Why Sample Size Matters
Sample size directly determines the statistical power of your study. Too small a sample risks missing real effects (Type II error). Too large a sample makes trivial differences appear significant. Thesis committees frequently ask: "How did you determine your sample size?" — and "convenience" is not an acceptable answer.
What Is G*Power?
G*Power is a free, widely used statistical power analysis program developed at Heinrich Heine University. It calculates required sample sizes for t-tests, ANOVA, regression, correlation, chi-square, and many other analyses.
Key Concepts
- Effect size: The expected magnitude of the effect. Cohen's benchmarks: small (d=0.20), medium (d=0.50), large (d=0.80).
- Alpha (α): Type I error rate — typically set at 0.05.
- Power (1-β): The probability of detecting a true effect — the standard is 0.80 (80%).
Sample Size for an Independent T-Test
- Open G*Power: Test family → t tests → Means: Difference between two independent means (two groups).
- Input: Effect size d=0.50, α=0.05, Power=0.80, Allocation ratio=1.
- Click Calculate → the required total sample size appears (approximately 128 for a medium effect).
Sample Size for One-Way ANOVA
- Test family → F tests → ANOVA: Fixed effects, omnibus, one-way.
- Input: Effect size f=0.25, α=0.05, Power=0.80, Number of groups=3.
- Click Calculate → minimum total N is approximately 159.
Estimating Effect Size from Literature
Use effect sizes reported in similar studies or meta-analyses for a more realistic estimate. If no data are available, a medium effect size is a conservative and defensible starting point.
APA Reporting Example
A priori power analysis was conducted using G*Power 3.1. Assuming a medium effect size (d=0.50), α=.05, and 80% power, a minimum sample of 128 participants was required for an independent samples t-test.