60. * Another PRE measure of association for nominal variables is called lambda. For this measure, rule 1 predicts for each observation the modal category for the marginal distri- bution of the response variable. For Table 8 35, for example, rule 1 predicts Oppose al- ways. Rule 2 predicts the modal category for the conditional distribution of the response variable, within cach level of the predictor variable For each row in Table 8.35, rule 2 predicts Oppose.

a) Show thai E = 381, E = 103 + 182+80+16= 381, and = (E - E)/E = 0.

b) Explain why lambda equals 0 when the modal category of the response variable is the same for cach level of the explanatory variable. (The main difference between lambda and tau is that lambda can equal 0 even when the variables are statistically dependent.)

61. * In cross-classifications of ordinal vanables, not all pairs are concordant or discordant. Subjects in the same category of a variable are tied on that variable. Two observations that fall in the same row are bed on the row variable, and two observations that fall in the same column are tied on the column vanable Let T, denote the number of pairs tied on X, and let T, denote the number of pairs tied on Y. The sample value of Kendall's tau-b is C-D V[( 1)/2 T][n-1){2-T] = Show that when Ty Ty 0. (The common value is then known as Kendall's tau )