Test for Homogeneity

Statistics · Axiom Academy

Understanding when and how to test if multiple populations share the same distribution 1. Purpose: Testing Distribution Equality The test for homogeneity answers the question: "Do different populations have the same distribution for a categorical variable?" Multiple populations: We start with two or more distinct populations or groups Same variable measured: Each population is measured on the same categorical variable Comparing distributions: We want to know if the proportions across categories are the same 2. Key Difference: Data Collection Method While the test for homogeneity and test for independence use identical calculations, they differ fundamentally in how data is collected and what question is asked . 3. Calculation: Same as Independence Test The test for homogeneity uses the chi-square test statistic with the exact same formula as the test for independence: O = Observed frequency in each cell E = Expected frequency in each cell Expected frequencies are calculated using: where r = number of rows (categories) and c = number of columns (populations) 4. Example: Comparing Preferences Across Regions Suppose a company wants to know if product preferences are the same across three different regions. They survey: 200 customers from the East region 200 customers from the West region 200 customers from the South region Each customer chooses their preferred product (A, B, or C).

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