Assumptions and Conditions

Statistics · Axiom Academy

LESSON Chi-Square Test: Assumptions and Conditions Understanding when and how to use chi-square tests properly 1. Random Sampling Requirement The data must come from a random sample or randomized experiment. This ensures that observations are representative of the population and that probability theory applies. Makes sample representative of population Allows generalization of results Justifies use of probability distributions 2. Independence of Observations Each observation must be independent of all others. This means one person's response cannot influence another's, and the same individual cannot be counted multiple times. No duplicate observations: Each subject counted exactly once No pairing: Observations not matched or related (e.g., before/after on same person) 10% condition: If sampling without replacement, sample size should be less than 10% of population Random assignment: In experiments, subjects randomly assigned to groups 3. Expected Frequency Condition All expected cell counts must be at least 5. This ensures the chi-square distribution adequately approximates the sampling distribution of the test statistic. For tests of independence/homogeneity: Verify that all expected counts satisfy The total sample size must be large enough to satisfy the expected frequency condition for all cells. Larger samples provide more reliable results and greater statistical power. Minimum: Large enough so all expected counts ≥ 5

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