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 passcheck failcheck
0 0 44 0
0 1 55 2
1 0 57 1
1 1 43 0

Alright, that leaves us with 199. 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 41 2 0 1
0 1 45 7 3 0
1 0 47 3 4 3
1 1 43 0 0 0

Alright. That’s 176. We can run the analyses with and without them, and see if the patterns differ.

Demographics

Race

race N Perc
asian 13 6.53
black 19 9.55
hispanic 5 2.51
multiracial 4 2.01
white 152 76.38
NA 6 3.02

Gender

gender N Perc
1 0.50
man 124 62.31
woman 72 36.18
NA 2 1.01

Age

age_mean age_sd
39.40704 11.70341

Education

edu N Perc
noHS 1 0.50
GED 51 25.63
2yearColl 31 15.58
4yearColl 82 41.21
MA 24 12.06
PHD 6 3.02
NA 4 2.01

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 1.70 1.56
0 1 1.98 1.33
1 0 1.98 1.04
1 1 1.51 1.14

Benefit A: Two-way ANOVA

Effect DFn DFd F p p<.05 ges
informed 1 195 0.279 0.598 0.001
rational 1 195 0.283 0.595 0.001
informed:rational 1 195 4.228 0.041
0.021

We’re seeing an interaction of rational X informed on buyer’s benefit. Not something we’re particularly interested in, as they’re all likely much higher than seller benefit, but still potentially noteworthy. When the seller is both informed and rational - the buyer benefits the least.

Condition -> Benefit B

Let’s take a look at the seller.

Descriptives

informed rational benefit_B_M benefit_B_SD
0 0 -1.57 1.39
0 1 -0.89 1.79
1 0 -1.21 1.62
1 1 0.56 1.59

Benefit B: Two-way ANOVA

Effect DFn DFd F p p<.05 ges
informed 1 195 15.268 1.29e-04
0.073
rational 1 195 27.983 3.00e-07
0.125
informed:rational 1 195 5.571 1.90e-02
0.028
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.

Analysis of Variance Model
  Df Sum Sq Mean Sq F value Pr(>F)
cond 3 115.3 38.42 14.68 1.164e-08
Residuals 195 510.2 2.617 NA NA

Bonferroni-corrected post-hoc comparisons: Rational

rational Effect DFn DFd F p p<.05 ges p.adj
0 informed 1 99 1.366 2.45e-01 0.014 0.4900000
1 informed 1 96 17.376 6.72e-05
0.153 0.0001344

Bonferroni-corrected post-hoc comparisons: Informed

informed Effect DFn DFd F p p<.05 ges p.adj
0 rational 1 97 4.246 4.2e-02
0.042 8.4e-02
1 rational 1 98 29.573 4.0e-07
0.232 8.0e-07

Plot: Condition -> Buyer and Seller Benefit


Very cool. This fits very well with our predictions. The only thing that we might not have predicted is the difference between rational and irrational in the uninformed conditions (although this become non-significant when adjusting the p-value with a bonferroni correction). And still, no difference between rational/uninformed and irrational/informed.

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 -1.86 1.21
0 1 -1.25 1.78
1 0 -1.18 1.45
1 1 0.44 1.58

Power: Two-way ANOVA

Effect DFn DFd F p p<.05 ges
informed 1 195 29.730 1.0e-07
0.132
rational 1 195 25.915 8.0e-07
0.117
informed:rational 1 195 5.314 2.2e-02
0.027

Power: Planned contrasts

Here, we’ll compare the rational/informed condition to the rest of the conditions with a planned contrasts analysis.

Analysis of Variance Model
  Df Sum Sq Mean Sq F value Pr(>F)
cond 3 127.5 42.51 18.16 1.964e-10
Residuals 195 456.5 2.341 NA NA

Bonferroni-corrected post-hoc comparisons: Rational

rational Effect DFn DFd F p p<.05 ges p.adj
0 informed 1 99 6.417 1.3e-02
0.061 2.6e-02
1 informed 1 96 24.240 3.5e-06
0.202 7.1e-06

Bonferroni-corrected post-hoc comparisons: Informed

informed Effect DFn DFd F p p<.05 ges p.adj
0 rational 1 97 3.765 5.5e-02 0.037 1.1e-01
1 rational 1 98 28.193 7.0e-07
0.223 1.4e-06

Plot: Condition -> Power


The rational and informed sellers are as powerful as the buyers. Wow.

