Replication of Study 5 by Rentzsch & Gross (2015, European Journal of Personality)

Introduction

I have chosen to replicate Rentzsch and Gross’s (2015) study on predicting state envy in didactic interactions using their Domain-Specific Envy Scale (DSES; Study 5). Rentzsch and Gross (2015) argue that state envy varies across comparison domains, suggesting that dispositional envy also varies across domains and may function relatively independently across them. To capture this, they developed a scale that separates dispositional envy into three domains: Wealth, Attraction, and Competence.

In Study 5, Rentzsch and Gross induced envy in the laboratory using a Rock-Paper-Scissors paradigm, in which only the game winner receives a reward. Rewards have included a chocolate bar (Rentzsch & Gross, 2015) or money (Rentzsch et al., 2023). They found that participants who did not receive a reward reported greater envy toward those who did, and dispositional envy predicted situational envy: individuals with higher dispositional envy experienced stronger envy during upward comparisons.

This project is a conceptual replication of this paradigm in an online setting. The attached repository provides: 1) the experimental paradigm, 2) the analytic pipeline, and 3) anonymized data. Links to the pre-registration and experiment are also included below. For any additional information, please contact me at ckoffler@ucsd.edu.

github link: https://github.com/Carsonkoffler/rentzsch2015 experiment link: https://carsonkoffler.github.io/rentzsch2015/ pre-registration link: https://osf.io/rcpt7/overview

##Methods The only inclusion criterion for this study is fluency in English. Data collected from participants will include basic demographics (age and gender) and responses to the following measures: dispositional envy (using the DSES), state emotions toward the other player, situational appraisals, and outcome attribution. Except for the outcome attribution measure, which uses a 4-point scale, all other items are rated on a 7-point Likert scale. Participants with missing data on key variables or who fail attention checks will be excluded. Scale scores (DSES, state emotions, appraisals, outcome attributions) will be computed as the mean of the corresponding items, with reverse coding applied where appropriate. The manipulation variable will be dummy coded as 0 = loser (high envy condition) and 1 = winner (low envy condition).

The primary confirmatory test will be an independent-samples Welch’s t-test comparing state envy between winners and losers. Welch’s t-test was used because the assumption of equal variances was violated. This test directly evaluates the hypothesis that individuals will experience greater envy when they do not receive a reward, consistent with the original study.

Additionally, a linear regression was conducted to examine whether dispositional envy predicts state envy. This analysis tests whether individuals with higher dispositional envy report higher state envy in response to upward comparisons, extending the original findings.

Original findings: Participants who lost (did not receive a reward) reported higher envy (M = 2.00, SD = 1.08) than winners (M = 1.31, SD = 0.89), t(57) = 2.67, p = 0.01. A successful replication would reproduce this effect in the same direction and of similar magnitude.

Power Analysis

I will conduct a power analysis using the results of the t-test comparing the winner and loser group means of envy. The results from the original study are: “Analysing the main effect of the situation revealed that participants who did not receive the reward reported stronger feelings of envy (M = 2.00, SD = 1.08) than participants who received the reward (M = 1.31, SD = 0.89), t(57) = 2.67, p = .01.”

library(pwr)
## calculate cohen's d 
m1 = 2.0
s1 = 1.08
m2 = 1.31
s2 = 0.89
s_pooled = sqrt(((s1^2)+(s2^2))/2)
d = (m1-m2)/s_pooled

#power analysis to find required sample size
cat("Cohen's d is", d)

Cohen's d is 0.6972721

print(pwr.t.test(n = NULL, d=d, sig.level = 0.05, power = .8, 
           type = "two.sample", alternative = "two.sided"))

     Two-sample t test power calculation 

              n = 33.27551
              d = 0.6972721
      sig.level = 0.05
          power = 0.8
    alternative = two.sided

NOTE: n is number in *each* group

###Planned Sample

Based on the power analyses (Cohen’s d = .70), I will collect data from 68 participants and data collection will stop once complete data from all 68 participants has been collected from Prolific. The experiment should take about 12 minutes to complete.

###Procedure

This study will follow the original procedure as closely as possible, though moving to an online format will require a few changes. The original procedure is as follows:

” The study consisted of two parts (see supporting information S11 for details). In the first part, participants filled out an online questionnaire at home. In the second part, participants met in dyads in the interaction laboratory at the university. Two weeks before meeting in the interaction lab, participants filled out questionnaires measuring traits such as dispositional envy and individual differences in socially desirable responding. Dispositional envy was assessed with the DSES (α = 91) using 7-point Likert scales ranging from 1 (not at all) to 7 (very much). Social desirability was assessed as a control measure with the other-deceptions scale of the BIDR (Paulhus, 1994; German version by Musch et al., 2002, α = .62) on 7-point Likert scales ranging from 1 (strongly disagree) to 7 (strongly agree). Before arriving in the interaction lab, participants were matched by sex to dyads at zero acquaintance, as research has shown that similarity is an important condition for feelings of envy (Salovey & Rodin, 1984). Participants sat face to face at a table (seating position was randomized; the distance between participants was held constant across settings, i.e. 140 cm). Then, participants played a game called ‘Rock, Paper, Scissors’. The rules of the game were provided on a handout. Participants had three trials to test the game. Afterwards, the game started: participants were informed that the game was over when one of the two participants won a trial and that the winner would receive a small reward for purposes of motivation. The reward was a highly valued chocolate bar (Milka Nussini) that was placed in an opaque box next to both participants (the position of the box was held constant across settings). The winner was instructed to take the reward and leave it on the table next to him or herself. Participants completed a questionnaire assessing their perceptions of the situation and their feelings towards the ther person. For state measures, participants were asked to rate the intensity of their feelings on a 7-point Likert scale ranging from 1 (not at all) to 7 (very much). The intensity of feelings of envy was measured with two items (i.e. ‘I am envious of the other person’ and ‘I envy the other person’, α = .76). As control measures, participants rated the intensity of their experience of sadness (‘I am sad’) and anger (‘I am angry’) on the same rating scale. Furthermore, participants indicated their previous experience with the Rock, Paper, Scissors game and their attributions of the outcome of the game to luck, task difficulty, ability or effort. Additionally, on a 7-point Likert scale from 1 (not at all) to 7 (very much), participants indicated how much they thought that they could have won the game. At the end, participants were thanked and fully debriefed. ”

Here are the changes that I have made to format this design to online:

1. The study will be completed in only one part. For increased feasibility, The DSES measure was placed at the end of the survey.

2. Participants will enter a simulated pairing process, and they will be randomly assigned to 1 of 4 computer names. The pairings are not constrained by any demographic data.

3. The reward for the winner of game was $1 (versus a chocolate bar).

4. Instead of having a physical box containing a reward that was moved positionally towards the winner, a fixed on-screen scoreboard was displayed in the upper-right corner of the browser window. The element consisted of a blue rectangular panel with a black 2-pixel border, rounded corners (8 px radius), and 10 px padding. Its size was not fixed; instead, its width and height adjusted automatically to the text content (approximately 150–200 px wide and 70–100 px tall, depending on the user’s browser and font rendering). The scoreboard presented the label “Player Earnings,” followed by the participant’s current score and the opponent’s score.

Beyond this, all else was the same.

