Taboo Transactions: Informed/Uninformed X Rational/Irrational Seller Replication
Background
In a 2 (informed vs. uninformed) X 2 (rational vs. irrational) between-subjects design, participants read about a transaction involving storing hazardous chemicals, and were asked to indicate to what extent the seller benefited from each of them, to what extent the buyer benefited from each of them, and the power balance in each of them.
Attention check
What are the roles of Person A and Person B in the transaction
that took place?
The correct answer is: Person A paid money and Person B received
money
| informed | rational | failcheck | passcheck |
|---|---|---|---|
| 0 | 0 | 5 | 199 |
| 0 | 1 | 5 | 197 |
| 1 | 0 | 7 | 194 |
| 1 | 1 | 10 | 194 |
Alright, that leaves us with 784. Let’s see how participants fared with the manipulation checks:
Manipulation checks
Participants responded indicated whether the following statements are
TRUE or FALSE:
1. They have been given all the available information about the
risks associated with this transaction
2. They have the ability to think rationally about this
transaction
| informed | rational | pass_both | fail_rational | fail_informed | fail_both |
|---|---|---|---|---|---|
| 0 | 0 | 173 | 13 | 5 | 8 |
| 0 | 1 | 159 | 33 | 3 | 2 |
| 1 | 0 | 159 | 18 | 12 | 5 |
| 1 | 1 | 184 | 2 | 5 | 3 |
Ok, they had the hardest time with 1-0 and 0-1 combinations, which is understandable. But still pretty good. We’ll run all analyses with and without them, as preregistered.
Demographics
Race
| race | N | Perc |
|---|---|---|
| asian | 59 | 7.53 |
| black | 93 | 11.86 |
| hispanic | 32 | 4.08 |
| multiracial | 42 | 5.36 |
| white | 550 | 70.15 |
| NA | 8 | 1.02 |
Gender
| gender | N | Perc |
|---|---|---|
| man | 375 | 47.83 |
| woman | 397 | 50.64 |
| NA | 12 | 1.53 |
Age
| age_mean | age_sd |
|---|---|
| 39.42347 | 12.34681 |
Education
| edu | N | Perc |
|---|---|---|
| noHS | 2 | 0.26 |
| GED | 224 | 28.57 |
| 2yearColl | 85 | 10.84 |
| 4yearColl | 337 | 42.98 |
| MA | 103 | 13.14 |
| PHD | 30 | 3.83 |
| NA | 3 | 0.38 |
Income
Analysis (ALL PARTICIPANTS WHO PASSED ATTENTION CHECK)
Condition -> Benefit A
To avoid a three-way interaction, I’ll look at the effect of condition on each party’s benefit separately. And only then I’ll show everything in one plot.
Descriptives
| informed | rational | benefit_A_M | benefit_A_SD |
|---|---|---|---|
| 0 | 0 | 2.16 | 1.14 |
| 0 | 1 | 2.08 | 1.29 |
| 1 | 0 | 1.94 | 1.06 |
| 1 | 1 | 2.01 | 1.05 |
Benefit A: Two-way ANOVA
| Effect | DFn | DFd | F | p | p<.05 | ges |
|---|---|---|---|---|---|---|
| informed | 1 | 780 | 3.028 | 0.082 | 4.00e-03 | |
| rational | 1 | 780 | 0.012 | 0.914 | 1.51e-05 | |
| informed:rational | 1 | 780 | 0.868 | 0.352 | 1.00e-03 |
Great. No effect on buyer’s benefit. So far so good.
Condition -> Benefit B
Let’s take a look at the seller.
Descriptives
| informed | rational | benefit_B_M | benefit_B_SD |
|---|---|---|---|
| 0 | 0 | -1.69 | 1.46 |
| 0 | 1 | -1.63 | 1.54 |
| 1 | 0 | -0.98 | 1.61 |
| 1 | 1 | 0.02 | 1.77 |
Benefit B: Two-way ANOVA
| Effect | DFn | DFd | F | p | p<.05 | ges |
|---|---|---|---|---|---|---|
| informed | 1 | 780 | 105.917 | 0.00e+00 |
|
0.120 |
| rational | 1 | 780 | 21.531 | 4.10e-06 |
|
0.027 |
| informed:rational | 1 | 780 | 17.000 | 4.14e-05 |
|
0.021 |
Main effects and interaction. Cool cool.
