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.

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1. When to Use Non-parametric Tests

• Data is ordinal or ranked

• Small sample size

• Non-normal distribution

• Presence of outliers

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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)

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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

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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.