Lecture 7: Non-parametric tests
February 3, 2026Assumptions & Non-parametric tests
Statistical conclusions are statements about statistical evidence given ASSUMPTIONS
Parametric methods (e.g., t-tests, ANOVA):
- Assume that data within each group (equivalently, the residuals) are approximately normally distributed (TODAY).
- Parameter estimates (e.g., regression slopes) can be sensitive to departures from normality in extreme cases.
- Hypothesis tests (e.g., p-values) are often robust to moderate non-normality.
- Observations are independent across space, time, or individuals, and variability is constant across groups (homoscedasticity).
Non-parametric methods:
- Do not assume a specific probability distribution for the data.
- Often more robust to non-normality and outliers but typically test medians or ranks rather than means, which are less sensitive to extreme values.
- Observations are independent across space, time, or individuals.
- They are generally considered more robust to heteroscedasticity than traditional parametric methods (like OLS), but they are not entirely immune to it.
In this lecture we will cover non-parametric inferential methods.
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 scheme 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
Slides will be posted here prior to the lecture