <- sem(
med.model.cov,
data = Set,
se = "bootstrap",
bootstrap = 1000
)
summary(fit.reverse.cov, standardized=TRUE, fit.measures=TRUE, ci=TRUE)## lavaan 0.6-19 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 7
##
## Number of observations 1360
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 976.331
## Degrees of freedom 5
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4143.763
## Loglikelihood unrestricted model (H1) NA
##
## Akaike (AIC) 8301.527
## Bayesian (BIC) 8338.034
## Sample-size adjusted Bayesian (SABIC) 8315.797
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Bootstrap
## Number of requested bootstrap draws 1000
## Number of successful bootstrap draws 1000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## Heroism ~
## Help (a) -0.016 0.078 -0.210 0.834 -0.172 0.136
## Crediblty (d) 0.294 0.028 10.492 0.000 0.237 0.348
## Attitude ~
## Heroism (b) 0.522 0.022 23.954 0.000 0.478 0.564
## Help (cp) -0.105 0.048 -2.182 0.029 -0.197 -0.009
## Crediblty (e) 0.053 0.017 3.119 0.002 0.021 0.086
## Std.lv Std.all
##
## -0.016 -0.005
## 0.294 0.301
##
## 0.522 0.652
## -0.105 -0.044
## 0.053 0.068
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .Heroism 2.002 0.079 25.491 0.000 1.836 2.150
## .Attitude 0.759 0.038 19.853 0.000 0.684 0.833
## Std.lv Std.all
## 2.002 0.909
## 0.759 0.537
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## indirect -0.009 0.041 -0.210 0.834 -0.094 0.070
## total -0.113 0.064 -1.779 0.075 -0.234 0.015
## Std.lv Std.all
## -0.009 -0.004
## -0.113 -0.048## [1] 8301.527## [1] 8338.034## Warning: lavaan->lavTestLRT():
## some models have the same degrees of freedom##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit.cov 0 8301.5 8338 0
## fit.reverse.cov 0 8301.5 8338 0 0 0 0Halo effects further analyses
We can assess how Risk manipulation influence helpfulness and bravery, and conversely how Motivation manipulation influences perceptions of bravery and exposure to danger. Let’s just look at Cohen’s d.
outcomes <- c("Danger", "Helpfulness", "Selfless", "Brave")
predictors <- c("Risk", "Help")
# Ensure correct factor level for Risk
Set$Risk <- factor(Set$Risk, levels = c("R", "B"))
# Initialize dataframe
effect_sizes <- data.frame()
# Loop through all predictor-outcome combinations
for (outcome in outcomes) {
for (predictor in predictors) {
if (length(unique(Set[[predictor]])) == 2) {
Set[[predictor]] <- as.factor(Set[[predictor]])
# Get levels
levels_pred <- levels(Set[[predictor]])
# Compute group means
group_means <- Set %>%
group_by(!!sym(predictor)) %>%
summarise(mean_outcome = mean(!!sym(outcome), na.rm = TRUE)) %>%
pivot_wider(names_from = !!sym(predictor), values_from = mean_outcome, names_prefix = "Mean_")
# Compute Cohen's d (positive if level[2] > level[1])
d <- cohens_d(as.formula(paste(outcome, "~", predictor)), data = Set, pooled_sd = TRUE, ci = 0.95)
# Build mean label
mean_label <- paste0(
levels_pred[1], " = ", round(group_means[[paste0("Mean_", levels_pred[1])]], 2), ", ",
levels_pred[2], " = ", round(group_means[[paste0("Mean_", levels_pred[2])]], 2)
)
# Store results
effect_sizes <- bind_rows(effect_sizes, tibble(
Effect = paste0(predictor, " → ", outcome),
Cohen_d = d$Cohens_d,
CI = paste0("[", round(d$CI_low, 2), ", ", round(d$CI_high, 2), "]"),
Group = predictor,
Group_Means = mean_label
))
}
}
}
# Format table
effect_sizes_gt <- effect_sizes %>%
gt(groupname_col = "Group") %>%
fmt_number(
columns = c("Cohen_d"),
decimals = 2
) %>%
tab_header(
title = "Effect Sizes (Cohen's d)"
) %>%
cols_label(
Effect = "Effect",
Cohen_d = "Cohen's d",
CI = "95% CI",
Group_Means = "Group Means"
)
effect_sizes_gt| Effect Sizes (Cohen's d) | |||
| Effect | Cohen's d | 95% CI | Group Means |
|---|---|---|---|
| Risk | |||
| Risk → Danger | 0.99 | [0.87, 1.1] | R = 6.28, B = 5.11 |
| Risk → Helpfulness | 0.25 | [0.15, 0.36] | R = 6.1, B = 5.81 |
| Risk → Selfless | 0.17 | [0.07, 0.28] | R = 5.61, B = 5.38 |
| Risk → Brave | 0.28 | [0.18, 0.39] | R = 5.98, B = 5.62 |
| Help | |||
| Help → Danger | 0.00 | [-0.1, 0.11] | H = 5.7, S = 5.7 |
| Help → Helpfulness | 0.27 | [0.17, 0.38] | H = 6.11, S = 5.8 |
| Help → Selfless | 0.26 | [0.15, 0.37] | H = 5.67, S = 5.32 |
| Help → Brave | 0.18 | [0.07, 0.29] | H = 5.92, S = 5.69 |
Analysis of Heroism scores in the Non-Hero condition (Bored and self-centered)
What does heroism in each occupation look like when we attempt to frame them as bored and self-centered?
NonHeroes <- subset(Set, Set$Risk == "B" & Set$Help == "S")
df_summary <- NonHeroes %>%
group_by(Job) %>%
summarize(
mean_score = mean(Heroism, na.rm = TRUE),
sd_score = sd(Heroism, na.rm = TRUE),
.groups = "drop"
)
# 2. Create the ggplot using the long format data
ggplot(NonHeroes, aes(x = Heroism)) +
geom_histogram(aes(fill = after_stat(count)),
binwidth = 1,
color = "black", show.legend = FALSE) +
facet_grid( ~ Job, scales = "free") +
scale_fill_gradientn(
colours = brewer.pal(9, "YlOrBr"),
name = "Count"
) +
labs(
title = "Histograms of Variable by Occupation",
x = "Score",
y = "Count"
) +
# Annotate each facet with the mean and standard deviation
geom_text(data = df_summary,
aes(x = 7, y = Inf,
label = paste0("Mean = ", round(mean_score, 2),
"\nSD = ", round(sd_score, 2))),
vjust = 1.5, hjust = 1.1, size = 3) +
theme_classic() +
theme(panel.grid.major.y = element_line(linewidth = 0.5),
panel.grid.minor.y = element_line(linewidth = 0.5))