Introduction
This topic covers how to check whether a numerical variable follows a normal distribution, with emphasis on the one-sample Kolmogorov-Smirnov test, and how to describe relative variability with the coefficient of variation. Normality matters because many parametric methods, including the t-test and confidence intervals based on the mean, assume it. Knowing how to test for it, and when a test is or is not appropriate, is a core skill in an oral answer.
Why normality is checked
Many classical methods assume that the variable, or the residuals of a model, are approximately normal in the population. Checking this guides both the choice of summary measures and the choice of inferential test. The check concerns the population distribution, so a sample never shows perfect normality, and visual inspection should always accompany any formal test.
- Normality is an assumption about the population, not a property the sample must display perfectly.
- Histograms, box plots and Q-Q plots are the first step; a formal test supplements them.
- Skewness and kurtosis (topic 21) give a quick numerical sense of departure from normality.