Premium
Small Sample Properties of the Mantel‐Haenszel Test Statistic for Density Follow‐Up Studies
Author(s) -
Boshuizen H. C.
Publication year - 1988
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710300613
Subject(s) - contingency table , mathematics , statistic , statistics , cumulant , skewness , test statistic , continuity correction , edgeworth series , chi square test , wald test , pearson's chi squared test , statistical hypothesis testing , econometrics , poisson distribution , negative binomial distribution , beta binomial distribution
For the analysis of combinations of 2×2 non‐contingency tables as obtained from density follow‐up studies (relating a number of events to a number of person‐years of follow‐up) an analogue of the Mantel‐Haenszel test for 2×2 contingency tables is widely used. In this paper the small sample properties of this test, both with and without continuity correction, are evaluated. Also the improvement of the test‐statistic by using the first four cumulants via the Edgeworth expansion was studied. Results on continuity correction agree with similar studies on the Mantel‐Haenszel statistic for 2×2 contingency tables: Continuity correction gives a p ‐value which approximates the exact p ‐value better than the p ‐value obtained without this correction; both the exact test and its approximations show considerable conservatism in small samples; the uncorrected Mantel‐Haenszel test statistic gives a p ‐value that agrees more with the nominal significance level, but can be anti‐conservative. The p ‐value based on the first four cumulants gives a better approximation of the exact p ‐value than the continuity corrected test, especially when the distribution has marked skewness.