Benefit B: Planned contrasts
Here, we’ll compare the rational/informed condition to the rest of the conditions with a planned contrasts analysis.
| Â | Df | Sum Sq | Mean Sq | F value | Pr(>F) |
|---|---|---|---|---|---|
| cond | 3 | 367.7 | 122.6 | 48.03 | 1.723e-28 |
| Residuals | 780 | 1991 | 2.552 | NA | NA |
Bonferroni-corrected post-hoc comparisons: Rational
| rational | Effect | DFn | DFd | F | p | p<.05 | ges | p.adj |
|---|---|---|---|---|---|---|---|---|
| 0 | informed | 1 | 391 | 20.605 | 7.5e-06 |
|
0.050 | 1.51e-05 |
| 1 | informed | 1 | 389 | 96.427 | 0.0e+00 |
|
0.199 | 0.00e+00 |
Bonferroni-corrected post-hoc comparisons: Informed
| informed | Effect | DFn | DFd | F | p | p<.05 | ges | p.adj |
|---|---|---|---|---|---|---|---|---|
| 0 | rational | 1 | 394 | 0.153 | 0.695 | 0.000389 | 1 | |
| 1 | rational | 1 | 386 | 33.856 | 0.000 |
|
0.081000 | 0 |
Plot: Condition -> Buyer and Seller Benefit
That’s great stuff. As predicted!
Condition -> Power
Let’s take a look at the effect on power. Power was rated from -3 (Buyer has much more power) to 3 (Seller has much more power).
Descriptives
| informed | rational | power_M | power_SD |
|---|---|---|---|
| 0 | 0 | -1.75 | 1.42 |
| 0 | 1 | -1.41 | 1.67 |
| 1 | 0 | -1.16 | 1.54 |
| 1 | 1 | -0.01 | 1.68 |
Power: Two-way ANOVA
| Effect | DFn | DFd | F | p | p<.05 | ges |
|---|---|---|---|---|---|---|
| informed | 1 | 780 | 77.331 | 0.000000 |
|
0.090 |
| rational | 1 | 780 | 44.315 | 0.000000 |
|
0.054 |
| informed:rational | 1 | 780 | 13.108 | 0.000313 |
|
0.017 |
Power: Planned contrasts
Here, we’ll compare the rational/informed condition to the rest of the conditions with a planned contrasts analysis.
| Â | Df | Sum Sq | Mean Sq | F value | Pr(>F) |
|---|---|---|---|---|---|
| cond | 3 | 335.4 | 111.8 | 44.8 | 1.019e-26 |
| Residuals | 780 | 1947 | 2.496 | NA | NA |
Bonferroni-corrected post-hoc comparisons: Rational
| rational | Effect | DFn | DFd | F | p | p<.05 | ges | p.adj |
|---|---|---|---|---|---|---|---|---|
| 0 | informed | 1 | 391 | 15.219 | 0.000113 |
|
0.037 | 0.000226 |
| 1 | informed | 1 | 389 | 68.682 | 0.000000 |
|
0.150 | 0.000000 |
Bonferroni-corrected post-hoc comparisons: Informed
| informed | Effect | DFn | DFd | F | p | p<.05 | ges | p.adj |
|---|---|---|---|---|---|---|---|---|
| 0 | rational | 1 | 394 | 4.846 | 0.028 |
|
0.012 | 0.056 |
| 1 | rational | 1 | 386 | 50.278 | 0.000 |
|
0.115 | 0.000 |
Plot: Condition -> Power
Great stuff.
Mediation model 1: informed -> power -> seller benefit
0 = uninformed; 1 = informed
a = 0.99 (p = 0); b = 0.39 (p = 0); direct = 1.17
(p = 0); indirect = 0.79 (p = 0).
Mediation model 2: rational -> power -> seller benefit
0 = irrational; 1 = rational
a = 0.75 (p = 0); b = 0.44 (p = 0); direct = 0.53 (p = 0); indirect = 0.2 (p = 0.082).
