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Multiple Comparisons and P Values

THOMAS B. NEWMAN, MD, MPH; WARREN S. BROWNER, MD, MPH
Am J Dis Child. 1991;145(3):250. doi:10.1001/archpedi.1991.02160030014005.
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Sir.—We would like to comment on the multiple-comparisons problem posed by Brown1 in his recent contribution about P values. The problem is: why should an investigator who wishes to compare treatments A and B be required to demonstrate a greater level of statistical significance if he or she studies treatment C at the same time? On the one hand, there is an apparent need to protect against the increased risk of a type I error associated with making multiple comparisons. On the other hand, it is counterintuitive that the conclusion for the comparison between A and B differs depending on whether the investigator had the resources to study treatment C at the same time.

Brown suggested leaving this enigma to experts in probability. While we do not claim such expertise, we have offered an explanation of this apparent contradiction that some of our colleagues have found helpful.2

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