59 Refer to the previous problem. A contingency table relating race (the rows) to opinion (the columns) has counts (490, 410) in row 1 and (10.90) in row 2. A contingency table relating gender (the rows) to opinion has counts (350, 150) in row I and (150.350) in row 2.

a) Compute the difference of proportions in each table. Which table seems to have the stronger association?

b) Repeat

(a) using the odds ratio.

c) Now compare the tables using Goodman and Kruskal's tau. This reveals the depen- dence of this incasure on the margins It is easier to get a larger value for the second la- ble. for which row totals are similar for each gender, than for the first table, for which row totals are quite different for the races. One should use tau to compare tables only if they have similar marginals.

d) For the first table. suppose the counts equal (50. 450) instead of (10.90) in row 2. Show that the conditional distributions do not change, the difference of proportions does not change, the odds ratio does not change, but tau changes.