Testing Procedures to Compare the Equality of Three Proportions for Small Sample Correlated Binary Data

10.29973/JCSA.200806.0004

Hong-Long Wang；Chun-Chao Wang

Correlated binary data ； Cochran's Q statistics ； Standardized square D statistics ； modified likelihood ratio L statistics ； the equality of proportions

中國統計學報

46卷2期（2008 / 06 / 01）

130 - 143

英文

To compare proportions for multi-dimension binary data, we often need large samples to fulfill the requirement of the asymptotic procedure. We might adapt similar procedure for small samples if we are willing to suffer low power. In study, we proposed the standardized square D statistics, the Cochran's Q statistics and the modified likelihood ratio L statistics to test the equality of proportions for three dimensional correlated binary data. We find that all three proposed statistics we can detect the differences of proportions at significant level 0.05 for the sample size is as small as 6, at least 8 samples at significant level 0.01 and at least 9 samples at significant level 0.005. We compute the exact p-value upto around 10% for all the possible sample points with size less than 20. We also compare the performance of three proposed statistics in terms of the mean power. And found that none of the proposed statistics can dominate the mean power for sample size less than or equal to 20. The D statistics seems to perform better at 5% significant levels while L statistics performs better at 0.01 and 0.005 significant level. Q only performs well for n=6, 7 at 5% level, n=8, 9 at 1% level and n=9 at 0.5% level.

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