Chi-square is an interesting nonparametric test that allows you to determine if what you observe in a distribution of frequencies is what you would expect to occur by chance. Here’s what we mean when we say “would expect by chance”: If there are three possible categories that a thing can fall into, there should be a one-third chance for each thing to be in each category and, by chance alone, we would expect a one third of things to fall into each category. If in a sample, the things fall into the categories at some different rate from one third and one third and one third,
