Bhapkar Marginal Homogeneity Test for Comparing Paired Marginal Distributions Across Multiple Categories

An asymptotic chi-squared test for marginal homogeneity in square contingency tables for dependent samples, similar to the Stuart-Maxwell test but based on a different test statistic and generally slightly more powerful.

Usage

bhapkarTest(x, y = NULL)

Arguments

x

either a 2-way \(k \times k\) contingency table in matrix form, or a factor.

y

a factor with the same levels as x; ignored if x is a matrix.

Value

A list with class "htest" containing the following components:

statistic

the value of the chi-squared test statistic.

parameter

the degrees of freedom of the approximate chi-squared distribution of the test statistic.

p.value

the p-value of the test.

method

a character string indicating the test performed.

data.name

a character string giving the name of the data.

Details

Bhapkar's test (Bhapkar, 1966) is used to assess marginal homogeneity in square contingency tables. It is based on the asymptotic normality of marginal proportions and is closely related to the generalized McNemar test, as implemented in stuartMaxwellTest().

The two tests differ only in the estimation of the variance-covariance matrix of the marginal proportions and are asymptotically equivalent (Keefe, 1982), meaning that for large sample sizes they yield the same chi-squared statistic. For finite samples, however, the Bhapkar test is generally more powerful and is therefore preferred in practice.

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.

Keefe T.J. (1982) On the relationship between two tests for homogeneity of the marginal distributions in a two-way classification. Biometrika, 69: 683-684.

Sun X., Yang Z. (2008) Generalized McNemar's Test for Homogeneity of the Marginal Distributions. SAS Global Forum 2008: Statistics and Data Analysis, Paper 382-208.

See also

mcnemar.test,chisq.test

Other test.categorical: barnardTest(), breslowDayTest(), cochranQTest(), gTest(), lehmacherTest(), mantelTrendTest(), stuartMaxwellTest(), woolfTest()

Examples

# Source: https://john-uebersax.com/stat/mcnemar.htm#bhapkar
mc <- as.table(matrix(c(20,3,0,10,30,5,5,15,40), nrow=3))

bhapkarTest(mc)
#> 
#> 	Bhapkar test for marginal homogeneity
#> 
#> data:  mc
#> chi-squared = 15.423, df = 2, p-value = 0.0004476
#>