Mediation model 3: Interaction term -> power -> seller benefit
fitM <- lm(power ~ informed*rational, data = df_tt_elg) #linear model with interaction term predicting the mediator
fitY <- lm(benefit_B~ informed*rational + power, data = df_tt_elg) #linear model with interaction term predicting the outcome, adjusting for the mediator
fitMedBoot <- mediation::mediate(fitM,fitY,boot = T,sims = 10000,treat = "informed",mediator = "power") #mediation model with 10,000 bootstrap
pander(summary(fitMedBoot$model.m))| Â | Estimate | Std. Error | t value | Pr(>|t|) |
|---|---|---|---|---|
| (Intercept) | -1.749 | 0.112 | -15.62 | 4.916e-48 |
| informed | 0.5838 | 0.1594 | 3.663 | 0.0002665 |
| rational | 0.3427 | 0.1588 | 2.158 | 0.03123 |
| informed:rational | 0.8171 | 0.2257 | 3.621 | 0.000313 |
| Observations | Residual Std. Error | \(R^2\) | Adjusted \(R^2\) |
|---|---|---|---|
| 784 | 1.58 | 0.147 | 0.1437 |
pander(summary(fitMedBoot$model.y))| Â | Estimate | Std. Error | t value | Pr(>|t|) |
|---|---|---|---|---|
| (Intercept) | -1.068 | 0.1216 | -8.785 | 9.822e-18 |
| informed | 0.4968 | 0.1523 | 3.261 | 0.001156 |
| rational | -0.06255 | 0.1509 | -0.4146 | 0.6786 |
| power | 0.3547 | 0.03393 | 10.46 | 4.913e-24 |
| informed:rational | 0.6511 | 0.2156 | 3.019 | 0.002616 |
| Observations | Residual Std. Error | \(R^2\) | Adjusted \(R^2\) |
|---|---|---|---|
| 784 | 1.497 | 0.2598 | 0.256 |
plot(fitMedBoot)
Moderated mediation
using this guide: https://cran.r-project.org/web/packages/manymome/vignettes/mome_lm.html
library(manymome)
#path parameters, estimated by two multiple regressions
lm_m <- lm(power ~ informed*rational,df_tt_elg)
lm_y <- lm(benefit_B ~ power + informed,df_tt_elg)
#combine into one object
fit_lm <- lm2list(lm_m,lm_y)
#generating bootstrap estimated
boot_out_lm <- do_boot(fit_lm,
R = 10000,
seed = 54532,
ncores = 1)
#conditional indirect effects
out_xmy_on_w <- cond_indirect_effects(wlevels = "rational",
x = "informed",
y = "benefit_B",
m = "power",
fit = fit_lm,
boot_ci = TRUE,
boot_out = boot_out_lm)
#index of moderated mediation
out_mome <- index_of_mome(x = "informed",
y = "benefit_B",
m = "power",
w = "rational",
fit = fit_lm,
boot_ci = TRUE,
boot_out = boot_out_lm)
#standardized conditional indirect effects
std_xmy_on_w <- cond_indirect_effects(wlevels = "rational",
x = "informed",
y = "benefit_B",
m = "power",
fit = fit_lm,
boot_ci = TRUE,
boot_out = boot_out_lm,
standardized_x = TRUE,
standardized_y = TRUE)
