Statistical Power and Estimation of the Number of Required Subjects for a Study Based on the t-Test: A Surgeon's Primer

The underlying concepts for calculating the power of a statistical test elude most investigators. Understanding them helps to know how the various factors contributing to statistical power factor into study design when calculating the required number of subjects to enter into a study. Most journals and funding agencies now require a justification for the number of subjects enrolled into a study and investigators must present the principals of powers calculations used to justify these numbers. For these reasons, knowing how statistical power is determined is essential for researchers in the modern era. The number of subjects required for study entry, depends on the following four concepts: 1) The magnitude of the hypothesized effect (i.e., how far apart the two sample means are expected to differ by); 2) the underlying variability of the outcomes measured (standard deviation); 3) the level of significance desired (e.g., α = 0.05); 4) the amount of power desired (typically 0.8). If the sample standard deviations are small or the means are expected to be very different then smaller numbers of subjects are required to ensure avoidance of type 1 and 2 errors. This review provides the derivation of the sample size equation for continuous variables when the statistical analysis will be the Student's t-test. We also provide graphical illustrations of how and why these equations are derived.