9.56 McNemar’s test. In Exercise 9.39 (page 551), you examined the relationship between being harassed online and being harassed in person for a sample of 1002 girls. An additional question can be asked about these data. Suppose we wanted to compare the proportions of girls who were harassed online and the proportion who were harassed in person. This is very much like the type of question that we studied in Section 8.2 (page 505). There, however, we used the assumption that the two samples used to calculate the proportions were independent. This assumption is not valid for our harassment data because the proportions are calculated from data provided by the same girls. McNemar’s test is the recommended procedure. The null hypothesis is that the two population proportions are equal and the alternative is two-sided. The test examines the counts in the cells where the two responses do not agree. In our case, these are 200 and 40. Note that if these two counts are equal, then the proportions will be equal for any possible values of counts in the other two cells. McNemar’s test is equivalent to the goodness-of-fit test that we examined in Example 9.16. Find the sample proportions, report the results of the significance test, and write a short summary of your conclusions.