Sample Size Estimation for Unpaired Student t Tests in Biostatistics

In biostatistics, when comparing the means of two independent groups of subjects using an unpaired Student t test, the effect size is expressed as the ratio of Δ (delta, the difference between the means of two groups) divided by σ (sigma, the within-group standard deviation).

Each chart in the following figure shows overlapping bell curves that indicate the amount of separation between two groups, along with the effect size (Δ/σ) and the required number of analyzable subjects in each group. Pick the chart that looks like an important amount of separation between the two groups. For example, if the middle chart (corresponding to a between-group difference that’s three-fourths as large as the within-group standard deviation) looks like an important amount of separation, then you need about 29 analyzable subjects per group (for a total of 58 analyzable subjects).

Credit: Illustration by Wiley, Composition Services Graphics

For other Δ/σ values, use this rule of thumb to estimate sample size: You need about 16/(Δ/σ)² analyzable subjects in each group.