Parametric vs Non-Parametric Tests
Once you know what kind of comparison or relationship you want to test, the next question is often whether to use a parametric or a non-parametric test. The answer depends mainly on your data and the assumptions each test makes. In this blog, we'll explain the difference and give a practical way to decide.
What Parametric Tests Are:
- Parametric tests make assumptions about the distribution of your data, most commonly that it is approximately normal.
- Examples include the t-test, ANOVA and Pearson correlation.
- When their assumptions are met, they are generally more powerful, meaning they are better at detecting real effects.
What Non-Parametric Tests Are:
- Non-parametric tests make fewer assumptions about the distribution of your data.
- Many work with ranks rather than raw values, which makes them less affected by outliers and skewed data.
- They are often used for ordinal data, small samples, or data that clearly breaks parametric assumptions.
Common Pairs:
- Independent-samples t-test and Mann-Whitney U test.
- Paired-samples t-test and Wilcoxon signed-rank test.
- One-way ANOVA and Kruskal-Wallis test.
- Repeated-measures ANOVA and Friedman test.
- Pearson correlation and Spearman correlation.
How to Decide:
- Check your level of measurement. Continuous data may suit parametric tests; ordinal data often suits non-parametric tests.
- Check normality using plots and, where appropriate, formal tests. See our post on checking normality in SPSS.
- Check other assumptions, such as similar variances across groups for t-tests and ANOVA.
- Consider sample size. With larger samples, many parametric tests are fairly robust to moderate departures from normality.
- Look for outliers and decide how to handle them before choosing a test.
Reporting Your Choice:
- State which test you used and why, including the assumption checks you carried out.
- Report the appropriate statistics for that test, for example medians for many non-parametric tests rather than means.
Parametric tests are powerful when their assumptions hold, while non-parametric tests offer a safer choice when they do not. Check your data carefully, choose the test that fits, and explain your reasoning so that readers can trust your results.