# otherwise we return the type itself.
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
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Jupiter will be the easiest of the six to find, shining brightly in the constellation Gemini and high enough to stay in view for much of the night, even from light-polluted towns and cities.
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