ANOVA and the test of normality

One still occasionally gets whinging from some corner or other about not being able to run Analysis of Variance statistical procedures (ANOVA) because the data didn’t pass a test of normality. I.e., a test of whether they appear to fit a normal distribution.

Paper reviewers, trainees, colleagues….this can come from any corner. It betrays a grad-school class level of understanding of what statistical analysis of data is supposed to do…but not a grasp of what it is doing for us at a fundamental level within the conduct of science.

Your stock response should be “the ANOVA is robust against violations of normality, move along“.

I note that the company GraphPad, which makes the Prism statistical/curve fitting package beloved of behavioral pharmacologists, has a tidy FAQ answer.

The extract version:

A population has a distribution that may be Gaussian or not. A sample of data cannot be Gaussian or not Gaussian. That term can only apply to the entire population of values from which the data were sampled…In almost all cases, we can be sure that the data were not sampled from an ideal Gaussian distribution… an ideal Gaussian distribution includes some very low negative numbers and some superhigh positive values…When collecting data, there are constraints on the possible values…Other variables can…have physical or physiological limits that don’t allow super large values… plenty of simulations have shown that these tests work well even when the population is only approximately Gaussian…It is hard to define what “close enough” means, and the normality tests were not designed with this in mind.