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:

  1. Both normality and homoscedasticity are met (remember we say assumptions are met).
  2. Normality is met but not homoscedasticity.
  3. Normality is not met but homoscedasticity is met.
  4. 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.


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