Independence Test Examples

Statistics · Axiom Academy

EXAMPLE Independence Test Examples Worked examples using the Chi-Square Test for Independence Example 1: Gender and Career Choice Problem: A researcher surveys 400 college students to determine if gender and career choice are independent. Test at α = 0.05 . Step 2: Calculate Expected Frequencies Example calculation for Male-STEM: All expected frequencies must be at least 5 for the chi-square test to be valid. This ensures the sampling distribution approximates chi-square. Step 3: Calculate Chi-Square Test Statistic Step 4: Find Critical Value and Make Decision Example 2: Smoking and Lung Disease Problem: A medical study examines 500 patients to test if smoking status and lung disease are related. Test at α = 0.01 . Step 2: Calculate Expected Frequencies and Test Statistic Step 3: Critical Value and Conclusion Interpretation: There is sufficient evidence to conclude that smoking status and lung disease are related. Smokers have a significantly higher rate of lung disease than expected under independence. Statistical association does not prove causation. While this test shows smoking and lung disease are related, additional research designs (like controlled experiments) are needed to establish causal relationships. Example 3: Political Affiliation and Policy Support Problem: A poll surveys 600 voters about support for a new environmental policy. Test if political affiliation and policy support are independent at α = 0.05 .

This is the written version of the interactive lesson above. See the full Statistics course.