It is widely used to assess for homogeneity, the goodness of fit, and the independence of two categorical variables. The chi-square test is based on the chi-square distribution, a distribution of the sum of the squares of k independent standard normal random variables.

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Under the null hypothesis for the chi-square test, there is no difference between the expected and observed frequencies, while the alternative hypothesis is that there is a substantial difference. There are several kinds of chi-square tests:

• Chi-square test for independence, which asks a question of relationship
• The chi-square goodness of fit test, which determines how well the sample data fits a distribution from a population with a normal distribution
• Chi-square test for homogeneity, which analyses the proportions of responses from two or more populations in relation to a dichotomous variable or a variable with more than two outcome categories

The formula for chi-square test is

χ2 = ∑(Oi – Ei)2/Ei

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Where, Oi = the observed value 

             Ei = the expected value

Chi-square test is used for categorical features and with minimum number of labels in a feature is greater than 2. The default threshold is 0.05 in AryaXAI.