Percent more data for a stricter alpha

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You currently run a two-sided test at \alpha = 0.05 with 80\% power. You are considering tightening to \alpha = 0.01, keeping the same power and effect. By roughly what percentage would the required sample size increase?

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The constants. Required sample scales with (z{\alpha/2} + z\beta)^2: - \alpha = 0.05: (1.96 + 0.84)^2 = 7.84. - \alpha = 0.01: (2.576 + 0.84)^2 = 11.67. The percentage increase. \frac{11.67}{7.84} \approx 1.49 \quad\Rightarrow\quad 	ext{about a } 49\% 	ext{ increase}. So a five-fold stricter false-positive standard costs only about half again as much data. The reason the increase is modest is that the critical value moves from 1.96 to 2.576, a much smaller relative change than the change in \alpha itself. Takeaway. Tightening \alpha from 0.05 to 0.01 at 80% power raises the required sample …

Percent more data for a stricter alpha

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