Non-parametric Tests
Non-parametric tests are statistical methods that do not assume a specific distribution for the data. They are useful when data violate assumptions such as normality or equal variances.
1. When to Use Non-parametric Tests
Data is ordinal or ranked
Small sample size
Non-normal distribution
Presence of outliers
2. Common Non-parametric Tests
a. Mann–Whitney U Test
Alternative to the independent t-test
Compares the ranks of two independent groups
# Example in R
wilcox.test(group1, group2)b. Wilcoxon Signed-Rank Test
Alternative to the paired t-test
Compares matched or paired samples
c. Kruskal–Wallis Test
Alternative to one-way ANOVA
Compares ranks across three or more independent groups
d. Friedman Test
Alternative to repeated-measures ANOVA
Compares ranks in matched groups
3. Advantages and Limitations
Advantages
Fewer assumptions
Can be used with ordinal data
More robust to outliers
Limitations
Less power than parametric tests
Harder to interpret effect size
4. Summary
Non-parametric tests provide flexible alternatives when traditional parametric assumptions are violated. They are especially valuable in exploratory analysis, clinical trials, and small sample research.
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