###Materials For the filler task between the game and the self-report measures, a semantic categorization task was completed. Participants saw 10 words and were asked to select the category that these words belonged too. The semantic categorization task was not explicitly shared in the procedures, so a simple semantic task was created using the word list from Patel, Bullinaria & Levy (1997). The dependent variables used the same measures as outlined in the original paper and the supplementary paper for the 2023 replication. The only change was the measures gathered was the removal of the BIDR from the study.

Analysis Plan

There are 2 different criterion that we are judging attention on: 1. Three attention checks within the survey 2. At least a score of 60% on the semantic categorizarion task

We will exclude participants who fail 2/3 of the survey attention check questions and those who receive less than an accuracy score of 60% on the semantic categorization task.

The first analysis of interest is comparing which condition of the game (Winner, Loser) made participants more envious by conducting a Welch’s t-test on a state-envy composite between conditions. The composite was comprised of 4-items: “I am jealous of that person”/“I feel envious of that person”/“I feel jealous”/“I feel envy”. Envy and jealousy were averaged together because of their semantic similarity in everyday speech.

The second analysis is to test whether dispositional envy predicts state envy by conducting a linear regression.

In addition to these two confirmatory analyses, some exploratory analyses of interest comparing how the game conditions impact anger and seeing how the game conditions impact appraisals of the situation, specifically fairness evaluations.

Differences from Original Study

There are four main differences between this study and the original:

1. Setting: This experiment is conducted online rather than in person. This change introduces procedural differences, as outlined above. It is possible that state envy may be stronger in in-person comparisons; however, numerous online studies have successfully elicited envy, suggesting that the effect is not limited to face-to-face interactions.

2. Sample: We are recruiting participants through Prolific, whereas the original study used undergraduate students in education and learning at a German university. While there may be some population differences, we do not expect this change to substantially alter the results.

3. Attention Checks: We have added additional attention checks to ensure data quality. The original study only excluded participants based on whether they found the reward valuable (screening for allergies or disliking of chocolate). Since this replication uses a monetary reward, that criterion is no longer relevant. We do not anticipate that this modification will affect the results.

4. Procedure: This experiment is conducted in a single session rather than two. To reduce participant burden, we focused on dispositional envy and removed the BIDR measure. Some original analyses controlled for social desirability using BIDR scores, so analyses in this replication may differ from the original on that account.

In summary, the known differences involve sample, setting, procedure, and analysis plan. While we aim to minimize these differences, some are unavoidable. Based on the original article and subsequent research on conditions for obtaining the effect, none of these changes are expected to substantially alter the core findings.

Actual Sample

There were 68 participants recruited from Prolific.

Differences from pre-data collection methods plan

None.

Results

Data preparation

Data preparation following the analysis plan.

### Data Preparation

#### Load Relevant Libraries and Functions
library(jsonlite)
library(dplyr)

Attaching package: 'dplyr'

The following objects are masked from 'package:stats':

    filter, lag

The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union

library(tidyr)
library(purrr)

Attaching package: 'purrr'

The following object is masked from 'package:jsonlite':

    flatten

library(stringr)
library(readr)
library(kableExtra)

Attaching package: 'kableExtra'

The following object is masked from 'package:dplyr':

    group_rows

library(ggplot2)
#### Import data
# Set working directory
path <- "/Users/carsonkoffler/Documents/R_Coding/rentzsch2015/data/osfstorage/Study1"
setwd(path)

files <- list.files(path = path, pattern = "\\.csv$", full.names = T) #list all files folder

length(files) #number of files --> should match n 

[1] 68

head(files) #View

[1] "/Users/carsonkoffler/Documents/R_Coding/rentzsch2015/data/osfstorage/Study1/0l093yjbnt.csv"
[2] "/Users/carsonkoffler/Documents/R_Coding/rentzsch2015/data/osfstorage/Study1/0qju2rq59j.csv"
[3] "/Users/carsonkoffler/Documents/R_Coding/rentzsch2015/data/osfstorage/Study1/1bwf45xvm9.csv"
[4] "/Users/carsonkoffler/Documents/R_Coding/rentzsch2015/data/osfstorage/Study1/1v426cwnau.csv"
[5] "/Users/carsonkoffler/Documents/R_Coding/rentzsch2015/data/osfstorage/Study1/1xazcwqq3k.csv"
[6] "/Users/carsonkoffler/Documents/R_Coding/rentzsch2015/data/osfstorage/Study1/29ah5oq1ex.csv"

#read and combine participant data into one file 
all_data <- files %>%
  map_dfr(function(file_path){
    read_csv(
      file_path,
      col_types = cols(
        prolific_id_last4 = col_character(),  # force character type
        participant_name = col_character(),   # force character type
        .default = col_guess()                # let all other columns be guessed
      )
    )
  })

all_data <- as_tibble(all_data)


#summarize participant data 
participants <- all_data %>%
  group_by(subject_id) %>%
  summarise(success = first(success), #complete = T/F
            experiment_data = first(experiment_date), #date study done
            game_condition = first(random_condition), #condition: Winner/Loser
            prolific_id = first(prolific_id_last4),  #Last 4 of prolific id
            total_time = max(time_elapsed, na.rm = T),  #total time to complete study
            version = first(version)) #study version 



# Identify survey rows want to keep 
survey_data <- all_data %>%
  dplyr::filter(str_detect(trial_type, "survey")) %>%
  dplyr::select(subject_id, trial_type, response)

# Convert JSON strings to lists and expand (1 column per Q)
survey_expanded <- survey_data %>%
  mutate(response_list = map(response, ~ {
    # Convert string JSON to R list
    if (!is.na(.x) && .x != "") {
      as.list(fromJSON(.x))
    } else {
      NA
    }
  })) %>%
  dplyr::select(-response) %>%
  unnest_wider(response_list)

# fix data that was not named (Q0 contains psuedonym)
columns_fixed <- survey_expanded %>%
  group_by(subject_id) %>%
  summarise(
    pseudonym = Q0[!map_lgl(Q0, is.null)][1],
  )

#join columns_fixed to survey_expanded
survey_expanded <- survey_expanded %>%
  left_join(columns_fixed, by = "subject_id")

#add attention check 1 that was filtered out earlier
attention_check_1 <- all_data %>%
  filter(str_detect(stimulus, "Who won the last round you played\\?")) %>%
  dplyr::select(subject_id, attention_check_1=response)

#add attention check 1 to the df 
survey_expanded <- survey_expanded %>%
  left_join(attention_check_1, by = "subject_id")

#rename attention check 2 to fit format 
survey_expanded <- survey_expanded %>% 
  rename(attention_check_2 = DV5_attention_check, 
         psuedonum = Q0)


# Join expanded survey data back to main dataframe
# If multiple survey rows per subject, we can summarize by taking the first non-NA per column
df <- survey_expanded %>%
  group_by(subject_id) %>%
  summarise(across(everything(), ~ first(na.omit(.x)), .names = "{.col}"))

df <- df %>%
  left_join(participants, by = "subject_id")

rm(list = setdiff(ls(), c("df", "path"))) #cleaning the enviornment 
#### Data exclusion / filtering
#Exclude participants who didn't complete the experiment
data_complete <- df %>%
  filter(success == "TRUE")

n_total <- df %>%
  distinct(subject_id) %>%
  nrow()

n_excluded_incomplete <- n_total - n_distinct(data_complete$subject_id)

print(paste("Excluded for incompletion:", n_excluded_incomplete))

