What is a Chi-square test?

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A chi-square statistic is a test that measures how well a model fits the actual observed data. There are two types of chi-square tests: The chi-square goodness of fit test is used to test whether the frequency distribution of a categorical variable is different from your expectations. The goodness of fit measures how well a statistical model fits a set of observations. When the goodness of fit is high, the values expected based on the model are close to the observed values. When the goodness of fit is low, the values expected based on the model are far from the observed values.

Another type of chi-square test, the chi-square test of independence, is used to examine whether two categorical variables are independent. The test compares the observed frequencies to the evenly distributed frequencies you expected if the two variables are unrelated. The observed and expected frequencies will be similar when the variables are unrelated.