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). Generalized to handle tables of any dimensionality beyond 3. For 4-dimensional tables, optionally provides a two-way decomposition of the homogeneity test into row effects, column effects, and residual.
Usage
woolf_test(x, decompose = FALSE)
# S3 method for class 'woolf_test'
print(x, ...)Arguments
- x
An object of class
"woolf_test"- decompose
Logical. If
TRUEandxis 4-dimensional (a \(2 \times 2 \times R \times C\) table), the test is decomposed into row effects, column effects, and residual (interaction). Defaults toFALSE. Ignored for non-4-dimensional tables.- ...
Additional arguments (currently unused)
Value
A list of class "woolf_test" (also inheriting from "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 of the data.
- or_vars
names of the first two dimensions (the 2x2 table variables).
- strata_vars
names of the stratifying variables (dimensions 3 and beyond).
- observed
the observed log odds ratios.
- expected
the expected log odds ratio under the null hypothesis (weighted mean).
- decomposed
logical indicating if decomposition was performed.
When decompose = TRUE (only for 4-dimensional tables), additional components:
- rows
list with statistic, df, p.value, observed, expected for row effects.
- cols
list with statistic, df, p.value, observed, expected for column effects.
- residual
list with statistic, df, p.value for residual (interaction).
References
Woolf, B. (1955). On estimating the relation between blood group and disease. Annals of Human Genetics, 19, 251-253.
See also
Other association tests:
CMHtest(),
GKgamma(),
HLtest(),
zero.test()
Examples
# 3-way tables
data(CoalMiners, package = "vcd")
woolf_test(CoalMiners)
#>
#> Woolf-test on Homogeneity of Odds Ratios (no 3-way association)
#>
#> Data: CoalMiners
#> OR variables: Breathlessness, Wheeze
#> Strata: Age
#>
#> X-squared = 26.2034, df = 8, p-value = 0.0009694
data(Heart, package = "vcdExtra")
woolf_test(Heart)
#>
#> Woolf-test on Homogeneity of Odds Ratios (no 3-way association)
#>
#> Data: Heart
#> OR variables: Disease, Gender
#> Strata: Occup
#>
#> X-squared = 81.0807, df = 2, p-value = 0
# 4-way table without decomposition
data(Fungicide, package = "vcdExtra")
woolf_test(Fungicide)
#>
#> Woolf-test on Homogeneity of Odds Ratios (no 4-way association)
#>
#> Data: Fungicide
#> OR variables: group, outcome
#> Strata: sex, strain
#>
#> X-squared = 0.8548, df = 3, p-value = 0.8363
# 4-way table with decomposition
woolf_test(Fungicide, decompose = TRUE)
#>
#> Woolf-test on Homogeneity of Odds Ratios (no 4-way association)
#>
#> Data: Fungicide
#> OR variables: group, outcome
#> Strata: sex, strain
#>
#> Overall homogeneity test:
#> X-squared = 0.8548, df = 3, p-value = 0.8363
#>
#> Decomposition:
#> Rows (sex): X-squared = 0.0086, df = 1, p-value = 0.9261
#> Cols (strain): X-squared = 0.8257, df = 1, p-value = 0.3635
#> Residual: X-squared = 0.0205, df = 1, p-value = 0.8861
#>
#> Note: Overall = Rows + Columns + Residual
# 4-way table, but need to rearrange dimensions
# How does association between `Preference` and `M_User` vary over strata?
data(Detergent, package = "vcdExtra")
dimnames(Detergent) |> names()
#> [1] "Temperature" "M_User" "Preference" "Water_softness"
Detergent <- aperm(Detergent, c(3, 2, 1, 4))
woolf_test(Detergent)
#>
#> Woolf-test on Homogeneity of Odds Ratios (no 4-way association)
#>
#> Data: Detergent
#> OR variables: Preference, M_User
#> Strata: Temperature, Water_softness
#>
#> X-squared = 8.0132, df = 5, p-value = 0.1555