Non_parametric_Tests.md
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
# Example in R
wilcox.test(before, after, paired = TRUE)c. Kruskal–Wallis Test
Alternative to one-way ANOVA
Compares ranks across three or more independent groups
# Example in R
kruskal.test(score ~ group, data = data)d. Friedman Test
Alternative to repeated-measures ANOVA
Compares ranks in matched groups
# Example in R
friedman.test(values ~ time | subject, data = data)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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