[1] "Excluded for incompletion: 0"

print(paste("Remaining participants:", n_distinct(data_complete$subject_id)))

[1] "Remaining participants: 68"

#==============================================================================================
### Exclude participants who failed 2/3 attention checks

#create pass/fail for attention_check_1
data_complete <- data_complete %>%
  mutate(
    attention_check_1 = case_when(
      (game_condition == "winner" & attention_check_1 == 0) ~ "pass", # 0 if select participant won --> winner = participant win
      (game_condition == "loser" & attention_check_1 == 1) ~ "pass", # 1 if select computer win --> loser = computer win
      TRUE ~ "fail"
    )
  )

#LIKERT SCALES coded 0-6 NOT 1-7 

#filter if fail 2/3 attention checks 
data_attention <- data_complete %>%
  mutate(
    fail1 = attention_check_1 != "pass", 
    fail2 = attention_check_2 != 6, 
    fail3 = attention_check_3 <= 1
  ) %>%
  filter(fail1 + fail2 + fail3 < 2)

n_excluded_attention <- n_distinct(data_complete$subject_id) - n_distinct(data_attention$subject_id)

print(paste("Excluded for failed attention checks:", n_excluded_attention))

[1] "Excluded for failed attention checks: 0"

print(paste("Remaining participants:", n_distinct(data_attention$subject_id)))

[1] "Remaining participants: 68"

data_complete <- data_attention #override dataset to keep only those that failed <= 1 

#==============================================================================================

# Check the filler Qs 
#create a key 
correct_answers <- c(
  filler_1 = "Fruits",
  filler_2 = "Jewels",
  filler_3 = "Family Members",
  filler_4 = "Body Parts",
  filler_5 = "Kitchen Utensils"
)

#check if each participant data matches key and compute an accuracy score
data_complete <- data_complete %>%
  mutate(across(
    .cols = names(correct_answers),
    .fns  = ~ .x == correct_answers[cur_column()],
    .names = "correct_{col}"
  )) %>%
  rowwise() %>%
  mutate(accuracy = mean(c_across(starts_with("correct_")))) %>%
  ungroup()

data_accuracy <- data_complete %>% 
  filter(accuracy >= 0.60)

# Count total and excluded
n_excluded_accuracy <- n_distinct(data_complete$subject_id) - n_distinct(data_accuracy$subject_id)

# Print results
print(paste("Excluded for failing filler questions:", n_excluded_accuracy))

[1] "Excluded for failing filler questions: 0"

print(paste("Remaining participants:", n_distinct(data_accuracy$subject_id)))

[1] "Remaining participants: 68"

# plot data exclusions 
exclusion_summary <- tibble(
  Stage = c("Initial", 
            "After incompletion", 
            "After attention checks", 
            "After semantic categorization tasks"),
  N_Participants = c(n_total,
                     n_distinct(data_complete$subject_id),
                     n_distinct(data_attention$subject_id), 
                     n_distinct(data_accuracy$subject_id)),
  N_Excluded = c(0,
                 n_excluded_incomplete,
                 n_excluded_attention, 
                 n_excluded_accuracy)
)


exclusion_summary %>%
  knitr::kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover"))

Stage	N_Participants	N_Excluded
Initial	68	0
After incompletion	68	0
After attention checks	68	0
After semantic categorization tasks	68	0

# Visualize exclusion cascade 
ggplot(exclusion_summary %>% filter(!is.na(Stage)), 
       aes(x = reorder(Stage, -N_Participants), y = N_Participants)) +
  geom_bar(stat = "identity", fill = "#1976D2", alpha = 0.7) +
  geom_text(aes(label = N_Participants), vjust = -0.5) +
  labs(title = "Participant Exclusion Cascade",
       x = "Stage",
       y = "Number of Participants") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

data_complete <- data_accuracy #make this df the final one for analyses 

Demographic data

library(ggplot2)

#plot ages 
data_complete$age <- as.numeric(data_complete$age)

summary(data_complete$age)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  20.00   28.00   35.50   39.18   48.25   83.00 

#histogram
ggplot(data = data_complete, aes(x= age))+
  geom_histogram(
    binwidth = 2, 
    fill = "#39568CFF") +
  labs(
    title = "Distribution of Participant Ages",
    x = "Age", 
    y = "Count")+
  theme_minimal()

#plot gender 
names(which.max(table(data_complete$demo_gender)))

[1] "Male"

#histogram
ggplot(data = data_complete, aes(x= demo_gender))+
  geom_bar(fill = "#39568CFF") +
  labs(
    title = "Number of Participant's by Gender", 
    x = "Gender", 
    y = "Count")+
  theme_minimal()

#plot time taken
summary(data_complete$total_time/60000) #time taken in minutes ms:min --> 60000:1 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  4.003   6.387   8.093   9.693  11.190  30.209 

#histogram
ggplot(data = data_complete, aes(x= total_time/60000))+
  geom_density(fill = "#39568CFF") +
  labs(
    title = "Amount of Time Taken to Complete Survey",
    x = "Time to Complete Survey (minutes)", 
    y = "Count")+
  theme_minimal()

#plot conditions 
data_complete$game_condition_coded <- ifelse(data_complete$game_condition == "winner", 1, 0)
table(data_complete$game_condition_coded)

 0  1 
35 33 

ggplot(data = data_complete, aes(x= factor(game_condition_coded)))+
  geom_bar(fill = "#39568CFF") +
  labs(
    title = "Number of Participants in the Game Conditions",
    x = "Random Conditon", 
    y = "Count")+
  theme_minimal()

Confirmatory analysis

First, I will analyze the group differences in envy. #### Group differences in state envy by game condition

library(ggplot2)
library(papaja)

Loading required package: tinylabels

#--- Does game outcome predict state envy? ---#

#code game condition
data_complete$game_condition_coded <- ifelse(data_complete$game_condition == "winner", 1, 0)

#state envy composite 
data_complete$state_envy_composite <- rowMeans(
  data_complete[, c("DV2_emotion_envy",
                    "DV2_emotion_envy_2",
                    "DV2_emotion_jealousy",
                    "DV2_emotion_jealousy_2")],
  na.rm = TRUE
)
hist(data_complete$state_envy_composite, main="State Envy Composite", xlab="Envy Score")

#state envy by game condition
envy.mod <- lm(data=data_complete, state_envy_composite ~ game_condition_coded)

t_envy_result <- t.test(state_envy_composite ~ game_condition_coded,data=data_complete)

t_envy_result

    Welch Two Sample t-test

data:  state_envy_composite by game_condition_coded
t = 5.1264, df = 42.993, p-value = 6.687e-06
alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
95 percent confidence interval:
 0.8417625 1.9335621
sample estimates:
mean in group 0 mean in group 1 
      1.7285714       0.3409091 

