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Data processing

1. Descriptive data Outgroup

1.1 Table over Participants:

Characteristic N = 7411
Age 41 (33, 53)
Ethnicity.simplified
    Black 369 (50%)
    White 372 (50%)
Country.of.residence
    United States 741 (100%)
Highest.education.level.completed
    Doctorate degree (PhD/other) 22 (3.0%)
    Graduate degree (MA/MSc/MPhil/other) 108 (15%)
    High school diploma/A-levels 175 (24%)
    Secondary education (e.g. GED/GCSE) 19 (2.6%)
    Technical/community college 115 (16%)
    Undergraduate degree (BA/BSc/other) 302 (41%)
Employment.status
    DATA_EXPIRED 156 (21%)
    Due to start a new job within the next month 4 (0.5%)
    Full-Time 329 (44%)
    Not in paid work (e.g. homemaker', 'retired or disabled) 72 (9.7%)
    Other 14 (1.9%)
    Part-Time 98 (13%)
    Unemployed (and job seeking) 68 (9.2%)
1 Median (IQR); n (%)

1.2 Table displaying means for most important variables:

1.3 Scatterplots for Empathic reactions & Donation:

1.3.1 Scatterplots for Empathic reactions & Donation for Control:

1.3.2 Scatterplots for Empathic reactions & Donation for Limited:

1.3.3 Scatterplots for Empathic reactions & Donation for Unlimited:

1.3.4 Scatterplots for Empathic reactions & Donation for Malleable:

1.3.5 Scatterplots for Empathic reactions & Donation for Normative:

1.4. Scatterplots for Empathic drivers & Donation:

1.4.1 Scatterplots for Empathic drivers & Donation for Control:

1.4.2 Scatterplots for Empathic drivers & Donation for Limited:

1.4.3 Scatterplots for Empathic drivers & Donation for Unlimited:

1.4.4 Scatterplots for Empathic reactions & Donation for Malleable:

1.4.5 Scatterplots for Empathic drivers & Donation for Normative:

1.5. Scatterplots for Empathic beliefs & Donation:

1.5.1 Scatterplots for Empathic beliefs & Donation for Control:

1.4.2 Scatterplots for Empathic beliefs & Donation for Limited:

1.5.3 Scatterplots for Empathic beliefs & Donation for Unlimited:

1.5.4 Scatterplots for Empathic beliefs & Donation for Malleable:

1.5.5 Scatterplots for Empathic beliefs & Donation for Normative:

1.6 Correlation matrix for Empathy measures, Donation & Intervention for Outgroup:

1.6.1 Correlation matrix for Control:

1.6.2 Correlation matrix for Limited:

1.6.3 Correlation matrix for Unlimitied:

1.6.4 Correlation matrix for Malleable:

1.6.5 Correlation matrix for Normative:

1.7. Cronbach’s Alpha for Empathic reactions:

## 
## Cronbach's alpha for the 'empathic_reactions_df' data-set
## 
## Items: 3
## Sample units: 741
## alpha: 0.932

1.7.1 Cronbach’s Alpha for Empathic drivers:

## 
## Cronbach's alpha for the 'empathic_drivers_df' data-set
## 
## Items: 3
## Sample units: 741
## alpha: 0.812

1.7.2 Cronbach’s Alpha for Empathic beliefs:

## 
## Cronbach's alpha for the 'empathic_beliefs_df' data-set
## 
## Items: 3
## Sample units: 741
## alpha: 0.524

2. Replication of Hasson et als results

We look at manipulation check and contrasts between conditions for groups Outgroup (i.e. participants that stated that they perceived protagonist as an outgroup member) and Whole group (i.e. all participants).

2.1 Outgroup

Manipulation check:

Background:

“Regarding the manipulation check, an independent-samples t-test revealed a significant effect of condition, t(1, 198) = −4.11, p < 0.001, d = 0.58, such that participants in the unlimited condition believed empathy is unlimited (M = 4.92, SD = 1.89) more than did those in the limited condition (M = 3.9, SD = 1.58).”, Hasson et al(2022).

