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Biometrika 1994 81(2):359-372; doi:10.1093/biomet/81.2.359
© 1994 by Biometrika Trust
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Simple robust tests for scale differences in paired data

PATRICIA M. GRAMBSCH

Division of Biostatistics, School of Public Health, University of Minnesota A-460 Mayo Building, Box 197, 420 Delaware Street S.E., Minneapolis, Minnesota 55455, U.S.A.

The classical statistical test for assessing the difference between the two scale parameters in paired data due to Pitman (1939) and Morgan (1939) is not robust. This paper explores robust alternatives to Pitman's test, using the framework of the one-sample t-test. The asymptotic behaviour of the tests under the null hypothesis is examined. In general, it is easy to construct tests that are asymptotically distribution-free, provided the data come from a symmetric bivariate distribution. Versions of these tests that do not require symmetry are derived. Monte Carlo simulation experiments are done to assess small sample behaviour and power characteristics. The tests are applied to a small data set comparing cancerous and noncancerous lungs.

Key Words: Levene's test • Matched pairs • Pitman's test • Signed-rank test • Spearman's correlation • Variance heterogeneity


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