Woolf Test for Comparing Odds Ratios Across Stratified 2×2 Tables

A test for homogeneity of odds ratios across several 2×2 contingency tables, similar to the Breslow-Day test but based on a different test statistic.

Usage

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 per-stratum log odds ratios (not the raw table counts).

expected

the inverse-variance-weighted mean log odds ratio across strata.

Details

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).

Note

Based on code by David Meyer, Achim Zeileis, Kurt Hornik, Michael Friendly previously published as woolf_test() in the vcd package, adapted to conform to package standards.

References

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

See also

mantelhaen.test()

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

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 = 1.4808, df = 1, p-value = 0.2236
#>