Friedman's Test is the non-parametric equivalent of which statistical analysis?

Friedman's Test serves as the non-parametric equivalent of within-groups ANOVA, which is used to analyze data where repeated measures are taken from the same subjects under different conditions. This test is particularly useful when the assumptions required for parametric tests, like normality of the data, cannot be met.

Within-groups ANOVA, also known as repeated measures ANOVA, examines the differences between the means of the same participants across different conditions or time points, allowing researchers to determine whether there are statistically significant differences due to the interventions or treatments administered. The Friedman's Test accomplishes this without the assumption of normally distributed data, making it ideal for ordinal data or continuous data that do not meet parametric criteria.

In contrast, other statistical analyses listed—such as between-groups ANOVA, one-way ANOVA, and mixed-design ANOVA—focus on different groupings or manipulate when subjects are only measured once or under varying group conditions, making them incompatible for the comparisons that Friedman's Test is designed for. Thus, the choice of within-groups ANOVA as the equivalent is justified based on the nature of the data and the design of the study being analyzed.