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Statistical analysis of binary data from matched designs that require multiple observations on the same herd, litter or animal.

To determine the effectiveness of a vaccine for bovine respiratory disease, an investigator randomizes feedlot cattle to vaccine and control groups and then uses a chi-square test to compare morbidity rates. To control for confounding factors such as the environment, he may assign one half of each pen to a treatment. But here some care is needed. The chi-square test is valid only if the individual animal responses are independent: the similarity of responses within each pen may bias the test statistic and yield invalid results. This paper discusses this problem, which is called clustering, and reports on a computer simulation of three strategies for dealing with it in matched designs.