Journal of Mental Science (1962) 108: 406-410. doi: 10.1192/bjp.108.455.406
© 1962 The Royal College of Psychiatrists
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Use of Chi-Square in Simple Crossover Designs

Seymour Fisher

Psychopharmacology Service Center, National Institute of Mental Health, Department of Health, Education and Welfare, Bethesda 14, Maryland, U.S.A.

ABSTRACT

By taking into account the correlation within patients who are exposed to two different treatments in a crossover design, one has a much better chance of detecting valid treatment differences than if this correlation is ignored. Given categorical measures of "improvement" and "non-improvement", chi-square analysis is appropriate, but must be used in a modified form, based on independent observations. When the data are presented merely in terms of the percentage of patients who improved on drug compared to the percentage of the same patients who improved on placebo, one may not be able to say anything about the effectiveness of the drug without additional information concerning how each patient responded to both treatments. Using hypothetical examples, it is shown how a relatively unimpressive over-all difference in percentage improvement may obscure a marked drug-placebo difference which can be detected by appropriate statistical analysis.

If an investigator insists upon using the kind of crossover design under discussion (and there are many excellent reasons why this design should generally be avoided), it is particularly important for him to have a clear understanding of the processes and assumptions underlying his technique of analysis.




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