Sample Size Determination

Sample size determination chooses $n$ large enough to detect a practically meaningful effect with a pre-specified power and significance level.

In STA305, the required sample size typically increases when:

• the target power increases
• the variability increases
• the clinically meaningful effect size decreases

For known variance and equal allocation in two arms, the total sample size has the form

$$n \propto \frac{\sigma^2 (z_{\alpha/2} + z_\beta)^2}{\delta^2}.$$

Unequal allocation modifies the formula through the allocation ratio $r$.

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Related

• STA305
• Power of a Statistical Test
• Power of the Two-Sample t-Test
• Power and Sample Size for Comparing Proportions