#calculate a cohen's d of the group differences 
envy_cohensd<- effectsize::cohens_d(state_envy_composite ~ game_condition_coded,
  data = data_complete
)

envy_cohensd$Cohens_d

[1] 1.215477

#calculate summary data: means, sd, 95% CI, n 
summary_envy <- data_complete %>%
  group_by(game_condition_coded) %>%
  summarise(
    mean_envy = mean(state_envy_composite, na.rm = TRUE),
    sd_envy = sd(state_envy_composite, na.rm = TRUE),
    se_envy = sd(state_envy_composite, na.rm = TRUE) / sqrt(n()),
    ci95 = 1.96 * se_envy
  )

print(summary_envy)

# A tibble: 2 × 5
  game_condition_coded mean_envy sd_envy se_envy  ci95
                 <dbl>     <dbl>   <dbl>   <dbl> <dbl>
1                    0     1.73    1.50   0.254  0.498
2                    1     0.341   0.537  0.0935 0.183

Analyzing the main effect of the game condition revealed that participants who did not receive the reward reported stronger feelings of envy (\(M = 1.73, SD = 1.50\)) than participants who received the reward (\(M = 0.34, SD = 0.54\)), \(t(42.99) = 5.13\), \(p < .001\). The effect of this group difference has a Cohen’s d equal to 1.22. This mirrors the findings from Rentzsch and Gross (2015) who find a significant group difference of (\(M_{Loser}~ = 2.00, SD = 1.08\)) than participants who received the reward (\(M_{Winner} = 1.31, SD = 0.89),\hspace{.5mm}t(57) = 2.67, p = .01\).

The group differences in envy can be observed in the following figures. Note about coding: - game_condition_code = 0 are the losers of the game who did not receive the reward - game_condition_code = 1 are the winners of the game who did receive the reward

library(ggplot2)
library(ggpubr)

##bar plot 
ggplot() +
  # raw data points (jittered)
  geom_jitter(
    data = data_complete,
    aes(x = factor(game_condition_coded), y = state_envy_composite),
    width = 0.1, size = 2.5, alpha = 0.2, color = "black"
  ) +
  # bar showing means
  geom_col(
    data = summary_envy,
    aes(x = factor(game_condition_coded), y = mean_envy),
    fill = "gray50", alpha = 0.7
  ) +
  # 95% CI error bars
  geom_errorbar(
    data = summary_envy,
    aes(
      x = factor(game_condition_coded),
      ymin = mean_envy - ci95,
      ymax = mean_envy + ci95
    ),
    width = 0.15
  ) +
  labs(
    x = "Game Condition (0 = Loser, 1 = Winner)",
    y = "State Envy Composite",
    title = "State Envy by Condition with Raw Data and 95% CI"
  ) +
  theme_minimal()

##violin plot
envy_violin<- ggplot(data_complete, aes(x = factor(game_condition_coded), y = state_envy_composite)) +
  geom_violin(fill = "lightblue", alpha = 0.7) +  # distribution
  geom_jitter(width = 0.1, size = 3, alpha = 0.3, color = "gray50") + # individual points
  stat_summary(fun = mean, geom = "point", shape = 18, size = 4, color = "black") + # mean
  labs(
    x = "Game Condition (0 = Loser, 1 = Winner)",
    y = "State Envy Composite",
    title = "State Envy by Game Condition"
  ) +
  theme_minimal() +
  theme(plot.title = element_text(hjust = 0.5)) + 
  stat_compare_means(method = "t.test", label = "p.signif", size = 8, 
                     label.y = max(data_complete$state_envy_composite)-.3, 
                     label.x = 1.5)
envy_violin

ggsave("envy_violin.png", plot = envy_violin, width = 6, height = 4, units = "in", dpi = 300)



##density plot 
ggplot(data_complete, aes(x = state_envy_composite, fill = factor(game_condition_coded))) +
  geom_density(alpha = 0.5) + 
  labs(
    x = "Game Condition (0 = Loser, 1 = Winner)",
    y = "State Envy Composite",
    title = "State Envy by Game Condition",
    fill = "Game Codition"
  ) +
  theme_minimal() +
  theme(plot.title = element_text(hjust = 0.75)) +
  scale_fill_discrete(labels = c("Loser", "Winner"))

The relationship between dispositional envy and state envy

Second, I will analyze the relationship between dispostional envy (measured using the DSES scale) and state envy.

#---- corrlation between dispositional envy and state envy ----


#total dispositional envy corr with state envy 
disp_envy_cols <- grep("DV5", names(data_complete), value = TRUE)

data_complete$total_dispositional_envy <- rowMeans(data_complete[, disp_envy_cols], na.rm = TRUE)

cor(data_complete$total_dispositional_envy, data_complete$state_envy_composite)

[1] 0.4352135

summary(lm(data = data_complete, state_envy_composite~total_dispositional_envy))

Call:
lm(formula = state_envy_composite ~ total_dispositional_envy, 
    data = data_complete)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.3383 -0.5693 -0.3515  0.6591  3.1314 

Coefficients:
                         Estimate Std. Error t value Pr(>|t|)    
(Intercept)                0.3515     0.2314   1.519 0.133508    
total_dispositional_envy   0.4082     0.1040   3.927 0.000208 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.208 on 66 degrees of freedom
Multiple R-squared:  0.1894,    Adjusted R-squared:  0.1771 
F-statistic: 15.42 on 1 and 66 DF,  p-value: 0.0002081

#lm broken by game condition to resemble Rentzsch and Gross 
summary(lm(state_envy_composite ~ total_dispositional_envy, data = subset(data_complete, game_condition_coded == 0))) #lose 

Call:
lm(formula = state_envy_composite ~ total_dispositional_envy, 
    data = subset(data_complete, game_condition_coded == 0))

Residuals:
     Min       1Q   Median       3Q      Max 
-2.18279 -0.66191  0.02447  0.72129  2.64673 

Coefficients:
                         Estimate Std. Error t value Pr(>|t|)    
(Intercept)                0.3428     0.3299   1.039    0.306    
total_dispositional_envy   0.7977     0.1545   5.163 1.14e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.135 on 33 degrees of freedom
Multiple R-squared:  0.4469,    Adjusted R-squared:  0.4301 
F-statistic: 26.66 on 1 and 33 DF,  p-value: 1.14e-05

summary(lm(state_envy_composite ~ total_dispositional_envy, data = subset(data_complete, game_condition_coded == 1))) #win

Call:
lm(formula = state_envy_composite ~ total_dispositional_envy, 
    data = subset(data_complete, game_condition_coded == 1))

Residuals:
     Min       1Q   Median       3Q      Max 
-0.78558 -0.14717 -0.10022  0.05589  1.59935 

Coefficients:
                         Estimate Std. Error t value Pr(>|t|)  
(Intercept)               0.10022    0.12773   0.785   0.4386  
total_dispositional_envy  0.14083    0.05509   2.556   0.0157 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4958 on 31 degrees of freedom
Multiple R-squared:  0.1741,    Adjusted R-squared:  0.1474 
F-statistic: 6.534 on 1 and 31 DF,  p-value: 0.01571

## ensuring that the scale was picking up dispositional envy and not just the game condition 
lm(data=data_complete, total_dispositional_envy ~ game_condition_coded)

Call:
lm(formula = total_dispositional_envy ~ game_condition_coded, 
    data = data_complete)

