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Biometrika 1996 83(4):928-933; doi:10.1093/biomet/83.4.928
© 1996 by Biometrika Trust
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MISCELLANEA

Is the Simes improved Bonferroni procedure conservative?

ESTER SAMUEL-CAHN

Department of Statistics, The Hebrew University of Jerusalem Jerusalem 91905, Israel

Simes (1986) proposed a modified Bonferroni procedure for conducting multiple tests of significance. He proved that, when the n test statistics are independent, his procedure has exact size {alpha}. Already Hommel(1983) had considered a similar procedure and shown that it need not be conservative. He gave an attainable upper bound for its anticonservativeness. Here we show that, for one-sided tests based on positively correlated bivariate normal test statistics, the procedure is conservative, and for negatively correlated such variables it is anticonservative. Two-sided tests based on bivariate normal variables are always conservative. Some numerical values are given, which show that for all practical purposes the nominal {alpha}-value can be used.

Key Words: Anticonservative test • Bivariate normal distribution • Conservative test • Modified Bonferroni procedure


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