Key Nonparametric Statistical Tests to Know for Advanced Quantitative Methods

Nonparametric statistical tests are essential tools in Advanced Quantitative Methods, especially when data doesn't meet normality assumptions. These tests, like the Mann-Whitney U and Wilcoxon signed-rank tests, help analyze ordinal and non-normally distributed continuous data effectively.

1. Mann-Whitney U test

   • Compares differences between two independent groups when the dependent variable is ordinal or continuous but not normally distributed.
   • Ranks all data points from both groups together, then calculates the U statistic based on these ranks.
   • Useful for small sample sizes and when assumptions of parametric tests (like normality) are violated.

2. Wilcoxon signed-rank test

   • Tests for differences between two related samples or matched observations, focusing on the ranks of the differences.
   • Suitable for ordinal data or continuous data that do not meet normality assumptions.
   • Provides a nonparametric alternative to the paired t-test.

3. Kruskal-Wallis test

   • Extends the Mann-Whitney U test to compare three or more independent groups.
   • Ranks all data points across groups and assesses whether the rank distributions differ significantly.
   • Ideal for ordinal data or continuous data that is not normally distributed.

4. Friedman test

   • A nonparametric alternative to the repeated measures ANOVA, used for comparing three or more related groups.
   • Analyzes the ranks of the data across different conditions or time points.
   • Useful for ordinal data or continuous data that does not meet the assumptions of parametric tests.

5. Spearman's rank correlation coefficient

   • Measures the strength and direction of association between two ranked variables.
   • Suitable for ordinal data or continuous data that is not normally distributed.
   • Provides insight into monotonic relationships, where one variable tends to increase as the other does.

6. Chi-square test of independence

   • Assesses whether there is a significant association between two categorical variables in a contingency table.
   • Compares observed frequencies with expected frequencies under the assumption of independence.
   • Requires a sufficient sample size to ensure validity of results.

7. Sign test

   • A simple nonparametric test used to determine if there is a median difference between paired observations.
   • Focuses on the direction of differences (positive or negative) rather than their magnitude.
   • Useful for small sample sizes and when data does not meet normality assumptions.

8. Kolmogorov-Smirnov test

   • Compares the distribution of a sample with a reference probability distribution or compares two samples.
   • Tests for differences in the shape of distributions, making it useful for assessing normality.
   • Nonparametric and applicable to continuous data.

9. Kendall's tau

   • Measures the strength and direction of association between two variables using the ranks of the data.
   • More robust to ties than Spearman's rank correlation and provides a measure of ordinal association.
   • Suitable for small sample sizes and non-normally distributed data.

10. McNemar's test

    • A nonparametric test used for paired nominal data to determine if there are differences in proportions.
    • Commonly applied in before-and-after studies or matched case-control studies.
    • Focuses on changes in responses rather than the magnitude of changes.