Coefficients:
         (Intercept)  game_condition_coded  
             1.73714              -0.02805  

t.test(total_dispositional_envy ~ game_condition_coded,data=data_complete)

    Welch Two Sample t-test

data:  total_dispositional_envy by game_condition_coded
t = 0.080307, df = 60.957, p-value = 0.9363
alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
95 percent confidence interval:
 -0.6704445  0.7265483
sample estimates:
mean in group 0 mean in group 1 
       1.737143        1.709091 

Results revealed that dispositional envy significantly predicted state levels of envy for the non-reward condition (\(b = 0.80\), 95% CI \([0.48, 1.11]\), \(t(33) = 5.16\), \(p < .001\)), and for the reward condition (\(b = 0.14\), 95% CI \([0.03, 0.25]\), \(t(31) = 2.56\), \(p = .016\)). Higher levels of dispositional envy predicted higher levels of envy experienced in an upward-comparison situation. Since dispositional envy in this replication was measured in the same sitting as state envy, there was a chance that game condition was impacting people’s survey responses, such that losers may indicate more dispositional envy as a function of having higher state envy. A t-test was conducting to see if there were group differences in dispositional envy between those who received and did not receive the reward. The analysis shows no significant result indicating the dispositional scale is picking up true disposition outside of situational envy triggered by the game, \(\Delta M = 0.03\), 95% CI \([-0.67, 0.73]\), \(t(60.96) = 0.08\), \(p = .936\).

This mirrored the original results which found “that dispositional envy significantly predicted state levels of envy for the non-reward condition (β = .48, SE = 0.16, p < .01; see the lower path in Figure 1), but not for the reward condition (β = .08, SE = 0.16, p = .67; see the upper path in Figure 1)” (pg 542).

See below visualizations of the relationship between dispositional envy and state envy.

#visualizations 
ggplot(data = data_complete, mapping = aes(x = total_dispositional_envy, y=state_envy_composite)) +
  geom_jitter(color="#440154FF", alpha=.5, size = 3) +
  geom_smooth(method = "lm", color = "#31688EFF", se = TRUE) +
  labs(
    x = "Total Dispositional Envy", 
    y = "State Envy", 
    title = "The Relationship Between Dispositional Envy and State Envy") +
  theme_minimal(base_size = 12) +
  theme(plot.title = element_text(hjust = 0.5))

`geom_smooth()` using formula = 'y ~ x'

#visualizations split by condition
corr_envyXcondition<- ggplot(data = data_complete, mapping = aes(x = total_dispositional_envy, y=state_envy_composite, color = factor(game_condition_coded))) +
  geom_jitter(alpha=.3, size = 3) +
  geom_smooth(method = "lm", se = TRUE) +
  labs(
    x = "Total Dispositional Envy", 
    y = "State Envy", 
    title = "The Relationship Between Dispositional Envy and State Envy", 
    color = "Game Codition"
    ) +
  theme_minimal(base_size = 12) +
  theme(plot.title = element_text(hjust = 0.75)) +
  scale_color_discrete(labels = c("Loser", "Winner"))

corr_envyXcondition

`geom_smooth()` using formula = 'y ~ x'

ggsave("envy_corr.png", plot = corr_envyXcondition, width = 8, height = 6, units = "in", dpi = 300)

`geom_smooth()` using formula = 'y ~ x'

The results can be compared to the original results here:

Group differences in state envy by game condition controlling for dispositional envy

Because dispositional envy strongly predicts state envy, we included it as a covariate in an ANCOVA to isolate the effect of game condition on state envy. This approach ensures that differences between winners and losers reflect situational, game-induced envy rather than baseline trait differences.

library(emmeans)

Welcome to emmeans.
Caution: You lose important information if you filter this package's results.
See '? untidy'

summary(lm(state_envy_composite ~ game_condition_coded + total_dispositional_envy, data = data_complete))

Call:
lm(formula = state_envy_composite ~ game_condition_coded + total_dispositional_envy, 
    data = data_complete)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.9422 -0.7032  0.1280  0.3545  2.4612 

Coefficients:
                         Estimate Std. Error t value Pr(>|t|)    
(Intercept)               1.02783    0.22407   4.587  2.1e-05 ***
game_condition_coded     -1.37635    0.24091  -5.713  3.0e-07 ***
total_dispositional_envy  0.40338    0.08547   4.719  1.3e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.9928 on 65 degrees of freedom
Multiple R-squared:  0.4604,    Adjusted R-squared:  0.4438 
F-statistic: 27.73 on 2 and 65 DF,  p-value: 1.963e-09

summary(lm(state_envy_composite ~ game_condition_coded, data = data_complete))

Call:
lm(formula = state_envy_composite ~ game_condition_coded, data = data_complete)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.7286 -0.3753 -0.3409  0.4372  2.7714 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)             1.729      0.193   8.957 5.18e-13 ***
game_condition_coded   -1.388      0.277  -5.009 4.33e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.142 on 66 degrees of freedom
Multiple R-squared:  0.2755,    Adjusted R-squared:  0.2645 
F-statistic: 25.09 on 1 and 66 DF,  p-value: 4.334e-06

emmeans(lm(state_envy_composite ~ game_condition_coded + total_dispositional_envy, data = data_complete), "game_condition_coded")

 game_condition_coded emmean    SE df lower.CL upper.CL
                    0  1.723 0.168 65  1.38792    2.058
                    1  0.347 0.173 65  0.00157    0.692

Confidence level used: 0.95 

emmeans(lm(state_envy_composite ~ game_condition_coded, data = data_complete), "game_condition_coded")

 game_condition_coded emmean    SE df lower.CL upper.CL
                    0  1.729 0.193 66   1.3433    2.114
                    1  0.341 0.199 66  -0.0559    0.738

Confidence level used: 0.95 

After adjusting for dispositional envy, game condition still significantly predicted state envy, \(b = -1.38\), 95% CI \([-1.86, -0.90]\), \(t(65) = -5.71\), \(p < .001\), showing that winners reported lower state envy than losers.

Estimated marginal means (adjusted for dispositional envy) revealed that losers had higher state envy (\(M = 1.72\), 95% CI \([1.39, 2.06]\)) than winners (\(M = 1.72\), 95% CI \([1.39, 2.06]\)), confirming that the game manipulation produced situational envy independent of trait differences.

