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Maximally Selected x 2 Statistics for k × 2 Tables
Author(s) -
Betensky Rebecca A.,
Rabinowitz Daniel
Publication year - 1999
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.1999.00317.x
Subject(s) - statistics , statistic , mathematics , sample size determination , test statistic , population , summary statistics , sample (material) , outcome (game theory) , statistical hypothesis testing , medicine , econometrics , environmental health , chemistry , mathematical economics , chromatography
Summary. It is common in epidemiologic analyses to summarize continuous outcomes as falling above or below a threshold. With such a dichotomized outcome, the usual x 2 statistics for association or trend can be used to test for equality of proportions across strata of the study population. However, if the threshold is chosen to maximize the test statistic, the nominal x 2 reference distributions are incorrect. In this paper, the asymptotic distributions of maximally selected x 2 statistics for association and for trend for the k × 2 table are derived. The methodology is illustrated with data from an AIDS clinical trial. The results of simulation experiments that assess the accuracy of the asymptotic distributions in moderate sample sizes are also reported.