2.1.1 tibble with mean and sd on manipulation checks between conditions for Outgroup:

## # A tibble: 5 × 3
##   condition  mean    sd
##   <chr>     <dbl> <dbl>
## 1 Control    4.84  2.25
## 2 Limited    4.34  2.00
## 3 Malleable  4.66  2.21
## 4 Normative  4.65  2.23
## 5 Unlimited  5.33  1.95

2.1.2 anova to test manipulation check between conditions for Outgroup:

##              Df Sum Sq Mean Sq F value Pr(>F)   
## condition     4     77  19.209   4.219 0.0022 **
## Residuals   736   3351   4.553                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

2.1.3 Plotting manipulation check for Outgroup:

Contrasting conditions on Empathic reactions

Background:

“To test whether the manipulation influenced empathic reactions in response to each Syrian refugee’s testimony, we ran a repeated-measures ANOVA with testimony order (1–4) as a within-participant variable, and the condition (unlimited vs. limited) as a between-participants variable. We used testimony order as the within-participant variable because all testimonies were presented in a counterbalanced order to rule out the possibility that the content of the testimonies influences the results. We found a significant main effect of condition on empathic reactions, F(1, 198) = 8.93, p = 0.003, d = 0.423. On average, participants in the unlimited condition felt more empathy toward the outgroup members (M = 5.82, SD = 1.43), compared to those in the limited condition (M = 5.18, SD = 1.60). Pairwise comparisons between the effects of limited and unlimited conditions on empathy in each testimony were all significant (Testimony #1: p < 0.001; Testimony #2: p = 0.003; Testimony #3: p = 0.037; Testimony #4: p = 0.013). Moreover, we found a significant Testimony Order × Condition interaction, F(1, 196) = 2.78, p = 0.042, d = 0.41 (Fig. 2). While empathy changed across stories in the limited condition (between testimonies #1 and #4; p = 0.021), empathy remained stable in the unlimited condition, and there were no significant differences across stories (between testimonies #1 and #4; p = 0.917).”, Hasson et al (2022).

Testing H1a - For Empathic reactions we hypothesize the following directional relationships: Malleable == Unlimited > Social Norm > Limited == Control - to test if results from Hasson et als article replicate.

2.1.4 Plotting mean differences on Empathic reactions between Conditions for Outgroup:

2.1.5 Mean difference between Unlimited vs Control:

## [1] -0.04098423

Quantile interval:

##       2.5%      97.5% 
## -0.2640912  0.1817685

Histogram showing Mean difference between Unlimited & Control:

2.1.6 Mean difference for Malleable vs Control:

## [1] -0.1318073

Quantile interval:

##       2.5%      97.5% 
## -0.3606882  0.0932938

Histogram showing Mean difference between Malleable & Control:

2.1.7 Mean difference for Normative vs Control:

## [1] -0.08704801

Quantile interval:

##       2.5%      97.5% 
## -0.3170253  0.1441882

Histogram showing Mean difference between Normative & Control:

2.1.8 Mean difference for Limited vs Control:

## [1] -0.2503176

Quantile interval:

##        2.5%       97.5% 
## -0.47869445 -0.01976661

Histogram showing Mean difference between Limited & Control:

2.1.9 Mean difference for Unlimited vs Limited:

## [1] 0.2093334

Quantile interval:

##        2.5%       97.5% 
## -0.01802047  0.43670932

Histogram showing Mean difference between Unlimited & Limited:

2.1.10 Mean difference for Malleable vs Limited:

## [1] 0.1185103

Quantile interval:

##        2.5%       97.5% 
## -0.09948274  0.33956760

Histogram showing Mean difference between Malleable & Limited:

2.1.11 Mean difference for Normative vs Limited:

## [1] 0.1632696

Quantile interval:

##        2.5%       97.5% 
## -0.05790945  0.38196276

Histogram showing Mean difference between Normative & Limited:

2.1.12 Cohens d for condition Limited & Unlimited:

## [1] 0.2089973

Conclusion H1a for Outgroup:

There is a hypothesized mean difference between conditions Control & Limited (.25) and condition Unlimited & Limited (0.21) for Empathic reactions. For the rest of the contrast, HDI does not exclude zero and therefore we conclude no hypothesized mean difference between these conditions for Empathic reactions.

