Chi-Square Tests Summary

Statistics · Axiom Academy

Let's review the key concepts, formulas, and applications of chi-square testing methods. Definition: A right-skewed distribution used to test hypotheses about categorical data and variance Denoted as: ^2 (Greek letter "chi" squared) Shape: Right-skewed for small df, approaches normal distribution as df increases Degrees of Freedom: Determines the specific shape of the distribution; always positive values only Key Property: Never negative since it's based on squared differences Computing Expected Frequencies Purpose: Calculate what frequency we would expect if the null hypothesis were true For Goodness of Fit: E = n p_i where p_i is the expected proportion in category i Critical Rule: All expected frequencies should be at least 5 for valid test results Purpose: Tests if a single categorical variable follows a specified distribution Question: "Do these observed frequencies match what we expected?" Degrees of Freedom: df = k - 1 where k is the number of categories Example: Testing if a die is fair by comparing rolled outcomes to expected equal frequencies Purpose: Tests if two categorical variables are independent or associated Question: "Is there a relationship between these two variables?" Degrees of Freedom: df = (r-1)(c-1) where r = rows, c = columns Example: Testing if gender and political party affiliation are independent Purpose: Tests if different populations have the same distribution of a categorical variable Question: "Do these populations have the same proportions?"

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