Stricter alpha at 90% power

Question

A two-sided test at \alpha = 0.05 with 90\% power needs 1{,}000 users per arm. The team wants to tighten to \alpha = 0.01, keeping 90\% power and the same effect. Roughly how many users per arm are needed now?

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The two constants. For 90% power, z\beta = 1.28. - \alpha = 0.05: (1.96 + 1.28)^2 = (3.24)^2 = 10.51. - \alpha = 0.01: (2.576 + 1.28)^2 = (3.856)^2 = 14.87. The ratio. \frac{n{0.01}}{n{0.05}} = \frac{14.87}{10.51} \approx 1.42. Apply it. n{0.01} \approx 1.42 	imes 1{,}000 \approx 1{,}416 	ext{ per arm}. The inflation factor (about 42%) is a touch smaller than the 49% seen at 80% power, because the larger z\beta term dilutes the effect of changing the critical value. Takeaway. At 90% power, tightening from \alpha = 0.05 to 0.01 raises the sample by about 42%: 1,000 per arm becomes roughly 1,…

Stricter alpha at 90% power

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