Use of the Mantel-Haenszel chi 2 overestimates precision in studies with sparse data.

Probability values or "test-based" confidence limits computed on the basis of the Mantel-Haenszel chi 2 statistic may be invalid if minimum cell-size requirements are not met. In 30 studies of occupational proportionate mortality published from 1985 through 1987, the Mantel-Haenszel chi 2 was used in potential violation of cell-size requirements in 21 studies. Sixteen (76%) studies included at least one value that, when compared with testing with the Poisson distribution, was erroneously reported as statistically significant at the 0.05 level. We conclude that by using the Mantel-Haenszel chi 2 with sparse data, some epidemiologists overestimate precision.