Analysis of Categorical Data II: Log-Linear Models and Logistic Regression
The first question that might be asked about a three-dimensional contingency table is, why not simply attempt its analysis by examining the two-dimensional tables resulting from summing the observed counts over one of the variables? The example shown in Table 10.3 illustrates why such a procedure is not to be recommended: it can often lead to erroneous conclusions being drawn about the data. For example, analyzing the data aggregated over the race of the victim classification gives a chi-squared statistic of2.21 with a single degree of freedom and an associated p value of .14, implying that there is racial equality in the application of the death penalty. However, the separate analyses of the data for White victims and for Black victims lead to chi-squared values of 8.77, p = .003 and 5.54, p = .019, respectively. Claims of racial equality in the application of the death penalty now look a little more difficult to sustain.