Differentiate between Chi-square tests for association and homogeneity of proportions. Also mention the assumptions of these tests.

Chi-square tests for association and homogeneity of proportions are two distinct types of Chi-square tests used in biostatistics to analyze categorical data. While they are both based on the same statistical distribution, their purposes and applications differ.

The Chi-square test for association (also called the test of independence) is used to assess whether there is a relationship between two categorical variables in a single population. The goal of this test is to determine if the variables are independent or if they are associated with each other. For example, one might use the test to determine if gender (male/female) is associated with smoking status (smoker/non-smoker). The test compares the observed frequency of occurrences in a contingency ________ _________ _____ __________ _________ __________.
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