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Evaluation of an adjusted chi‐square statistic as applied to observational studies involving clustered binary data
Author(s) -
Jung SinHo,
Ahn Chul,
Donner Allan
Publication year - 2001
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.857
Subject(s) - statistics , statistic , chi square test , binary data , test statistic , observational study , ancillary statistic , mathematics , binary number , square (algebra) , statistical hypothesis testing , pearson's chi squared test , econometrics , press statistic , f test , arithmetic , geometry
A simple adjustment to the Pearson chi‐square test has been proposed for comparing proportions estimated from clustered binary observations. However, the assumptions needed to assure the validity of this test have not yet been thoroughly addressed. These assumptions will hold for experimental comparisons, but could be violated for some observational comparisons. In this paper we investigate the conditions under which the adjusted chi‐square statistic is valid and examine its performance when these assumptions are violated. We also introduce some alternative test statistics that do not require these assumptions. The test statistics considered are then compared through simulation and an example presented based on real data. The simulation study shows that the adjusted chi‐square statistic generally produces empirical type I errors close to nominal under the assumption of a common intracluster correlation coefficient. Even if the intracluster correlations are different, the adjusted chi‐square statistic performs well when the groups have equal numbers of clusters. Copyright © 2001 John Wiley & Sons, Ltd.