+Using Chi-Square Tests WiselyInference for RelationshipsBoth the chi-square test for homogeneity and the chi-square test forassociation/independence start with a two-way table of observed counts.They even calculate the test statistic, degrees of freedom, andP-value inthe same way.The questions that these two tests answer are different,however.A chi-square test for homogeneity tests whether the distribution of acategorical variable is the same for each of several populations ortreatments.Instead of focusing on the question asked, it’s much easier to look at how thedata were produced.If the data come from two or more independent random samples or treatmentgroups in a randomized experiment, then do a chi-square test for homogeneity.If the data come from a single random sample, with the individuals classifiedaccording to two categorical variables, use a chi-square test forassociation/independence.