A statistical measure of the fit, independence, or homogeneity of data. The chi-square test can be used to determine whether a sample of data comes from a normally distributed population by comparing its frequency distribution with that of the normal distribution. It can also be used to determine whether two variables are independent by comparing their observed joint occurrence with their expected joint occurrence. Finally, it can be used to determine whether categories of a single variable are represented in the same proportions in two or more populations.