For our primary DV, we used a probit regression on whether participants find J--- guilty with whether they got the genes or tbi condition [tbi =1, genes=0]. We found that, in the second half of the data, participants were less likely to find the actor guilty if his low self-control was caused by a brain tumor (M = 80.109%) than if it was caused by his genes (M = 93.023&, *b*probit = -.632, 95%CI = -.871 to -.393)
probit guilty i.tbi if first750 == 0
Iteration 0: log likelihood = -295.07662
Iteration 1: log likelihood = -281.16367
Iteration 2: log likelihood = -281.01716
Iteration 3: log likelihood = -281.01712
Iteration 4: log likelihood = -281.01712
Probit regression Number of obs = 754
LR chi2(1) = 28.12
Prob > chi2 = 0.0000
Log likelihood = -281.01712 Pseudo R2 = 0.0476
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guilty | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.tbi | -.6320046 .1221726 -5.17 0.000 -.8714585 -.3925507
_cons | 1.477525 .0966956 15.28 0.000 1.288005 1.667045
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. margins tbi
Adjusted predictions Number of obs = 754
Model VCE : OIM
Expression : Pr(guilty), predict()
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| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
tbi |
0 | .9302326 .0129499 71.83 0.000 .9048512 .9556139
1 | .8010899 .020837 38.45 0.000 .7602501 .8419298
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This result was replicated in the first 750, where participants were less likely to find the assailant guilty when his self-contorl failure was caused by tbi (M = 82.823%) than if caused by genes (M = 93.668, *b*probit = -.58, 95%CI = -.829 to -.331).
probit guilty i.tbi if first750 == 1
Iteration 0: log likelihood = -268.66448
Iteration 1: log likelihood = -257.83776
Iteration 2: log likelihood = -257.72504
Iteration 3: log likelihood = -257.725
Iteration 4: log likelihood = -257.725
Probit regression Number of obs = 746
LR chi2(1) = 21.88
Prob > chi2 = 0.0000
Log likelihood = -257.725 Pseudo R2 = 0.0407
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guilty | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.tbi | -.5798329 .1269398 -4.57 0.000 -.8286303 -.3310354
_cons | 1.52745 .1006881 15.17 0.000 1.330105 1.724795
------------------------------------------------------------------------------
. margins tbi
Adjusted predictions Number of obs = 746
Model VCE : OIM
Expression : Pr(guilty), predict()
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
tbi |
0 | .9366755 .0125101 74.87 0.000 .9121561 .9611948
1 | .8283379 .0196838 42.08 0.000 .7897584 .8669173
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These two effects corresponded to an significant overall effect as well, with participants being less likely to pronounce the man guilty if his self-control failure was caused by tbi (M = 81.471%) than if it was caused by genes (M = 93.342%, *b*probit = -.606, 95%CI = -.779 to -.434)
probit guilty i.tbi
Iteration 0: log likelihood = -564.18152
Iteration 1: log likelihood = -539.51658
Iteration 2: log likelihood = -539.25779
Iteration 3: log likelihood = -539.25771
Iteration 4: log likelihood = -539.25771
Probit regression Number of obs = 1500
LR chi2(1) = 49.85
Prob > chi2 = 0.0000
Log likelihood = -539.25771 Pseudo R2 = 0.0442
------------------------------------------------------------------------------
guilty | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.tbi | -.6063571 .0879943 -6.89 0.000 -.7788229 -.4338914
_cons | 1.501759 .0697289 21.54 0.000 1.365093 1.638425
------------------------------------------------------------------------------
. margins tbi
Adjusted predictions Number of obs = 1500
Model VCE : OIM
Expression : Pr(guilty), predict()
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
tbi |
0 | .9334203 .0090073 103.63 0.000 .9157663 .9510743
1 | .8147139 .0143409 56.81 0.000 .7866063 .8428215
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There was no difference in effect size between the first and second 750 participants (*b*probit = .052, *p*> .76)