Overview
This lecture explains the differences between parametric and nonparametric statistical tests, their assumptions, examples, and guidelines for choosing the appropriate test in counseling research.
Parametric Tests
- Parametric tests include independent samples t-test, paired/dependent samples t-test, and one-way ANOVA.
- These tests require random, independent samples and interval or ratio (scale) level data.
- The data should be normally distributed, with no significant outliers and homogeneity of variance.
- Larger sample sizes are typically needed for parametric tests.
- Parametric tests are more powerful, meaning they are more likely to detect real differences (lower risk of type 2 errors).
Nonparametric Tests
- Nonparametric test examples: Mann-Whitney, Wilcoxon signed-rank, Kruskal-Wallis, and Friedman's ANOVA.
- Used if parametric test assumptions are not met; still require random, independent samples.
- Specific tests have unique assumptions, such as equal shape or symmetric distributions.
- Nonparametric tests are more conservative and have less statistical power, increasing the risk of type 2 errors.
Choosing Tests & Corresponding Equivalents
- Check parametric test assumptions first; use nonparametric if assumptions fail.
- If independent samples t-test is not suitable, use Mann-Whitney.
- Wilcoxon signed-rank is the nonparametric equivalent of the paired samples t-test.
- Kruskal-Wallis corresponds to one-way ANOVA.
- Friedman's ANOVA matches to one-way repeated-measures ANOVA.
- Always verify assumptions for any statistical test before use.
Key Terms & Definitions
- Parametric Test — Statistical test requiring specific assumptions about data distribution and measurement.
- Nonparametric Test — Test with fewer, less strict assumptions about data distribution.
- Type 1 Error — Incorrectly rejecting a true null hypothesis.
- Type 2 Error — Failing to reject a false null hypothesis.
- Statistical Power — Probability that a test will detect a true effect.
- Homogeneity of Variance — Assumption that different groups have similar variances.
- Interval/Ratio (Scale) Data — Numeric data with equal intervals; ratio data also has a true zero.
Action Items / Next Steps
- Review the assumptions for each statistical test before analysis.
- Match your data and research design to the appropriate statistical test.
- Prepare to check sample size, measurement level, and distribution before selecting a test.