How to Calculate Sample Size for Your Research: G*Power Guide

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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

1. Open G*Power: Test family → t tests → Means: Difference between two independent means (two groups).
2. Input: Effect size d=0.50, α=0.05, Power=0.80, Allocation ratio=1.
3. Click Calculate → the required total sample size appears (approximately 128 for a medium effect).

Sample Size for One-Way ANOVA

1. Test family → F tests → ANOVA: Fixed effects, omnibus, one-way.
2. Input: Effect size f=0.25, α=0.05, Power=0.80, Number of groups=3.
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.

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