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Use of Chi-Square in Simple Crossover Designs

Published online by Cambridge University Press:  08 February 2018

Seymour Fisher
Seymour Fisher*
Affiliation:
Psychopharmacology Service Center, National Institute of Mental Healthy Department of Health, Education and Welfare, Bethesda 14, Maryland, U.S.A.
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Extract

In the clinical evaluation of new drugs, many investigators employ a simple crossover design, where half of the patients first receive the active drug for a given period of time, followed by a switch to an inert placebo for a similar period of time; the other half of the patients begin the trial on placebo, and are subsequently switched to the active drug. When the criterion measure consists of an over-all rating of, say, “Improved” or “Non-Improved”, the data lend themselves to a chi-square analysis. It is clear, however, that in many clinical circles, this analytic technique is being consistently misused, despite the fact that the various pitfalls and underlying assumptions have been widely emphasized (Lewis and Burke, 3). The purpose of this brief note is to demonstrate the proper use of chi-square, and also to show that, when incorrectly used, the clinical research investigator may increase the probability of prematurely discarding an effective drug.

Type
Methodology
Information
Journal of Mental Science , Volume 108 , Issue 455 , July 1962 , pp. 406 - 410
Copyright
Copyright © Royal College of Psychiatrists, 1962 

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References

1. Beecher, H. K., Keats, A. S., Mosteller, F., and Lasagna, L., “The effectiveness of oral analgesics (morphine, codeine, acetylsalicylic acid) and the problem of the placebo ‘reactors’ and ‘non-reactors’ ”, J. Pharmacol exp. Ther., 1953, 109, 393.Google Scholar
2. Jellinek, E. M., “Clinical tests on comparative effectiveness of analgesic drugs”, Biometrics, 1946, 2, 87.Google Scholar
3. Lewis, D., and Burke, C. J., “The use and misuse of the chi-square test”, Psychol. Bull., 1949, 46, 433.Google Scholar
4. McNemar, Q., Psychological statistics. (2nd ed.) New York: John Wiley & Sons, 1955.Google Scholar
5. Mosteller, F., “Statistical problems and their solution”. In Beecher, H. K., Measurement of subjective responses. New York: Oxford University Press, 1959. Pp 73–91.Google Scholar
6. Siegel, S., Nonparametric statistics for the behavioural sciences. New York: McGraw-Hill, 1956.Google Scholar
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