Assumptions for Two-Sample Tests

Statistics · Axiom Academy

LESSON Assumptions for Two-Sample Tests Understanding the foundation for valid statistical inference when comparing two groups The independence assumption requires that observations within and between groups are independent of each other. This is satisfied through proper study design: Random sampling: Subjects are randomly selected from their respective populations Independent groups: The two samples are completely separate (no matching or pairing) No clustering: Observations are not related through time, space, or shared characteristics Each population should follow a normal distribution. However, thanks to the Central Limit Theorem (CLT), this assumption becomes less critical with larger sample sizes. If n 1 , n 2 30: CLT applies; normality assumption is relaxed If 15 n 1 , n 2 < 30: Mild departures from normality are acceptable If n 1 , n 2 < 15: Data should be approximately normal with no strong skewness or outliers The pooled two-sample t-test assumes both populations have equal variances (homoscedasticity). This assumption allows us to pool the sample variances for more efficient estimation. Before conducting a two-sample test, verify assumptions using graphical and numerical methods: Histograms & Q-Q plots: Check normality within each group Box plots: Compare spreads and identify outliers Side-by-side plots: Visualize distributions and variances Levene's test or F-test: Test equality of variances Shapiro-Wilk test: Test normality (use with caution for large samples)

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