std_xmy_on_w##
## == Conditional indirect effects ==
##
## Path: informed -> power -> benefit_B
## Conditional on moderator(s): rational
## Moderator(s) represented by: rational
##
## [rational] (rational) std CI.lo CI.hi Sig power~informed benefit_B~power
## 1 M+1.0SD 0.999 0.156 0.110 0.207 Sig 1.400 0.385
## 2 Mean 0.499 0.110 0.080 0.144 Sig 0.991 0.385
## 3 M-1.0SD -0.002 0.065 0.032 0.100 Sig 0.582 0.385
## ind
## 1 0.540
## 2 0.382
## 3 0.225
##
## - [CI.lo to CI.hi] are 95.0% percentile confidence intervals by
## nonparametric bootstrapping with 10000 samples.
## - std: The standardized indirect effects.
## - ind: The unstandardized indirect effects.
## - 'power~informed','benefit_B~power' is/are the path coefficient(s)
## along the path conditional on the moderators.Using this guide: http://www.regorz-statistik.de/en/moderated_mediation_process_for_r.html
# PROCESS Model 7
process(data = df_tt_elg,
y = "benefit_B",
x = "informed",
m = "power",
w = "rational",
model = 7,
center = 2,
moments = 1,
modelbt = 1,
boot = 10000,
seed = 654321)##
## ********************* PROCESS for R Version 4.3.1 *********************
##
## Written by Andrew F. Hayes, Ph.D. www.afhayes.com
## Documentation available in Hayes (2022). www.guilford.com/p/hayes3
##
## ***********************************************************************
##
## Model : 7
## Y : benefit_B
## X : informed
## M : power
## W : rational
##
## Sample size: 784
##
## Custom seed: 654321
##
##
## ***********************************************************************
## Outcome Variable: power
##
## Model Summary:
## R R-sq MSE F df1 df2 p
## 0.3834 0.1470 2.4957 44.8013 3.0000 780.0000 0.0000
##
## Model:
## coeff se t p LLCI ULCI
## constant -1.7487 0.1120 -15.6154 0.0000 -1.9686 -1.5289
## informed 0.5838 0.1594 3.6626 0.0003 0.2709 0.8967
## rational 0.3427 0.1588 2.1581 0.0312 0.0310 0.6543
## Int_1 0.8171 0.2257 3.6205 0.0003 0.3741 1.2602
##
## Product terms key:
## Int_1 : informed x rational
##
## Test(s) of highest order unconditional interaction(s):
## R2-chng F df1 df2 p
## X*W 0.0143 13.1082 1.0000 780.0000 0.0003
## ----------
## Focal predictor: informed (X)
## Moderator: rational (W)
##
## Conditional effects of the focal predictor at values of the moderator(s):
## rational effect se t p LLCI ULCI
## 0.0000 0.5838 0.1594 3.6626 0.0003 0.2709 0.8967
## 1.0000 1.4009 0.1598 8.7673 0.0000 1.0873 1.7146
##
## ***********************************************************************
## Outcome Variable: benefit_B
##
## Model Summary:
## R R-sq MSE F df1 df2 p
## 0.4962 0.2462 2.2760 127.5625 2.0000 781.0000 0.0000
##
## Model:
## coeff se t p LLCI ULCI
## constant -1.0508 0.0920 -11.4229 0.0000 -1.2313 -0.8702
## informed 0.7917 0.1126 7.0286 0.0000 0.5706 1.0129
## power 0.3854 0.0330 11.6763 0.0000 0.3206 0.4502
##
## ***********************************************************************
## Bootstrapping progress:
##
|
| | 0%
|
| | 1%
|
|> | 1%
|
|> | 2%
|
|>> | 2%
|
|>> | 3%
|
|>> | 4%
|
|>>> | 4%
|
|>>> | 5%
|
|>>> | 6%
|
|>>>> | 6%
|
|>>>> | 7%
|
|>>>>> | 7%
|
|>>>>> | 8%
|
|>>>>> | 9%
|
|>>>>>> | 9%
|
|>>>>>> | 10%
|
|>>>>>>> | 10%
|
|>>>>>>> | 11%
|
|>>>>>>> | 12%
|
|>>>>>>>> | 12%
|
|>>>>>>>> | 13%
|
|>>>>>>>> | 14%
|
|>>>>>>>>> | 14%
|
|>>>>>>>>> | 15%
|
|>>>>>>>>>> | 15%
|
|>>>>>>>>>> | 16%
|
|>>>>>>>>>> | 17%
|
|>>>>>>>>>>> | 17%
|
|>>>>>>>>>>> | 18%
|
|>>>>>>>>>>> | 19%
|
|>>>>>>>>>>>> | 19%
|
|>>>>>>>>>>>> | 20%
|
|>>>>>>>>>>>>> | 20%
|
|>>>>>>>>>>>>> | 21%
|
|>>>>>>>>>>>>> | 22%
|
|>>>>>>>>>>>>>> | 22%
|
|>>>>>>>>>>>>>> | 23%
|
|>>>>>>>>>>>>>>> | 23%
|
|>>>>>>>>>>>>>>> | 24%
|
|>>>>>>>>>>>>>>> | 25%
|
|>>>>>>>>>>>>>>>> | 25%
|
|>>>>>>>>>>>>>>>> | 26%
|
|>>>>>>>>>>>>>>>> | 27%
|
|>>>>>>>>>>>>>>>>> | 27%
|
|>>>>>>>>>>>>>>>>> | 28%
|
|>>>>>>>>>>>>>>>>>> | 28%
|
|>>>>>>>>>>>>>>>>>> | 29%
|
|>>>>>>>>>>>>>>>>>> | 30%
|
|>>>>>>>>>>>>>>>>>>> | 30%
|
|>>>>>>>>>>>>>>>>>>> | 31%
|
|>>>>>>>>>>>>>>>>>>>> | 31%
|
|>>>>>>>>>>>>>>>>>>>> | 32%
|
|>>>>>>>>>>>>>>>>>>>> | 33%
|
|>>>>>>>>>>>>>>>>>>>>> | 33%
|
|>>>>>>>>>>>>>>>>>>>>> | 34%
|
|>>>>>>>>>>>>>>>>>>>>> | 35%
|
|>>>>>>>>>>>>>>>>>>>>>> | 35%
|
|>>>>>>>>>>>>>>>>>>>>>> | 36%
|
|>>>>>>>>>>>>>>>>>>>>>>> | 36%
|
|>>>>>>>>>>>>>>>>>>>>>>> | 37%
|
|>>>>>>>>>>>>>>>>>>>>>>> | 38%
|
|>>>>>>>>>>>>>>>>>>>>>>>> | 38%
|
|>>>>>>>>>>>>>>>>>>>>>>>> | 39%
|
|>>>>>>>>>>>>>>>>>>>>>>>> | 40%
|
|>>>>>>>>>>>>>>>>>>>>>>>>> | 40%
|
