Converting a two-sided p into a one-sided p

Question

A colleague reports a two-sided p-value of $0.08$ for a strategy's edge and concludes "not significant." But the alternative had been pre-registered as directional (edge $> 0$ ), and the observed effect was indeed positive.

Find the corresponding one-sided p-value, and explain the simple relationship between the two.

Accepted Answer

The conversion. For a symmetric test statistic (like a z or a t), the two-sided p-value is just twice the one-sided tail area, as long as the effect falls in the predicted direction. So when the effect went the way you predicted: p{	ext{one}} = \frac{p{	ext{two}}}{2} = \frac{0.08}{2} = 0.04. No z-table needed: the two-sided p already added up both tails, so halving it recovers the single predicted tail. The catch on direction. This halving is only valid because the observed effect is positive, matching the pre-registered side. If the effect had come out negative, the one-sided p (for an "ed…

Converting a two-sided p into a one-sided p

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