Woolf Test For Homogeneity in 2x2xk Tables

Test for homogeneity on \(2 \times 2 \times k\) tables over strata (i.e., whether the log odds ratios are the same in all strata).

WoolfTest(x)

Arguments

x

a \(2 \times 2 \times k\) table, where the last dimension refers to the strata.

Value

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

statistic

the chi-squared test statistic.

parameter

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

p.value

\(p\)-value for the test.

method

a character string indicating the type of test performed.

data.name

a character string giving the name(s) of the data.

observed

the observed counts.

expected

the expected counts under the null hypothesis.

See also

mantelhaen.test, BreslowDayTest

Note

This function was previously published as woolf_test() in the vcd package and has been integrated here without logical changes.

Author

David Meyer, Achim Zeileis, Kurt Hornik, Michael Friendly

References

Woolf, B. 1955: On estimating the relation between blood group and disease. Ann. Human Genet. (London) 19, 251-253.

Examples

migraine <- xtabs(freq ~ .,
            cbind(expand.grid(treatment=c("active","placebo"),
                               response=c("better","same"),
                               gender=c("female","male")),
                  freq=c(16,5,11,20,12,7,16,19))
            )

WoolfTest(migraine)
#> 
#> 	Woolf Test on Homogeneity of Odds Ratios (no 3-Way assoc.)
#> 
#> data:  migraine
#> X-squared = 1, df = 1, p-value = 0.2
#>