|>>>>>>>>>>>>>>>>>>>>>>>>> | 41%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>> | 41%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>> | 42%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>> | 43%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>> | 43%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>> | 44%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 44%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 45%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 46%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 46%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 47%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 48%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 48%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 49%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 49%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 50%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 51%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 51%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 52%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 52%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 53%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 54%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 54%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 55%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 56%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 56%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 57%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 57%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 58%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 59%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 59%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 60%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 60%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 61%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 62%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 62%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 63%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 64%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 64%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 65%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 65%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 66%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 67%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 67%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 68%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 69%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 69%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 70%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 70%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 71%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 72%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 72%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 73%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 73%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 74%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 75%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 75%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 76%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 77%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 77%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 78%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 78%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 79%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 80%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 80%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 81%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 81%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 82%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 83%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 83%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 84%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 85%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 85%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 86%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 86%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 87%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 88%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 88%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 89%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 90%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 90%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 91%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 91%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 92%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 93%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 93%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 94%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 94%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 95%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 96%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 96%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 97%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 98%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 98%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 99%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>| 99%
|
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>| 100%
##
## **************** DIRECT AND INDIRECT EFFECTS OF X ON Y ****************
##
## Direct effect of X on Y:
## effect se t p LLCI ULCI
## 0.7917 0.1126 7.0286 0.0000 0.5706 1.0129
##
## Conditional indirect effects of X on Y:
##
## INDIRECT EFFECT:
##
## informed -> power -> benefit_B
##
## rational Effect BootSE BootLLCI BootULCI
## 0.0000 0.2250 0.0623 0.1072 0.3533
## 1.0000 0.5400 0.0847 0.3849 0.7185
##
## Index of moderated mediation
## (differences beween conditional indirect effects):
## Index BootSE BootLLCI BootULCI
## rational 0.3150 0.0945 0.1392 0.5110
##
## ********** BOOTSTRAP RESULTS FOR REGRESSION MODEL PARAMETERS **********
##
## Outcome variable: power
##
## Coeff BootMean BootSE BootLLCI BootULCI
## constant -1.7487 -1.7482 0.1003 -1.9390 -1.5477
## informed 0.5838 0.5848 0.1512 0.2817 0.8840
## rational 0.3427 0.3391 0.1553 0.0341 0.6428
## Int_1 0.8171 0.8199 0.2280 0.3703 1.2625
## ----------
## Outcome variable: benefit_B
##
## Coeff BootMean BootSE BootLLCI BootULCI
## constant -1.0508 -1.0498 0.1012 -1.2454 -0.8485
## informed 0.7917 0.7928 0.1156 0.5653 1.0190
## power 0.3854 0.3859 0.0388 0.3106 0.4630
##
## ******************** ANALYSIS NOTES AND ERRORS ************************
##
## Level of confidence for all confidence intervals in output: 95
##
## Number of bootstraps for percentile bootstrap confidence intervals: 10000Analysis (ONLY PARTICIPANTS WHO PASSED MANIPULATION CHECKS)
Condition -> Benefit A
Descriptives
| informed | rational | benefit_A_M | benefit_A_SD |
|---|---|---|---|
| 0 | 0 | 2.28 | 1.02 |
| 0 | 1 | 2.18 | 1.16 |
| 1 | 0 | 1.97 | 1.05 |
| 1 | 1 | 2.03 | 1.04 |
Benefit A: Two-way ANOVA
| Effect | DFn | DFd | F | p | p<.05 | ges |
|---|---|---|---|---|---|---|
| informed | 1 | 671 | 8.166 | 0.004 |
|
1.20e-02 |
| rational | 1 | 671 | 0.066 | 0.797 | 9.83e-05 | |
| informed:rational | 1 | 671 | 0.940 | 0.333 | 1.00e-03 |
Condition -> Benefit B
Descriptives
| informed | rational | benefit_B_M | benefit_B_SD |
|---|---|---|---|
| 0 | 0 | -1.82 | 1.38 |
| 0 | 1 | -1.60 | 1.57 |
| 1 | 0 | -1.11 | 1.57 |
| 1 | 1 | 0.09 | 1.75 |
Benefit B: Two-way ANOVA
| Effect | DFn | DFd | F | p | p<.05 | ges |
|---|---|---|---|---|---|---|
| informed | 1 | 671 | 97.295 | 0.00e+00 |
|
0.127 |
| rational | 1 | 671 | 33.383 | 0.00e+00 |
|
0.047 |
| informed:rational | 1 | 671 | 16.325 | 5.95e-05 |
|
0.024 |
Benefit B: Planned contrasts
Here, we’ll compare the rational/informed condition to the rest of the conditions with a planned contrasts analysis.
| Â | Df | Sum Sq | Mean Sq | F value | Pr(>F) |
|---|---|---|---|---|---|
| cond | 3 | 387.8 | 129.3 | 52 | 3.153e-30 |
| Residuals | 671 | 1668 | 2.486 | NA | NA |
Bonferroni-corrected post-hoc comparisons: Rational
| rational | Effect | DFn | DFd | F | p | p<.05 | ges | p.adj |
|---|---|---|---|---|---|---|---|---|
| 0 | informed | 1 | 330 | 19.060 | 1.7e-05 |
|
0.055 | 3.4e-05 |
| 1 | informed | 1 | 341 | 87.643 | 0.0e+00 |
|
0.204 | 0.0e+00 |
Bonferroni-corrected post-hoc comparisons: Informed
| informed | Effect | DFn | DFd | F | p | p<.05 | ges | p.adj |
|---|---|---|---|---|---|---|---|---|
| 0 | rational | 1 | 330 | 1.704 | 0.193 | 0.005 | 0.386 | |
| 1 | rational | 1 | 341 | 43.556 | 0.000 |
|
0.113 | 0.000 |
Plot: Condition -> Buyer and Seller Benefit
Condition -> Power
Power was rated from -3 (Buyer has much more power) to 3 (Seller has much more power).
Descriptives
| informed | rational | power_M | power_SD |
|---|---|---|---|
| 0 | 0 | -1.92 | 1.31 |
| 0 | 1 | -1.43 | 1.63 |
| 1 | 0 | -1.34 | 1.47 |
| 1 | 1 | 0.07 | 1.64 |
Power: Two-way ANOVA
| Effect | DFn | DFd | F | p | p<.05 | ges |
|---|---|---|---|---|---|---|
| informed | 1 | 671 | 78.103 | 0.000000 |
|
0.104 |
| rational | 1 | 671 | 65.393 | 0.000000 |
|
0.089 |
| informed:rational | 1 | 671 | 15.174 | 0.000108 |
|
0.022 |
Power: Planned contrasts
Here, we’ll compare the rational/informed condition to the rest of the conditions with a planned contrasts analysis.
| Â | Df | Sum Sq | Mean Sq | F value | Pr(>F) |
|---|---|---|---|---|---|
| cond | 3 | 391.6 | 130.5 | 56.49 | 1.443e-32 |
| Residuals | 671 | 1551 | 2.311 | NA | NA |
Bonferroni-corrected post-hoc comparisons: Rational
| rational | Effect | DFn | DFd | F | p | p<.05 | ges | p.adj |
|---|---|---|---|---|---|---|---|---|
| 0 | informed | 1 | 330 | 14.377 | 0.000178 |
|
0.042 | 0.000356 |
| 1 | informed | 1 | 341 | 71.068 | 0.000000 |
|
0.172 | 0.000000 |
Bonferroni-corrected post-hoc comparisons: Informed
| informed | Effect | DFn | DFd | F | p | p<.05 | ges | p.adj |
|---|---|---|---|---|---|---|---|---|
| 0 | rational | 1 | 330 | 9.224 | 0.003 |
|
0.027 | 0.006 |
| 1 | rational | 1 | 341 | 68.755 | 0.000 |
|
0.168 | 0.000 |
Plot: Condition -> Power
Mediation model 1: informed -> power -> seller benefit
0 = uninformed; 1 = informed
a = 1.1 (p = 0); b = 0.35 (p = 0); direct = 1.25
(p = 0); indirect = 0.86 (p = 0).
