One-tailed tests: legitimate shortcut or cheating?

Question

An analyst runs a two-sided test and gets $p = 0.07$ , not significant. They then re-run it as a one-sided test "because we only care if the effect is positive," and now $p = 0.035$ , significant. They ship.

Explain the relationship between one-sided and two-sided p-values, when a one-sided test is genuinely justified, and why this particular move is a red flag.

Accepted Answer

The arithmetic. For a symmetric test statistic, the one-sided p-value in the observed direction is exactly half the two-sided p-value. So 0.07 two-sided becomes 0.035 one-sided automatically, no new data, no new insight, just a redefinition. That is why the temptation exists: a one-sided test at 5% puts the entire rejection region in one tail, using critical value z = 1.645 instead of 1.96, making it easier to clear. When one-sided is legitimate. A one-sided test is valid only when, before seeing the data, a difference in the opposite direction is either impossible or completely irrelevant to…

One-tailed tests: legitimate shortcut or cheating?

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