Statistical Inference for Two Proportions

When comparing two proportions, it is common practice simply to quote a figure representing the contrast between them, such as their difference or ratio. Several such measures of association have already been introduced in Section 1.5 , and we discuss others in Section 6.3 . The properties of these measures and the choice of a “best” one are topics in descriptive statistics and the theory of measurement. There are interesting questions here, but what gives the subject its depth is the fact that the data summarized in the description may often be regarded as informative about some underlying population that is the real subject of interest. In such contexts, the data are used to test some hypothesis or to estimate some characteristic of that population. In testing hypotheses, a statistician computes the statistical significance of, say, the ratio of proportions observed in a sample to test the null hypothesis H0 that their ratio is 1 in the population. In making estimates, the statistician computes a confidence interval around the sample ratio to indicate the range of possibilities for the underlying population parameter that is consistent with the data. Methods for constructing confidence intervals are discussed in Section 5.3. We turn now to testing hypotheses.