Traditional statistics instruction emphasizes a .05 significance level for hypothesis tests. Here, we investigate the consequences of this training for researchers’ mental representations of probabilities — whether .05 becomes a boundary, that is, a discontinuity of the mental number line, and alters their reasoning about p‐values. Graduate students with statistical training (n = 25) viewed pairs of p‐values and judged whether they were “similar” or “different.” After controlling for several covariates, participants were more likely and faster to judge p‐values as “different” when they crossed the .05 boundary (e.g., .046 vs. .052) compared to when they did not (e.g., .026 vs. .032). This result suggests a categorical perception‐like effect for the processing of p‐values. It may be a consequence of traditional statistical instruction creating a psychologically real divide between so‐called statistical “significance” and “nonsignificance.” Such a distortion is undesirable given modern approaches to statistical reasoning that de‐emphasize dichotomizing the p‐value continuum.
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