# Load packages
library(ggplot2)
library(emmeans)

# Fit ANCOVA model (game condition and disp envy on state envy)
ancova_model <- lm(state_envy_composite ~ game_condition_coded + total_dispositional_envy, data = data_complete)

# Get adjusted means
emm <- emmeans(ancova_model, "game_condition_coded")

# Convert to data frame for plotting
emm_df <- as.data.frame(emm)
emm_df$game_condition <- factor(emm_df$game_condition_coded, labels = c("Loser", "Winner"))

# Prepare raw data for jitter
data_complete$game_condition <- factor(data_complete$game_condition_coded, labels = c("Loser", "Winner"))

# Plot
ggplot() +
  # Jittered raw data
  geom_jitter(data = data_complete, 
              aes(x = game_condition, y = state_envy_composite),
              width = 0.15, alpha = 0.5, color = "darkgray") +
  # Bars for adjusted means
  geom_bar(data = emm_df, 
           aes(x = game_condition, y = emmean), 
           stat = "identity", alpha = 0.6, width = 0.5) +
  # Error bars for 95% CI
  geom_errorbar(data = emm_df, 
                aes(x = game_condition, ymin = lower.CL, ymax = upper.CL), 
                width = 0.2, color = "black") +
  labs(x = "Game Condition", y = "Adjusted State Envy",
       title = "Adjusted State Envy by Game Condition (Controlling for Dispositional Envy)") +
  theme_minimal(base_size = 12)

Exploratory analyses

Group differences in state envy by game condition

Some of the research I am interested in conducting is disentangling envy and anger. I was curious how much this paradigm increased anger. Using the Recalibration Theory of anger (Sell, 2011), anger is understood to be trigger when someone imposes a cost onto us. I would predict that this game would not produce anger since the winner is produced by random chance rather than some kind of transgression or fairness violation. I will conduct some exploratory analyses to understand how the game conditions impact anger.

#Random Chance Resource Distribution on Anger?

# state anger composite 
data_complete$state_anger_composite <- rowMeans(
  data_complete[, c("DV2_emotion_anger",
                    "DV2_emotion_anger_2")],
  na.rm = TRUE
)

##density plot 
ggplot(data_complete, aes(x = state_anger_composite, fill = factor(game_condition_coded))) +
  geom_density(alpha = 0.5) + 
  labs(
    x = "Game Condition (0 = Loser, 1 = Winner)",
    y = "State Anger Composite",
    title = "State Anger by Game Condition", 
    fill = "Game Condition"
  ) +
  theme_minimal() + 
  theme(plot.title = element_text(hjust = 0.75)) +
  scale_fill_discrete(labels = c("Loser", "Winner"))

summary(lm(data=data_complete, state_anger_composite ~ game_condition_coded))

Call:
lm(formula = state_anger_composite ~ game_condition_coded, data = data_complete)

Residuals:
    Min      1Q  Median      3Q     Max 
-0.7000 -0.7000 -0.0606 -0.0606  3.8000 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)            0.7000     0.1478   4.735  1.2e-05 ***
game_condition_coded  -0.6394     0.2122  -3.013  0.00366 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.8745 on 66 degrees of freedom
Multiple R-squared:  0.1209,    Adjusted R-squared:  0.1076 
F-statistic: 9.079 on 1 and 66 DF,  p-value: 0.003664

t.test(data=data_complete, state_anger_composite ~ game_condition_coded)

    Welch Two Sample t-test

data:  state_anger_composite by game_condition_coded
t = 3.0991, df = 36.147, p-value = 0.003747
alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
95 percent confidence interval:
 0.2210255 1.0577624
sample estimates:
mean in group 0 mean in group 1 
     0.70000000      0.06060606 

#violin plot
anger_violin <- ggplot(data_complete, aes(x = factor(game_condition_coded), y = state_anger_composite)) +
  geom_violin(fill = "lightblue", alpha = 0.7, color = "darkblue") +  # distribution
  geom_jitter(width = 0.1, size = 3, alpha = 0.5, color = "darkred") + # individual points
  stat_summary(fun = mean, geom = "point", shape = 18, size = 4, color = "black") + # mean
  labs(
    x = "Game Condition (0 = Loser, 1 = Winner)",
    y = "State Anger Composite",
    title = "State Anger by Game Condition"
  ) +
  theme_minimal()+
  theme(plot.title = element_text(hjust = 0.5)) + 
  stat_compare_means(method = "t.test", label = "p.signif", size = 8, 
                     label.y = max(data_complete$state_anger_composite)-.3, 
                     label.x = 1.5)

anger_violin 

ggsave("anger_violin.png", plot = anger_violin, width = 6, height = 4, units = "in", dpi = 300)


summary(lm(state_anger_composite ~ state_envy_composite + total_dispositional_envy, data = data_complete))

Call:
lm(formula = state_anger_composite ~ state_envy_composite + total_dispositional_envy, 
    data = data_complete)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.44511 -0.32314  0.01815  0.12349  3.07300 

Coefficients:
                         Estimate Std. Error t value Pr(>|t|)    
(Intercept)              -0.12349    0.15152  -0.815    0.418    
state_envy_composite      0.33981    0.07923   4.289 6.08e-05 ***
total_dispositional_envy  0.08973    0.07432   1.207    0.232    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.7772 on 65 degrees of freedom
Multiple R-squared:  0.3162,    Adjusted R-squared:  0.2951 
F-statistic: 15.03 on 2 and 65 DF,  p-value: 4.323e-06

#visualizations of corr relationship between state envy and anger, split by condition
corr_envyXanger <- ggplot(data = data_complete, mapping = aes(x = state_anger_composite, y=state_envy_composite, color = factor(game_condition_coded))) +
  geom_jitter(alpha=.3, size = 3) +
  geom_smooth(method = "lm", se = TRUE) +
  labs(
    x = "State Anger", 
    y = "State Envy", 
    title = "The Relationship Between State Anger and State Envy", 
    color = "Game Codition"
    ) +
  theme_minimal(base_size = 12) +
  theme(plot.title = element_text(hjust = 0.75))

ggsave("angerXenvy.png", plot = corr_envyXanger, width = 8, height = 6, units = "in", dpi = 300)

`geom_smooth()` using formula = 'y ~ x'

## Does game condition still predict anger (or envy) when controlling for envy (or anger)
summary(lm(data=data_complete, state_anger_composite ~ game_condition_coded * state_envy_composite))

Call:
lm(formula = state_anger_composite ~ game_condition_coded * state_envy_composite, 
    data = data_complete)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.5770 -0.1358 -0.0396 -0.0326  3.1952 

Coefficients:
                                           Estimate Std. Error t value Pr(>|t|)
(Intercept)                                0.032623   0.202771   0.161    0.873
game_condition_coded                       0.006991   0.259335   0.027    0.979
state_envy_composite                       0.386086   0.089074   4.334 5.27e-05
game_condition_coded:state_envy_composite -0.324509   0.271972  -1.193    0.237
                                             
(Intercept)                                  
game_condition_coded                         
state_envy_composite                      ***
game_condition_coded:state_envy_composite    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.7806 on 64 degrees of freedom
Multiple R-squared:  0.3209,    Adjusted R-squared:  0.2891 
F-statistic: 10.08 on 3 and 64 DF,  p-value: 1.58e-05

summary(lm(data=data_complete, state_envy_composite ~ game_condition_coded * state_anger_composite))

Call:
lm(formula = state_envy_composite ~ game_condition_coded * state_anger_composite, 
    data = data_complete)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.2117 -0.3159 -0.3159  0.4341  2.6941 

Coefficients:
                                           Estimate Std. Error t value Pr(>|t|)
(Intercept)                                  1.3059     0.2022   6.458 1.65e-08
game_condition_coded                        -0.9899     0.2754  -3.594 0.000633
state_anger_composite                        0.6039     0.1470   4.109 0.000115
game_condition_coded:state_anger_composite  -0.1918     0.8893  -0.216 0.829948
                                              
