Chi-square test of association / independence

Runs a chi-square test to check whether two categorical variables are independent of one another.

Usage

associationTest(formula, data = NULL)

Arguments

formula

A one-sided formula of the form ~var1 + var2, specifying the two variables to be tested. Both variables must be factors.

data

An optional data frame containing the variables named in formula. If omitted, the variables are looked up in the workspace.

Value

Prints a summary of the test showing the variable names, null and alternative hypotheses, observed and expected frequency tables, test results (chi-square statistic, degrees of freedom, p-value), and Cramer's V as a measure of effect size. The underlying results are also returned as a list, so the output can be assigned to a variable and inspected if needed.

Details

The test checks whether two categorical variables are statistically independent. Both variables must be factors, and the formula must be one-sided with exactly two variables, e.g. ~gender + answer.

Missing values are removed before the test is run, and a warning is issued if any cases are dropped. When both variables have only two levels, Yates' continuity correction is applied automatically to the chi-squared statistic (though not to the Cramer's V effect size).

If either variable has unused factor levels (levels with zero observed cases), a warning is issued. Those levels are included in the contingency table with zero observed cases, which may give misleading results. Call droplevels on the data first if this is not intended.

See also

chisq.test, goodnessOfFitTest, cramersV

Examples

df <- data.frame(
  gender = factor(c("male", "male", "male", "male", "female", "female", "female")),
  answer = factor(c("heads", "heads", "heads", "heads", "tails", "tails", "heads"))
)

associationTest(~ gender + answer, df)
#> 
#>      Chi-square test of categorical association
#> 
#> Variables:   gender, answer 
#> 
#> Hypotheses: 
#>    null:        variables are independent of one another
#>    alternative: some contingency exists between variables
#> 
#> Observed contingency table:
#>         answer
#> gender   heads tails
#>   female     1     2
#>   male       4     0
#> 
#> Expected contingency table under the null hypothesis:
#>         answer
#> gender   heads tails
#>   female  2.14 0.857
#>   male    2.86 1.143
#> 
#> Test results: 
#>    X-squared statistic:  1.181 
#>    degrees of freedom:  1 
#>    p-value:  0.277 
#> 
#> Other information: 
#>    estimated effect size (Cramer's v):  0.73 
#>    Yates' continuity correction has been applied
#>    warning: expected frequencies too small, results may be inaccurate
#>