Lehmacher's Test for Marginal Homogenity

Performs Lehmacher's chi-squared test for marginal homogenity in a symmetric two-dimensional contingency table.

LehmacherTest(x, y = NULL)

# S3 method for class 'mtest'
print(x, digits = 4L, ...)

Arguments

x: either a two-dimensional contingency table in matrix form, or a factor object.
y: a factor object; ignored if x is a matrix.
digits: a non-null value for digits specifies the minimum number of significant digits to be printed in values. See details in print.default.
...: further arguments to be passed to or from other methods. They are ignored in this function.

Details

The null is that the probabilities of being classified into cells [i,j] and [j,i] are the same.

If x is a matrix, it is taken as a two-dimensional contingency table, and hence its entries should be nonnegative integers. Otherwise, both x and y must be vectors or factors of the same length. Incomplete cases are removed, vectors are coerced into factors, and the contingency table is computed from these.

Value

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

statistic: a vector with the value of the test statistics.
parameter: the degrees of freedom, which is always 1 in LehmacherTest.
p.value: a vector with the p-values of the single tests.
p.value.corr: a vector with the "hochberg" adjusted p-values of the single tests. (See p.adjust)
method: a character string indicating what type of test was performed.
data.name: a character string giving the name of the data.

References

Lehmacher, W. (1980) Simultaneous sign tests for marginal homogeneity of square contingency tables Biometrical Journal, Volume 22, Issue 8, pages 795-798

Author

Andri Signorell <andri@signorell.net>

Examples

x <- matrix(c(400,40,20,10, 
              50,300,60,20, 
              10,40,120,5, 
              5,90,50,80), nrow=4, byrow=TRUE)
              
LehmacherTest(x)
#> 
#> 	Lehmacher-Test on Marginal Homogeneity
#> 
#> data:  x
#>   X-squared      pval  pval adj    
#> 1    0.1852   0.66695   0.66695    
#> 2    5.3333   0.02092   0.04184   *
#> 3   30.4054 3.505e-08 1.052e-07 ***
#> 4   67.2222 2.220e-16 8.882e-16 ***
#> 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>