The difference between two t-tests doesn’t tell you what you think.

The situation is common. Let’s say you want to know if a drug increases sleep duration. You grab 20 mice, you give 10 of them the drug, and 10 of them vehicle. You measure their sleep durations and you do a t-test, and get p < 0.05. You conclude that the drug increases sleep time. Then you realize you did the experiment on all male mice, so you grab a cohort of 20 female mice, give 10 the drug and 10 placebo. You measure how long they sleep and you do a t-test and get p > 0.05. You conclude that the drug does not increase sleep time in female mice. Thus, you conclude that the drug has different effects in males and females.

Seems reasonable right? Well it’s not reasonable. In fact, it’s even less reasonable than I thought.

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