Which of the following is a non-parametric test?

Which of the following is a non-parametric test?

• A. Mann-Whitney U
• B. Pearson's correlation
• C. ANOVA
• D. t-test

Answer: (A)

Non-parametric methods powerfully handle data that don’t meet the assumptions of parametric tests, such as normal distribution, interval scaling, or equal variances, or when data are strictly ordinal. Mann-Whitney U is a non-parametric test used to compare two independent groups. It works by ranking all observations from both groups together and then examining whether the ranks differ between groups. Because it relies on ranks rather than the actual values and doesn’t assume normality, it’s appropriate for ordinal data or skewed distributions. By contrast, Pearson’s correlation analyzes the linear relationship between two continuous variables and assumes bivariate normality and linearity. ANOVA compares mean differences across groups and requires normal distributions within groups and homogeneity of variances. The t-test also assumes normality within each group (and equal variances for the pooled version). All of these are parametric assumptions, which is why they’re not the non-parametric choice here.

Non-parametric methods powerfully handle data that don’t meet the assumptions of parametric tests, such as normal distribution, interval scaling, or equal variances, or when data are strictly ordinal. Mann-Whitney U is a non-parametric test used to compare two independent groups. It works by ranking all observations from both groups together and then examining whether the ranks differ between groups. Because it relies on ranks rather than the actual values and doesn’t assume normality, it’s appropriate for ordinal data or skewed distributions.

By contrast, Pearson’s correlation analyzes the linear relationship between two continuous variables and assumes bivariate normality and linearity. ANOVA compares mean differences across groups and requires normal distributions within groups and homogeneity of variances. The t-test also assumes normality within each group (and equal variances for the pooled version). All of these are parametric assumptions, which is why they’re not the non-parametric choice here.