Which statistical approach would you use to analyze data that does not meet parametric assumptions?

Non-parametric tests are specifically designed for analyzing data that do not adhere to the normal distribution or other parametric assumptions, such as homogeneity of variance. These tests do not rely on assumptions about the parameters of the population from which the samples are drawn, making them suitable for data that may be ordinal or exhibit non-normal distributions. Examples of non-parametric tests include the Mann-Whitney U test for comparing two independent groups and the Kruskal-Wallis test for comparing more than two groups.

In contrast, regression analysis and ordinary least squares regression both rely on several parametric assumptions, such as the normality of residuals and homoscedasticity. Maximum likelihood estimation is a method often employed in parametric contexts and is contingent upon the model fitting particular distributional assumptions. As such, while these methods are powerful for certain types of data, they are not appropriate when the data violates the underlying assumptions. Non-parametric tests thus provide a valuable alternative for robust analysis of non-normally distributed data.