McNemar’s test, developed in Exercise 54, can also be used when individuals are paired (...

McNemar’s test, developed in Exercise 54, can also be used when individuals are paired (matched) to yield n pairs and then one member of each pair is given treatment 1 and the other is given treatment 2. Then X₁ is the number of pairs in which both treatments were successful, and similarly for X₂, X₃, and X₄. The test statistic for testing equal efficacy of the two treatments is given by which has approximately a standard normal distribution when H₀ is true. Use this to test whether the drug ergotamine is effective in the treatment of migraine headaches.

The data is fictitious, but the conclusion agrees with that in the article “Controlled Clinical Trial of Ergotamine Tartrate” (British Med. J., 1970: 325–327).