(Intercept)                                ***
game_condition_coded                       ***
state_anger_composite                      ***
game_condition_coded:state_anger_composite    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.03 on 64 degrees of freedom
Multiple R-squared:  0.4282,    Adjusted R-squared:  0.4014 
F-statistic: 15.98 on 3 and 64 DF,  p-value: 7.331e-08

# Create summary scores (mean, sd, ci95)
summary_emotions <- data_complete %>%
  pivot_longer(
    cols = c(state_envy_composite, state_anger_composite),
    names_to = "emotion",
    values_to = "score"
  ) %>%
  group_by(game_condition_coded, emotion) %>%
  summarize(
    mean_value = mean(score, na.rm = TRUE),
    sd = sd(score, na.rm = TRUE),
    n = sum(!is.na(score)),
    se = sd / sqrt(n),
    ci95 = 1.96 * se,
    .groups = "drop"
  )

summary_emotions

# A tibble: 4 × 7
  game_condition_coded emotion              mean_value    sd     n     se   ci95
                 <dbl> <chr>                     <dbl> <dbl> <int>  <dbl>  <dbl>
1                    0 state_anger_composi…     0.7    1.20     35 0.203  0.398 
2                    0 state_envy_composite     1.73   1.50     35 0.254  0.498 
3                    1 state_anger_composi…     0.0606 0.208    33 0.0361 0.0708
4                    1 state_envy_composite     0.341  0.537    33 0.0935 0.183 

# Bar Plot Mean Emotion Scores Between Game Conditions
ggplot(summary_emotions,
       aes(x = factor(game_condition_coded),
           y = mean_value,
           fill = emotion)) +
  geom_col(position = position_dodge(width = 0.9)) +
  geom_errorbar(aes(ymin = mean_value - ci95,
                    ymax = mean_value + ci95),
                position = position_dodge(width = 0.9),
                width = 0.2) +
  labs(
    title = "Mean Envy and Anger by Game Condition (with 95% CIs)",
    x = "Game Condition",
    y = "Mean Score",
    fill = "Emotion"
  ) +
  scale_fill_manual(values = c("red", "turquoise"),
                    labels = c("Anger", "Envy")) +
  scale_x_discrete(labels = c("Losers (0)", "Winners (1)")) +
  theme_bw(base_size = 14)

To examine the effects of the game on state anger, a Welch’s t-test revealed that losers reported significantly higher anger (\(M = 0.70, SD = 1.20\)) than winners (\(M = 0.06, SD = 0.21\)), \(t(36.15) = 3.10\), \(p = .004\). Next, we examined the relationship between state envy and anger. Regression analyses revealed that state envy significantly predicted anger,\(b = 0.34\), 95% CI \([0.18, 0.50]\), \(t(65) = 4.29\), \(p < .001\), controlling for dispositional envy. When both state envy and game condition were included in the model, game condition no longer significantly predicted anger (\(b = -0.15\), 95% CI \([-0.60, 0.29]\), \(t(65) = -0.68\), \(p = .499\)), suggesting that the initial effect of game condition on anger is likely attributable to its strong association with situational envy. The interaction for was excluded from the model because it was insignificant. Conversely, game condition remained a significant predictor of envy,\(b = -1.00\), 95% CI \([-1.53, -0.48]\), \(t(65) = -3.80\), \(p < .001\), and state anger significantly predicted state envy, . Interaction terms with game condition were nonsignificant in both regressions (all p > .2), indicating that the relationship between envy and anger did not differ between winners and losers.

Together, these results suggest that the game elicited higher anger among losers, but this effect is largely explained by situational envy rather than game outcome alone. These patterns are consistent with Recalibration Theory (Sell, 2011), which posits that anger primarily arises in response to perceived costs imposed by others rather than random outcomes.

####Game Condition on Situation Attributions

#library
library(dplyr)
library(ggplot2)
library(emmeans)
library(tidyr)

# --- transform reverse coded DVs ---
# Identify reverse-coded items
rev_vars <- c(
  "DV1_appraisal_deservingness_other_rev", 
  "DV1_appraisal_deservingness_self_rev", 
  "DV1_pleasantness_rev",
  "DV1_outcome_probability_rev",
  "DV1_reward_valence_rev"
)

max_scale <- 6

data_complete <- data_complete %>%
  mutate(across(all_of(rev_vars), ~ max_scale - .x))

# --- create different appraisal composites ---
data_complete <- data_complete %>%
  mutate(
    # Fairness / justice composite (higher = more fair)
    appraisal_fairness_composite = rowMeans(
      select(., DV1_appraisal_fairness, DV1_appraisal_injustice,
            DV1_appraisal_deservingness_other_rev, DV1_appraisal_deservingness_self_rev),
            na.rm = TRUE
        ),
    
    # Valence / pleasantness composite (higher = more positive)
    appraisal_valence_composite = rowMeans(
      select(., DV1_appraisal_valence, DV1_pleasantness_rev, DV1_reward_valence_rev, 
             DV1_appraisal_self_relevance),
             na.rm = TRUE
        ),
    
    # Control / probability composite (higher = more controllable / deterministic)
    appraisal_control_composite = rowMeans(
      select(., DV1_controllability, DV1_outcome_probability_rev),
             na.rm = TRUE
        )
  )

## --- summary statistics for the composites --- 
summary_appraisals <- data_complete %>%
  pivot_longer(
    cols = c(appraisal_fairness_composite, appraisal_valence_composite,
             appraisal_control_composite),
    names_to = "appraisal_type",
    values_to = "score"
  ) %>%
  group_by(game_condition_coded, appraisal_type) %>%
  summarize(
    mean_score = mean(score, na.rm = TRUE),
    sd = sd(score, na.rm = TRUE),
    n = sum(!is.na(score)),
    se = sd / sqrt(n),
    ci95 = 1.96 * se,
    .groups = "drop"
  )

summary_appraisals

# A tibble: 6 × 7
  game_condition_coded appraisal_type         mean_score    sd     n    se  ci95
                 <dbl> <chr>                       <dbl> <dbl> <int> <dbl> <dbl>
1                    0 appraisal_control_com…       3.34 1.19     35 0.202 0.395
2                    0 appraisal_fairness_co…       4.07 1.32     35 0.224 0.439
3                    0 appraisal_valence_com…       2.55 0.992    35 0.168 0.329
4                    1 appraisal_control_com…       3.91 0.914    33 0.159 0.312
5                    1 appraisal_fairness_co…       4.48 0.841    33 0.146 0.287
6                    1 appraisal_valence_com…       4.48 0.655    33 0.114 0.224

## -- compare appraisal types by group using ANCOVA (control for disp envy)

summary(lm(appraisal_fairness_composite ~ game_condition_coded, data = data_complete))

Call:
lm(formula = appraisal_fairness_composite ~ game_condition_coded, 
    data = data_complete)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.0714 -0.7348  0.0152  0.7652  1.9286 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)            4.0714     0.1886  21.585   <2e-16 ***
game_condition_coded   0.4134     0.2708   1.527    0.132    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.116 on 66 degrees of freedom
Multiple R-squared:  0.03412,   Adjusted R-squared:  0.01948 
F-statistic: 2.331 on 1 and 66 DF,  p-value: 0.1316

# no difference in the fairness judgements between conditions 


summary(lm(appraisal_valence_composite ~ game_condition_coded, data = data_complete))