2.2 Whole group

Manipulation check:

2.2.1 tibble with mean and sd for manipulation check for whole group:

## # A tibble: 5 × 3
##   condition  mean    sd
##   <chr>     <dbl> <dbl>
## 1 Control    4.76  2.21
## 2 Limited    4.43  2.00
## 3 Malleable  4.82  2.11
## 4 Normative  4.72  2.16
## 5 Unlimited  5.32  1.99

2.2.2 anova to test conditions for manipulation check for whole group:

##              Df Sum Sq Mean Sq F value  Pr(>F)   
## condition     4     72  18.122   4.123 0.00257 **
## Residuals   885   3890   4.396                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

2.2.3 Plotting manipulation check for whole group:

Contrasting conditions on Empathic reactions

Testing H1a - For Empathic reactions we hypothesize the following directional relationships: Malleable == Unlimited > Social Norm > Limited == Control - to test if results from Hasson et als article replicate.

2.2.4 Plotting mean differences on Empathic reactions between Conditions for Whole group:

2.2.5 Mean difference Unlimited vs Control:

## [1] 0.05643339

Quantile interval:

##       2.5%      97.5% 
## -0.1540099  0.2673820

Histogram showing Mean difference between Unlimited & Control:

2.2.6 Mean difference for Malleable vs Control:

## [1] -0.04619456

Quantile interval:

##       2.5%      97.5% 
## -0.2602826  0.1697739

Histogram showing Mean difference between Malleable & Control:

2.2.7 Mean difference for Normative vs Control:

## [1] -0.01747514

Quantile interval:

##       2.5%      97.5% 
## -0.2171557  0.1876975

Histogram showing Mean difference between Normative & Control:

2.2.8 Mean difference for Limited vs Control:

## [1] -0.1407821

Quantile interval:

##       2.5%      97.5% 
## -0.3452505  0.0655318

Histogram showing Mean difference between Limited & Control:

2.2.9 Mean difference for Unlimited vs Limited:

## [1] 0.1972155

Quantile interval:

##         2.5%        97.5% 
## -0.006665762  0.403572093

Histogram showing Mean difference between Unlimited & Limited:

2.2.10 Mean difference for Malleable vs Limited:

## [1] 0.09458758

Quantile interval:

##       2.5%      97.5% 
## -0.1107544  0.2989768

Histogram showing Mean difference between Malleable & Limited:

2.2.11 Mean difference for Normative vs Limited:

## [1] 0.123307

Quantile interval:

##        2.5%       97.5% 
## -0.08530215  0.33165025

Histogram showing Mean difference between Normative & Limited:

2.2.12 Cohens d for Limited & Unlimited:

## [1] 0.1946075

Conclusion H1a for Whole group:

There is a hypothesized mean difference between conditions Unlimited & Limited (.2) for Empathic reactions. For the rest of the contrasts, HDI does not exclude zero and therefore we conclude no hypothesized mean difference between these conditions for Empathic reactions.

General conclusion:

We replicate Hasson et als results for both groups, Outgroup and Whole group, that is - there is a hypothesized mean difference between condition Limited & Unlimited for Empathic reactions. Importantly, there is no difference between condition Unlimited & Control, or Unlimited and the other conditions for both groups. This suggests that the difference between Limited & Unlimited is partly driven by a negative impact on Empathic reactions caused by condition Limited. In accordance with this suggestion, we also found a mean difference between Limited & Condition for Outgroup.

3. Modeling Empathic drivers

H1b - For Empathic drivers we hypothesize the following directional relationships: Malleable == Unlimited > Social Norm > Limited == Control.

