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

(X2 2 X3)/ 1(X2 1 X3)

n 5 8 m 5 8 n 5 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).