Mediation model 2: rational -> power -> seller benefit
0 = irrational; 1 = rational
a = 1.01 (p = 0); b = 0.4 (p = 0); direct = 0.78 (p = 0); indirect = 0.37 (p = 0.004).
Mediation model 3: Interaction term -> power -> seller benefit
fitM <- lm(power ~ informed*rational, data = df_tt_elg_onlypass) #linear model with interaction term predicting the mediator
fitY <- lm(benefit_B~ informed*rational + power, data = df_tt_elg_onlypass) #linear model with interaction term predicting the outcome, adjusting for the mediator
fitMedBoot.1 <- mediation::mediate(fitM,fitY,boot = T,sims = 10000,treat = "rational",treat.value = 1,mediator = "power") #mediation model with 10,000 bootstrap
fitMedBoot.2 <- mediation::mediate(fitM,fitY,boot = T,sims = 10000,treat = "informed",treat.value = 1,mediator = "power") #mediation model with 10,000 bootstrap
pander(summary(fitMedBoot.1$model.m))| Â | Estimate | Std. Error | t value | Pr(>|t|) |
|---|---|---|---|---|
| (Intercept) | -1.919 | 0.1156 | -16.6 | 3.991e-52 |
| informed | 0.5795 | 0.167 | 3.47 | 0.0005547 |
| rational | 0.4914 | 0.167 | 2.942 | 0.00337 |
| informed:rational | 0.9134 | 0.2345 | 3.895 | 0.0001079 |
| Observations | Residual Std. Error | \(R^2\) | Adjusted \(R^2\) |
|---|---|---|---|
| 675 | 1.52 | 0.2016 | 0.1981 |
pander(summary(fitMedBoot.1$model.y))| Â | Estimate | Std. Error | t value | Pr(>|t|) |
|---|---|---|---|---|
| (Intercept) | -1.246 | 0.1365 | -9.128 | 8.136e-19 |
| informed | 0.5364 | 0.1676 | 3.201 | 0.001437 |
| rational | 0.06563 | 0.1672 | 0.3926 | 0.6948 |
| power | 0.2963 | 0.0384 | 7.718 | 4.302e-14 |
| informed:rational | 0.7119 | 0.2359 | 3.019 | 0.002637 |
| Observations | Residual Std. Error | \(R^2\) | Adjusted \(R^2\) |
|---|---|---|---|
| 675 | 1.512 | 0.2549 | 0.2504 |
pander(summary(fitMedBoot.2$model.m))| Â | Estimate | Std. Error | t value | Pr(>|t|) |
|---|---|---|---|---|
| (Intercept) | -1.919 | 0.1156 | -16.6 | 3.991e-52 |
| informed | 0.5795 | 0.167 | 3.47 | 0.0005547 |
| rational | 0.4914 | 0.167 | 2.942 | 0.00337 |
| informed:rational | 0.9134 | 0.2345 | 3.895 | 0.0001079 |
| Observations | Residual Std. Error | \(R^2\) | Adjusted \(R^2\) |
|---|---|---|---|
| 675 | 1.52 | 0.2016 | 0.1981 |
pander(summary(fitMedBoot.2$model.y))| Â | Estimate | Std. Error | t value | Pr(>|t|) |
|---|---|---|---|---|
| (Intercept) | -1.246 | 0.1365 | -9.128 | 8.136e-19 |
| informed | 0.5364 | 0.1676 | 3.201 | 0.001437 |
| rational | 0.06563 | 0.1672 | 0.3926 | 0.6948 |
| power | 0.2963 | 0.0384 | 7.718 | 4.302e-14 |
| informed:rational | 0.7119 | 0.2359 | 3.019 | 0.002637 |
| Observations | Residual Std. Error | \(R^2\) | Adjusted \(R^2\) |
|---|---|---|---|
| 675 | 1.512 | 0.2549 | 0.2504 |
plot(fitMedBoot.1)
plot(fitMedBoot.2)