Cramer's V

Calculates Cramer's V, a measure of the strength of association for chi-square tests.

Usage

cramersV(...)

Arguments

...

Arguments passed to chisq.test, in the same format accepted by that function. The correct argument is always set to FALSE internally and cannot be overridden.

Value

A single number giving the value of Cramer's V.

Details

Cramer's V summarises the strength of association from a chi-square test. It is appropriate for both tests of association (two categorical variables) and goodness of fit tests (one variable versus hypothesised probabilities). Values range from 0 (no association) to 1 (perfect association).

Yates' continuity correction is never applied, regardless of the table dimensions. This is intentional: applying the correction reduces the chi-squared statistic, which causes V to fall below 1 even for perfectly associated 2x2 tables — inconsistent with its definition as an effect size on the [0, 1] scale.

See also

chisq.test, associationTest, goodnessOfFitTest

Examples

# frequency table for two groups, each choosing from three options
condition1 <- c(30, 20, 50)
condition2 <- c(35, 30, 35)
X <- cbind(condition1, condition2)
rownames(X) <- c("choice1", "choice2", "choice3")

# chi-square test of association
chisq.test(X)
#> 
#> 	Pearson's Chi-squared test
#> 
#> data:  X
#> X-squared = 5.0317, df = 2, p-value = 0.0808
#> 

# effect size estimate
cramersV(X)
#> [1] 0.1586139