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Chapter 14

Chapter 14. Chi-Square Tests. Chi-Square Tests. Hypothesis testing procedures for nominal variables (whose values are categories) Focus on the number of people in different categories. Chi-Square Statistic. Observed frequency distribution Expected frequency distribution

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Chapter 14

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  1. Chapter 14 Chi-Square Tests

  2. Chi-Square Tests • Hypothesis testing procedures for nominal variables (whose values are categories) • Focus on the number of people in different categories

  3. Chi-Square Statistic • Observed frequency distribution • Expected frequency distribution • Chi-square statistic (χ2)

  4. Chi-Square Statistic • Chi-square distribution

  5. Chi-Square Statistic • Chi-square table

  6. The Chi-Square Test for Goodness of Fit • Levels of a single nominal variable

  7. The Chi-Square Test for Independence • Two nominal variables, each with several categories • Contingency table

  8. The Chi-Square Test for Independence • Independence • No relation between the variables in a contingency table • Sample and population

  9. The Chi-Square Test for Independence • Determining expected frequencies

  10. The Chi-Square Test for Independence • Figuring chi-square • Degrees of freedom

  11. Assumptions for Chi-Square Tests • No individual can be counted in more than one category or cell

  12. Effect Size for Chi-Square Test for Independence • 2 X 2 contingency table • Phi coefficient (φ) • small φ = .10 • medium φ = .30 • large φ = .50

  13. Effect Size for Chi-Square Test for Independence • Contingency tables larger than 2 x 2 • Cramer’s phi • Effect size for Cramer’s phi

  14. Power for Chi-Square Test for Independence (.05 significance level)

  15. Approximate Sample Size Needed for 80% Power (.05 significance level

  16. Controversies and Limitations • Minimum acceptable frequency for a category or cell • Small expected frequencies • At least 5 times as many individuals as categories (or cells) • Reduce power

  17. Chi-Square Tests in Research Articles • χ2(2, n = 101) = 11.89, p < .005

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