MarginalHomogeneityTest {coin}R Documentation

Marginal Homogeneity Test

Description

Testing marginal homogeneity in a complete block design.

Usage

## S3 method for class 'formula'
mh_test(formula, data, subset = NULL, ...)
## S3 method for class 'table'
mh_test(object, ...)
## S3 method for class 'SymmetryProblem'
mh_test(object, distribution = c("asymptotic", "approximate"), ...) 

Arguments

formula

a formula of the form y ~ x | block where y is a factor giving the data values and x a factor with two or more levels giving the corresponding replications. block is an optional factor (which is generated automatically when omitted).

data

an optional data frame containing the variables in the model formula.

subset

an optional vector specifying a subset of observations to be used.

object

an object inheriting from class SymmetryProblem or a table with identical dimnames attributes.

distribution

a character, the null distribution of the test statistic can be approximated by its asymptotic distribution (asymptotic) or via Monte-Carlo resampling (approximate). Alternatively, the functions approximate or asymptotic can be used to specify how the exact conditional distribution of the test statistic should be calculated or approximated.

...

further arguments to be passed to or from methods.

Details

The null hypothesis of independence of row and column totals is tested. The corresponding test for binary factors x and y is known as McNemar test. For larger tables, Stuart's W_0 statistic (Stuart, 1955, Agresti, 2002, page 422, also known as Stuart-Maxwell test) is computed. The marginal homogeneity statistic W of Bhapkar (1966) can be derived from W_0 via W = W_0 / (1 - W_0 / n) (see Agresti, 2002, page 422).

Scores must be a list of length one (row and column scores coincide). When scores are given or if x is ordered, the corresponding linear association test is computed (see Agresti, 2002).

Note that for a large number of observations, this function is rather inefficient.

Value

An object inheriting from class IndependenceTest with methods show, pvalue and statistic.

References

Alan Agresti (2002). Categorical Data Analysis. Hoboken, New Jersey: John Wiley & Sons.

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

Alan Stuart (1955). A test for homogeneity of the marginal distributions in a two-way classification. Biometrika 42(3/4), 412–416.

Examples


  ### Opinions on Pre- and Extramarital Sex, Agresti (2002), page 421
  opinions <- c("always wrong", "almost always wrong", 
                "wrong only sometimes", "not wrong at all")

  PreExSex <- as.table(matrix(c(144, 33, 84, 126, 
                                  2,  4, 14,  29, 
                                  0,  2,  6,  25, 
                                  0,  0,  1,  5), nrow = 4, 
                              dimnames = list(PremaritalSex = opinions,
                                              ExtramaritalSex = opinions)))

  ### treating response as nominal
  mh_test(PreExSex)

  ### and as ordinal
  mh_test(PreExSex, scores = list(response = 1:length(opinions)))

  ### example taken from 
  ### http://ourworld.compuserve.com/homepages/jsuebersax/mcnemar.htm
  rating <- c("low", "moderate", "high")
  x <- as.table(matrix(c(20, 10,  5,
                         3, 30, 15,
                         0,  5, 40), 
                       ncol = 3, byrow = TRUE,
                       dimnames = list(Rater1 = rating, Rater2 = rating)))
  ### test statistic W_0 = 13.76
  mh_test(x)


[Package coin version 1.0-20 Index]