One-sided versus two-sided, how much sample you save

Question

A study is powered at 80\% with a two-sided test at \alpha = 0.05. Suppose you switch to a one-sided test at the same \alpha = 0.05, keeping the same power and the same effect size. Roughly what fraction of the original (two-sided) sample size do you now need?

Accepted Answer

Where the sample size comes from. For a fixed effect and power, the required sample scales with (z{	ext{crit}} + z\beta)^2, where z{	ext{crit}} is the critical value for the test's tail(s). The two constants. - Two-sided at \alpha = 0.05 uses z{\alpha/2} = 1.96: (1.96 + 0.84)^2 = (2.80)^2 = 7.84. - One-sided at \alpha = 0.05 uses z{\alpha} = 1.645: (1.645 + 0.84)^2 = (2.485)^2 = 6.18. The ratio. \frac{n{	ext{one-sided}}}{n{	ext{two-sided}}} = \frac{6.18}{7.84} \approx 0.79. So a one-sided test needs about 79% of the two-sided sample, roughly a 21% saving. The reason: a one-sided test spen…

One-sided versus two-sided, how much sample you save

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