Call:
lm(formula = appraisal_valence_composite ~ game_condition_coded, 
    data = data_complete)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.55000 -0.30000  0.01515  0.26515  1.95000 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)            2.5500     0.1430  17.836  < 2e-16 ***
game_condition_coded   1.9348     0.2052   9.428 7.61e-14 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.8458 on 66 degrees of freedom
Multiple R-squared:  0.5739,    Adjusted R-squared:  0.5674 
F-statistic: 88.88 on 1 and 66 DF,  p-value: 7.612e-14

# winners report more positive outcomes 

summary(lm(appraisal_control_composite ~ game_condition_coded, data = data_complete))

Call:
lm(formula = appraisal_control_composite ~ game_condition_coded, 
    data = data_complete)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.3429 -0.8429 -0.3429  0.5909  2.6571 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)            3.3429     0.1803  18.538   <2e-16 ***
game_condition_coded   0.5662     0.2589   2.187   0.0323 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.067 on 66 degrees of freedom
Multiple R-squared:  0.0676,    Adjusted R-squared:  0.05347 
F-statistic: 4.785 on 1 and 66 DF,  p-value: 0.03225

# winners report more control over outcome 

Game condition significantly influenced several appraisal outcomes. For the composite scores, winners rated outcomes as more positive (\(b = 1.93\), 95% CI \([1.53, 2.34]\), \(t(66) = 9.43\), \(p < .001\)) than losers. Winners also perceived themselves as having slightly more control over the outcome (\(b = 0.57\), 95% CI \([0.05, 1.08]\), \(t(66) = 2.19\), \(p = .032\)) than losers did. There was no difference in the fairness or deservedness ratings between groups. This likely reflects the random nature of the game. Visualizations of the differences between groups for all of the appraisal items and for the composites can be seen below.

library(ggplot2)
library(dplyr)
library(tidyr)

##visualizations of appraisals 
#Pivot DV1 items to long format
dv1_long <- data_complete %>%
  pivot_longer(
    cols = starts_with("DV1_"),
    names_to = "DV1_item",
    values_to = "score"
  )

# Compute mean by item and game condition
dv1_summary <- dv1_long %>%
  group_by(DV1_item, game_condition_coded) %>%
  summarize(
    mean_score = mean(score, na.rm = TRUE),
    sd = sd(score, na.rm = TRUE),
    n = sum(!is.na(score)),
    se = sd / sqrt(n),
    ci95 = 1.96 * se,
    .groups = "drop"
  )

# Plot
ggplot(dv1_summary, aes(x = DV1_item, y = mean_score, fill = factor(game_condition_coded))) +
  geom_col(position = position_dodge(width = 0.8)) +
  geom_errorbar(aes(ymin = mean_score - ci95, ymax = mean_score + ci95),
                position = position_dodge(width = 0.8), width = 0.2) +
  labs(
    title = "Mean DV1 Appraisals by Game Condition",
    x = "Item",
    y = "Mean Score",
    fill = "Game Condition"
  ) +
  scale_fill_manual(values = c("lightblue", "darkblue"), labels = c("Loser (0)", "Winner (1)")) +
  theme_bw(base_size = 10) +
  theme(axis.text.x = element_text(angle = 50, hjust = 1))

## for composite 
# Pivot composites to long format
composite_long <- data_complete %>%
  pivot_longer(
    cols = c(appraisal_fairness_composite, appraisal_valence_composite,
             appraisal_control_composite),
    names_to = "composite",
    values_to = "score"
  )

# Compute mean, SE, CI
composite_summary <- composite_long %>%
  group_by(composite, game_condition_coded) %>%
  summarize(
    mean_score = mean(score, na.rm = TRUE),
    sd = sd(score, na.rm = TRUE),
    n = sum(!is.na(score)),
    se = sd / sqrt(n),
    ci95 = 1.96 * se,
    .groups = "drop"
  )

# Plot
ggplot(composite_summary, aes(x = composite, y = mean_score, fill = factor(game_condition_coded))) +
  geom_col(position = position_dodge(width = 0.8)) +
  geom_errorbar(aes(ymin = mean_score - ci95, ymax = mean_score + ci95),
                position = position_dodge(width = 0.8), width = 0.2) +
  labs(
    title = "Appraisal Composites by Game Condition",
    x = "Composite",
    y = "Mean Score",
    fill = "Game Condition"
  ) +
  scale_fill_manual(values = c("orangered", "turquoise"), labels = c("Loser (0)", "Winner (1)")) +
  theme_bw(base_size = 12) +
  theme(axis.text.x = element_text(angle = 33, hjust = 1))

Discussion

Summary of Replication Attempt

The primary result successfully replicated the original finding. Participants who did not receive the reward reported significantly higher envy toward their partner than those who did receive the reward, even when controlling for anger. This mirrors the pattern observed in the original study. Additionally, the original study reported a strong positive relationship between dispositional and situational envy. Our results align with this finding, indicating that individuals with higher dispositional envy experience greater envy in upward comparison situations. Overall, these results replicate the key findings of the original study and suggest that this paradigm can be effectively extended to an online format.

Commentary

People experience envy in situations where someone possesses something they desire, and the intensity of this emotion may vary depending on individual dispositions. This study replicates previous findings that the Dispositional State Envy Scale (DSES) is a valid measure of dispositional envy and provides evidence that this paradigm can be used to evoke envy in online formats.

One concern in designing this study was whether the game of rock-paper-scissors could serve as a reliable paradigm for eliciting envy. A common challenge with envy paradigms is the specificity of the targeted emotion. While upward social comparison often evokes envy, it can also trigger related emotions such as anger, sadness, inequity aversion, or general negative affect (Parrott, 1991). Our exploratory analyses provide some support for the envy-specificity of this design: the game condition did not significantly affect anger when controlling for envy, and there were no significant group differences in appraisals related to fairness.

Moving forward, I aim to extend this research to further establish that the observed effects are specific to envy rather than inequity aversion (i.e., feeling sensitive towards disadvantageous inequity, not envious). Additionally, I hope to gain deeper insights into the differences in cognitive appraisals between envy and anger—a topic I am currently pursuing in my graduate research.

References

Parrott, W. G. (1991). Experiences of envy and jealousy. The psychology of jealousy and envy, 1991, 3-30.

Patel, M., Bullinaria, J. A., & Levy, J. P. (1997). Extracting semantic representations from large text corpora. In J. A. Bullinaria, D. W. Glasspool, & G. Houghton (Eds.), Fourth Neural Computation and Psychology Workshop: Connectionist Representations (pp. 199-212). London: Springer.

Rentzsch, K., & Gross, J. J. (2015). Who Turns Green with Envy? Conceptual and Empirical Perspectives on Dispositional Envy. European Journal of Personality, 29(5), 530–547. https://doi.org/10.1002/per.2012

Rentzsch, K., Giese, A.-K., Hebel, V., & Lösch, T. (2023). Personality and Emotions in Social Interactions – The PESI Project. Personality Science, 4(1), e8241. https://doi.org/10.5964/ps.8241

Sell, A. N. (2011). The recalibrational theory and violent anger. Aggression and Violent Behavior, 16(5), 381–389. https://doi.org/10.1016/j.avb.2011.04.013