##  Family: gaussian 
##   Links: mu = identity; sigma = identity 
## Formula: empathic_reactions_z ~ 0 + condition 
##    Data: outgroup (Number of observations: 741) 
##   Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
##          total post-warmup draws = 4000
## 
## Population-Level Effects: 
##                    Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## conditionControl       0.10      0.08    -0.06     0.26 1.00     5827     2859
## conditionLimited      -0.15      0.08    -0.31     0.01 1.00     6052     3047
## conditionMalleable    -0.03      0.08    -0.19     0.13 1.00     6483     2935
## conditionNormative     0.01      0.08    -0.14     0.18 1.00     5488     3335
## conditionUnlimited     0.06      0.08    -0.10     0.22 1.00     5771     2812
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     1.00      0.03     0.95     1.05 1.00     5951     2809
## 
## Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: Dropping 'draws_df' class as required metadata was removed.
##       b_conditionControl b_conditionLimited b_conditionMalleable
## 2.5%          -0.1702859        -0.26659882           -0.1605880
## 97.5%          0.1407791         0.05476715            0.1671147
##       b_conditionNormative b_conditionUnlimited
## 2.5%           -0.05879902           -0.1469587
## 97.5%           0.26525970            0.1753830

Mean difference for Unlimited vs Control

## [1] 0.02863183

Quantile interval

##       2.5%      97.5% 
## -0.1986312  0.2564561

The HDI does not exclude zero, so we conclude no hypothesized difference between condition Control and Unlimitied for Empathic drivers

Mean difference for Malleable vs Control

## [1] 0.01720522

Quantile interval

##       2.5%      97.5% 
## -0.2068777  0.2415954

The HDI does not exclude zero, so we conclude no hypothesized difference between condition Malleable and Unlimitied for Empathic drivers

Mean difference for Normative vs Control

## [1] 0.1181297

Quantile interval

##       2.5%      97.5% 
## -0.1093017  0.3505581

The HDI does not exclude zero, so we conclude no hypothesized difference between condition Normative and Unlimitied for Empathic drivers

H1c - For Donated money we hypothesize the following directional relationships: Malleable == Unlimited > Social Norm > Limited == Control.

BRMS model empathic drivers

##  Family: gaussian 
##   Links: mu = identity; sigma = identity 
## Formula: donation_z ~ 0 + condition 
##    Data: outgroup (Number of observations: 741) 
##   Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
##          total post-warmup draws = 4000
## 
## Population-Level Effects: 
##                    Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## conditionControl      -0.01      0.08    -0.17     0.14 1.00     5571     2979
## conditionLimited      -0.03      0.08    -0.19     0.13 1.00     5159     2871
## conditionMalleable    -0.03      0.08    -0.19     0.14 1.00     5463     2672
## conditionNormative     0.11      0.08    -0.05     0.28 1.00     5427     3302
## conditionUnlimited    -0.03      0.08    -0.20     0.13 1.00     5833     3185
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     1.00      0.03     0.95     1.05 1.00     6963     3278
## 
## Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: Dropping 'draws_df' class as required metadata was removed.
##       b_conditionControl b_conditionLimited b_conditionMalleable
## 2.5%          -0.1688229         -0.1938809           -0.1880629
## 97.5%          0.1423076          0.1282579            0.1353247
##       b_conditionNormative b_conditionUnlimited
## 2.5%           -0.04986123           -0.1968648
## 97.5%           0.27561948            0.1319767

Mean difference for Unlimited vs Control

## [1] -0.01859229

Quantile interval

##       2.5%      97.5% 
## -0.2371990  0.2159797

The HDI does not exclude zero, so we conclude no hypothesized difference between condition Control and Unlimitied for Donation

Mean difference for Malleable vs Control

## [1] -0.01199492

Quantile interval

##       2.5%      97.5% 
## -0.2417528  0.2144014

The HDI does not exclude zero, so we conclude no hypothesized difference between condition Malleable and Unlimitied for Donation

Mean difference for Normative vs Control

## [1] 0.1228901

Quantile interval

##       2.5%      97.5% 
## -0.1005301  0.3581822

The HDI does not exclude zero, so we conclude no hypothesized difference between condition Normative and Unlimitied for Donation