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Chi-square goodness of fit test

Source: R/goodnessOfFitTest.R
goodnessOfFitTest.Rd

Runs a chi-square goodness of fit test to check whether the observed frequencies in a categorical variable match a set of hypothesised probabilities.

Usage

goodnessOfFitTest(x, p = NULL)

Arguments

x

A factor variable containing the observed outcomes.

p

A numeric vector of hypothesised probabilities, one per level of x. The values must sum to 1. If named, the names must match the levels of x (order does not matter). If omitted, all outcomes are assumed to be equally likely.

Value

Prints a summary of the test showing the variable name, null and alternative hypotheses, a table of observed frequencies, expected frequencies, and hypothesised probabilities, and the test results (chi-square statistic, degrees of freedom, p-value). 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 the observed frequencies for a categorical variable are consistent with the probabilities specified in p.

Missing values in x are removed before the test is run, and a warning is issued if any cases are dropped. If the probabilities in p do not sum exactly to 1, they are rescaled with a warning.

If x has unused factor levels (levels with zero observed cases), a warning is issued. Those levels are included in the test with zero observed cases, which changes the degrees of freedom and may give misleading results. Call droplevels on the data first if this is not intended.

See also

chisq.test, associationTest, cramersV

Examples

# raw data
gender <- factor(
  c(
    "male", "male", "male", "male", "female", "female",
    "female", "male", "male", "male"
  )
)

# goodness of fit test against the hypothesis that males and
# females occur with equal frequency
goodnessOfFitTest(gender)
#> 
#>      Chi-square test against specified probabilities
#> 
#> Data variable:   gender 
#> 
#> Hypotheses: 
#>    null:        true probabilities are as specified
#>    alternative: true probabilities differ from those specified
#> 
#> Descriptives: 
#>        observed freq. expected freq. specified prob.
#> female              3              5             0.5
#> male                7              5             0.5
#> 
#> Test results: 
#>    X-squared statistic:  1.6 
#>    degrees of freedom:  1 
#>    p-value:  0.206 
#> 

# goodness of fit test against the hypothesis that males appear
# with probability .6 and females with probability .4.
goodnessOfFitTest(gender, p = c(.4, .6))
#> 
#>      Chi-square test against specified probabilities
#> 
#> Data variable:   gender 
#> 
#> Hypotheses: 
#>    null:        true probabilities are as specified
#>    alternative: true probabilities differ from those specified
#> 
#> Descriptives: 
#>        observed freq. expected freq. specified prob.
#> female              3              4             0.4
#> male                7              6             0.6
#> 
#> Test results: 
#>    X-squared statistic:  0.417 
#>    degrees of freedom:  1 
#>    p-value:  0.519 
#>    warning: expected frequencies too small, results may be inaccurate
#> 
goodnessOfFitTest(gender, p = c(female = .4, male = .6))
#> 
#>      Chi-square test against specified probabilities
#> 
#> Data variable:   gender 
#> 
#> Hypotheses: 
#>    null:        true probabilities are as specified
#>    alternative: true probabilities differ from those specified
#> 
#> Descriptives: 
#>        observed freq. expected freq. specified prob.
#> female              3              4             0.4
#> male                7              6             0.6
#> 
#> Test results: 
#>    X-squared statistic:  0.417 
#>    degrees of freedom:  1 
#>    p-value:  0.519 
#>    warning: expected frequencies too small, results may be inaccurate
#> 
goodnessOfFitTest(gender, p = c(male = .6, female = .4))
#> 
#>      Chi-square test against specified probabilities
#> 
#> Data variable:   gender 
#> 
#> Hypotheses: 
#>    null:        true probabilities are as specified
#>    alternative: true probabilities differ from those specified
#> 
#> Descriptives: 
#>        observed freq. expected freq. specified prob.
#> female              3              4             0.4
#> male                7              6             0.6
#> 
#> Test results: 
#>    X-squared statistic:  0.417 
#>    degrees of freedom:  1 
#>    p-value:  0.519 
#>    warning: expected frequencies too small, results may be inaccurate
#>