6.9.1 Why Power Analysis is Mandatory

Sample size must be calculated prospectively, before a study begins — a power analysis performed retrospectively, after data collection, is statistically...

Sample size must be calculated prospectively, before a study begins — a power analysis performed retrospectively, after data collection, is statistically invalid and does not satisfy regulatory or ethical review requirements. A proper power calculation requires four components: the significance level, alpha (conventionally set at 0.05), the desired statistical power (1 − beta, conventionally set at 0.80 or 0.90), the anticipated effect size (commonly expressed as Cohen's d for two-group comparisons, or Cohen's f for ANOVA designs), and an estimate of the outcome variable's standard deviation, drawn from pilot data or the published literature.

For a two-sample t-test, the required sample size per group is given approximately by n = 2 × [(Zα/2 + Zβ)² × σ²] / δ², where δ represents the minimum clinically or biologically meaningful difference to be detected. Commonly used software for this calculation includes the free G*Power package, the R 'pwr' package, GraphPad StateMate, and SAS PROC POWER. As a worked example, for an anticipated large effect size (Cohen's d = 0.8), a significance level of 0.05, and a desired power of 0.80, the two-sample t-test formula yields a requirement of approximately 26 animals per group. CPCSEA explicitly expects that the minimum number of animals used in any protocol be justified by a formal power analysis, directly operationalising the Reduction principle of the 3Rs discussed in Phase 4.