In comparing two independent samples where data are ordinal or not normally distributed, which test is appropriate?

In comparing two independent samples where data are ordinal or not normally distributed, which test is appropriate?

• A. Mann-Whitney U test
• B. Paired t-test
• C. ANOVA
• D. Chi-squared test

Answer: (A)

When two independent samples are measured on an ordinal scale or show non-normal distributions, you want a method that doesn’t assume normality. The Mann-Whitney U test fits this need by ranking all observations from both samples and comparing these ranks to see which sample tends to yield larger values. This approach works with ordinal data because you can rank the categories, and it doesn’t rely on the data having a bell-shaped distribution or equal variances. It essentially tests whether the two distributions differ in a way that doesn’t depend on means. Paired data would call for a paired t-test, since the samples aren’t matched or related. ANOVA is meant for comparing means across three or more groups (and for two groups becomes equivalent to a t-test under normal assumptions, which aren’t met here). The chi-squared test handles categorical frequency data, not comparisons of numeric or ordinal values between two independent samples.

When two independent samples are measured on an ordinal scale or show non-normal distributions, you want a method that doesn’t assume normality. The Mann-Whitney U test fits this need by ranking all observations from both samples and comparing these ranks to see which sample tends to yield larger values. This approach works with ordinal data because you can rank the categories, and it doesn’t rely on the data having a bell-shaped distribution or equal variances. It essentially tests whether the two distributions differ in a way that doesn’t depend on means.

Paired data would call for a paired t-test, since the samples aren’t matched or related. ANOVA is meant for comparing means across three or more groups (and for two groups becomes equivalent to a t-test under normal assumptions, which aren’t met here). The chi-squared test handles categorical frequency data, not comparisons of numeric or ordinal values between two independent samples.