Remember the University of California Berkeley dataset that we first saw when discussing the relationship between two categorical variables in Chapter 3, Describing Relationships? Recall that UCB was sued because it appeared as though the admissions department showed preferential treatment to male applicants. Also recall that we used cross-tabulation to compare the proportion of admissions across categories.
If admission rates were, say 10%, you would expect about one out of every ten applicants to be accepted regardless of gender. If this is the case that gender has no bearing on the proportion of admits, then gender is independent.
Small deviations from this 10% proportion are, of course, to be expected in the real world and not necessarily indicative of a sexist admissions machine. However, if a test of independence of proportions is significant, that indicates that a deviation as extreme as the one we observed is very unlikely to occur if the variable...
