# Lecture 7: Non-parametric tests

January 31, 2023 (4th week of classes)**Non-parametric tests**

Parametric tests are those that assume parameters about the statistical population such as normality and homoscedasticity.

In this lecture we will cover classic rank-based statistical hypothesis testing. Rank transformations allow statistical testing when distributions cannot be assumed as normal (i.e., normality assessments fail). We will understand also a modern approach to classic rank-based tests which is based on using ANOVAs to perform statistical testing on ranked data.

ANOVA, ANOVA Multiple Comparisons & Kruskal Wallis, by MarinStatsLectures

The video runs ANOVA and the Kruskal-Wallis test on the same data in R. It helps understanding the links between the two; ANOVA being parametric and Kruskal-Wallis being non-parametric.

This lecture can be divided into the main parts:

**part 1: **The normality and homoscedasticity assumptions - a decisional schemes to select appropriate frameworks for each case. There are four possible cases here:

- Both normality and homoscedasticity are met (remember we say assumptions are met).

- Normality is met but not homoscedasticity.

- Normality is not met but homoscedasticity is met.

- Neither normality or homoscedasticity are met.

The frameworks covered in this lecture are not the only to tackle the issues involved with these two assumptions but the scheme provides a good support for understanding how to navigate through different existing and heavily used statistical options. We will see other frameworks that tackles

**part 2: **Potential issues with parametric tests when the assumption of normality is not met. Parametric tests (that assume normality) are known to be robust when samples come from non-normally distributed populations. That said, depending on the field of biology, it may become a requirement to use statistical tests that are more robust against normality.

**part 3: **Ranked-based statistical frameworks - the case of Krusal-Wallis and use of ANOVA on ranked-transformed data as a general solution.

**Lecture**