We then conducted pairwise comparisons using permutation tests (5,000 repetitions per test). While the rate of discovery for the Rule Confirming condition was lower (8.4%) than the rate for the Rule Disconfirming condition (14.1%), this difference was not statistically significant (diff = 5.7 percentage points, 95% CI [−-14.5 p.p., 2.9 p.p.], p=.143p=.143; H1b). The Rule Confirming condition discovered the rule more frequently than but not significantly different from the Default GPT condition (5.9%; diff = 2.5 p.p., 95% CI [−-4.6 p.p., 9.6 p.p.], p=.686p=.686, H1c).555An exploratory equivalence test (using 90% bootstrap confidence intervals for consistency) confirmed that these conditions were statistically equivalent. We defined the equivalence bounds as ±0.5SDDefault\pm 0.5SD_{Default} (±11.9\pm 11.9 p.p.), representing a medium effect size. The 90% confidence interval for the difference fell entirely within these bounds (90% CI [−-3.4 p.p., 8.2 p.p.]). Finally, consistent with our predictions, Default GPT showed significantly lower discovery rates than Rule Disconfirming (5.9% vs. 14.1% diff = 8.2 p.p., 95% CI [−-16.6 p.p., 0.1 p.p.], p=.043p=.043; H1d).666Note that the 95% CI overlaps zero as it corresponds to a two-sided test, whereas the significant pp-value reflects our pre-registered one-sided hypothesis.. One notable finding from our exploratory analyses is that Default GPT differed significantly from Random Sequence on both discovery (5.9% vs 29.5%; diff = 23.6 p.p., 95% CI [−34.0-34.0 p.p., −13.2-13.2 p.p.], p
[7] B. E. Bayer: “An optimum method for two-level rendition of continuous-tone pictures” (1973). ↑
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