Statistics for the Social Sciences A General Linear Model Approach

When the dependent variable consists of nominal data, it is necessary to conduct a χ2 test, of which there are two types in this chapter: the one-variable χ2 test and the two-variable χ2 test. The former procedure tests the null hypothesis that each group formed by the independent variable is equal to a hypothesized proportion. The two-variable χ2 test has the null hypothesis that the two variables are uncorrelated. Both procedures use the same eight steps as all NHSTs.

The effect sizes for χ2 tests are the odds ratio (for both χ2 tests) and the relative risk (for the two-variable χ2 test). When these effect sizes equal to 1.0, the outcome of interest is equally likely for both groups. When these effect sizes are greater than 1.0, the outcome of interest is more likely for the non-baseline group. When these values are less than 1.0, the outcome of interest is more likely for the baseline group. However, odds ratio and relative risk values are not interchangeable. When there are more than two groups or two outcomes, calculating an effect size requires either (1) calculating more than one odds ratio, or (2) combining groups together.