Mediation model 1: informed -> power -> seller benefit

0 = uninformed; 1 = informed

a = 1.05 (p = 0); b = 0.54 (p = 0); direct = 0.74 (p = 0.003); indirect = 0.18 (p = 0.431).

Ok, looks like we have a full mediation.

Mediation model 2: rational -> power -> seller benefit

0 = irrational; 1 = rational

a = 0.97 (p = 0); b = 0.51 (p = 0); direct = 1.11 (p = 0); indirect = 0.62 (p = 0.005).

Analysis (ONLY PARTICIPANTS WHO PASSED MANIPULATION CHECKS)

Condition -> Benefit A

Descriptives

informed rational benefit_A_M benefit_A_SD
0 0 1.90 1.37
0 1 1.98 1.34
1 0 2.13 0.92
1 1 1.51 1.14

Benefit A: Two-way ANOVA

Effect DFn DFd F p p<.05 ges
informed 1 172 0.441 0.508 0.003
rational 1 172 2.220 0.138 0.013
informed:rational 1 172 3.629 0.058 0.021

Condition -> Benefit B

Descriptives

informed rational benefit_B_M benefit_B_SD
0 0 -1.66 1.39
0 1 -0.84 1.76
1 0 -1.17 1.65
1 1 0.56 1.59

Benefit B: Two-way ANOVA

Effect DFn DFd F p p<.05 ges
informed 1 172 15.184 1.39e-04
0.081
rational 1 172 27.451 5.00e-07
0.138
informed:rational 1 172 3.550 6.10e-02 0.020

The interaction goes away.

Benefit B: Planned contrasts

Here, we’ll compare the rational/informed condition to the rest of the conditions with a planned contrasts analysis.

Analysis of Variance Model
  Df Sum Sq Mean Sq F value Pr(>F)
cond 3 116 38.66 14.96 1.064e-08
Residuals 172 444.4 2.584 NA NA

Bonferroni-corrected post-hoc comparisons: Rational

rational Effect DFn DFd F p p<.05 ges p.adj
0 informed 1 86 2.225 0.139000 0.025 0.278000
1 informed 1 86 15.340 0.000179
0.151 0.000358

Bonferroni-corrected post-hoc comparisons: Informed

informed Effect DFn DFd F p p<.05 ges p.adj
0 rational 1 84 5.604 2.0e-02
0.063 4.0e-02
1 rational 1 88 25.527 2.3e-06
0.225 4.7e-06

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 -2.02 1.08
0 1 -1.36 1.65
1 0 -1.26 1.42
1 1 0.44 1.58

Power: Two-way ANOVA

Effect DFn DFd F p p<.05 ges
informed 1 172 34.071 0e+00
0.165
rational 1 172 28.956 2e-07
0.144
informed:rational 1 172 5.470 2e-02
0.031

Power: Planned contrasts

Here, we’ll compare the rational/informed condition to the rest of the conditions with a planned contrasts analysis.

Analysis of Variance Model
  Df Sum Sq Mean Sq F value Pr(>F)
cond 3 140.8 46.94 22.13 3.629e-12
Residuals 172 364.8 2.121 NA NA

Bonferroni-corrected post-hoc comparisons: Rational

rational Effect DFn DFd F p p<.05 ges p.adj
0 informed 1 86 7.961 6.0e-03
0.085 1.2e-02
1 informed 1 86 27.163 1.3e-06
0.240 2.5e-06

Bonferroni-corrected post-hoc comparisons: Informed

informed Effect DFn DFd F p p<.05 ges p.adj
0 rational 1 84 4.819 3.1e-02
0.054 6.2e-02
1 rational 1 88 28.814 6.0e-07
0.247 1.3e-06

Plot: Condition -> Power


Mediation model 1: informed -> power -> seller benefit

0 = uninformed; 1 = informed

a = 1.23 (p = 0); b = 0.51 (p = 0); direct = 0.89 (p = 0.001); indirect = 0.26 (p = 0.301).

Mediation model 2: rational -> power -> seller benefit

0 = irrational; 1 = rational

a = 1.14 (p = 0); b = 0.47 (p = 0); direct = 1.24 (p = 0); indirect = 0.7 (p = 0.004).