# BhapkarTest: Bhapkar Marginal Homogeneity Test In AndriSignorell/DescTools: Tools for Descriptive Statistics

## 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

 `1` ```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.

## Author(s)

Andri Signorell <andri@signorell.net>

## 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.

`StuartMaxwellTest`, `mcnemar.test`, `chisq.test`, `MHChisqTest`, `BreslowDayTest`
 ```1 2 3 4``` ```# 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) ```