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The Comparative Effects of Varying Cell Sizes on Mcnemar's Test with the Χ^2 Test of Independence and T Test for Related Samples
Kenneth U. Black
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Abstract
This study compared the results for McNemar's test, the t test for related measures, and the chi-square test of independence as cell sized varied in a two-by-two frequency table. In this study. the probability results for McNemar's rest, the t test for related measures, and the chi-square test of independence were compared for 13,310 different combinations of cell sizes in a two-by-two design. Several conclusions were reached: With very few exceptions, the t test for related measures and McNemar's test yielded probability results within .002 of each other. The chi-square test seemed to equal the other two tests consistently only when low probabilities less than or equal to .001 were attained. It is recommended that the researcher consider using the t test for related measures as a viable option for McNemar's test except when the researcher is certain he/she is only interested in 'changes'. The chi-square test of independence not only tests a different hypothesis than McNemar's test, but it often yields greatly differing results from McNemar's test.