Checking the Assumptions
Parametric tests are statistical tests that make specific assumptions about the population distribution. They have greater statistical power than nonparametric tests when assumptions hold — you need smaller samples to detect effects. The trade-off: they're only valid when the assumptions are met.
Three assumptions most parametric tests share:
Assumption 1: Independence of Observations
Each observation must be independent of the others, both within and across groups. Check this by examining your data collection process:
- Did you measure the same subject multiple times? → Violation (use paired tests or repeated-measures designs).
- Is your data time-ordered and likely autocorrelated? → Violation.
- Are observations clustered (students within classrooms, patients within hospitals)? → Violation; may need hierarchical models.
Assumption 2: Normality
The data within each group should be approximately normally distributed. Three ways to check:
- Visual: Histogram and Q-Q plot. A Q-Q plot where points fall near the diagonal indicates normality.
- Shapiro-Wilk test: Most widely used. Null: sample came from a normal distribution. Significant p → reject normality. Best for n up to a few thousand.
- Anderson-Darling test: More sensitive to tail deviations.
Practical note: With very large samples, even tiny departures from normality show as significant. With very small samples, the tests have low power. Always pair formal tests with visual inspection.
Assumption 3: Homogeneity of Variance
The groups being compared should have approximately equal variances. Check with Levene's test: the null is that variances are equal; a significant p-value means they're not.
Points near the dashed line indicate normality. Curves or S-shapes suggest departures.
All assumptions hold. A Student's t-test or one-way ANOVA is appropriate.
Given a dataset, and run Shapiro-Wilk and Levene's tests. View Q-Q plots and histogram overlays to visually assess normality.
You run a Shapiro-Wilk test on each group in your dataset (n = 2,000 per group). Both return p < 0.001, suggesting non-normality. Before concluding the parametric test is invalid, what should you also check?