DescTools (version 0.99.40)

BhapkarTest: Bhapkar Marginal Homogeneity Test

Description

Bhapkar (1966) tested marginal homogeneity by exploiting the asymptotic normality of marginal proportion, and this test is also called Bhapkar's test. The idea of constructing test statistic is similar to the one of generalized McNemar's test statistic used in StuartMaxwellTest, and the major difference lies in the calculation of elements in variance-covariance matrix.

Usage

BhapkarTest(x, y = NULL)

Arguments

x

either a 2-way contingency table in matrix form, or a factor object.

y

a factor object; ignored if x is a matrix.

Details

Although the Bhapkar and Stuart-Maxwell tests are asymptotically equivalent (Keefe, 1982). Generally, the Bhapkar (1966) test is a more powerful alternative to the Stuart-Maxwell test. With a large N, both will produce the same chi-squared value. As the Bhapkar test is more powerful, it is preferred.

References

Bhapkar V.P. (1966). A note on the equivalence of two test criteria for hypotheses in categorical data. Journal of the American Statistical Association, 61: 228-235.

Ireland C.T., Ku H.H., and Kullback S. (1969). Symmetry and marginal homogeneity of an r x r contingency table. Journal of the American Statistical Association, 64: 1323-1341.

See Also

StuartMaxwellTest, mcnemar.test, chisq.test, MHChisqTest, BreslowDayTest

Examples

# NOT RUN {
# Source: http://www.john-uebersax.com/stat/mcnemar.htm#stuart
mc <- as.table(matrix(c(20,3,0,10,30,5,5,15,40), nrow=3))

BhapkarTest(mc)
# }