Chapter 14 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  Chi-square statistic (χ 2 )

Chi-Square Statistic  Chi-square distribution

Chi-Square Statistic  Chi-square table

The Chi-Square Test for Goodness of Fit  Levels of a single nominal variable

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

The Chi-Square Test for Independence  Independence –No relation between the variables in a contingency table  Sample and population

The Chi-Square Test for Independence  Determining expected frequencies

The Chi-Square Test for Independence  Figuring chi-square  Degrees of freedom

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

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

Effect Size for Chi-Square Test for Independence  Contingency tables larger than 2 x 2 –Cramer’s phi –Effect size for Cramer’s phi

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

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

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

Chi-Square Tests in Research Articles  χ 2 (2, n = 101) = 11.89, p <.005