How does a non-parametric test differ from a parametric test?

A non-parametric test is designed to be used when the data does not necessarily meet the assumptions required for parametric tests, such as normality of distribution and homogeneity of variance. Unlike parametric tests that are often used for interval or ratio data, non-parametric tests can handle ordinal data or data that do not strictly meet these criteria.

The correct distinction here is that non-parametric tests often investigate category variables or ranks instead of strictly focusing on numerical quantities. This makes them particularly valuable when dealing with small sample sizes or when the data is not normally distributed. The flexibility of non-parametric tests allows researchers to analyze a wider range of data types without imposing the strict requirements of parametric methods, making them an essential part of statistical analysis in psychology and other fields.

Different test types like the chi-square test for independence and the Mann-Whitney U test for comparing medians are examples of how non-parametric tests can be applied to categorical or ordinal data effectively.