Angela comments on Link: Writing exercise closes the gender gap in university-level physics - Less Wrong
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The students were split up into the control and values affirmation groups. If the values affirmation group happened by chance to contain more of the brighter women then the control group would contain fewer of them so the two samples cannot be treated as independent. The paper doesn't seem to mention any attempt to take this into account, so the actual p-values might be higher than those calculated in the paper, which weren't especially low to begin with.