Performs chi-squared tests, including goodness-of-fit, homogeneity and independence tests.

chisq_test(x, y = NULL, correct = TRUE, p = rep(1/length(x),
  length(x)), rescale.p = FALSE, simulate.p.value = FALSE, B = 2000)

pairwise_chisq_gof_test(x, p.adjust.method = "holm", ...)

pairwise_chisq_test_against_p(x, p = rep(1/length(x), length(x)),
  p.adjust.method = "holm", ...)

chisq_descriptives(res.chisq)

expected_freq(res.chisq)

observed_freq(res.chisq)

pearson_residuals(res.chisq)

std_residuals(res.chisq)

Arguments

x

a numeric vector or matrix. x and y can also both be factors.

y

a numeric vector; ignored if x is a matrix. If x is a factor, y should be a factor of the same length.

correct

a logical indicating whether to apply continuity correction when computing the test statistic for 2 by 2 tables: one half is subtracted from all \(|O - E|\) differences; however, the correction will not be bigger than the differences themselves. No correction is done if simulate.p.value = TRUE.

p

a vector of probabilities of the same length of x. An error is given if any entry of p is negative.

rescale.p

a logical scalar; if TRUE then p is rescaled (if necessary) to sum to 1. If rescale.p is FALSE, and p does not sum to 1, an error is given.

simulate.p.value

a logical indicating whether to compute p-values by Monte Carlo simulation.

B

an integer specifying the number of replicates used in the Monte Carlo test.

p.adjust.method

method to adjust p values for multiple comparisons. Used when pairwise comparisons are performed. Allowed values include "holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr", "none". If you don't want to adjust the p value (not recommended), use p.adjust.method = "none".

...

other arguments passed to the function {chisq_test}().

res.chisq

an object of class chisq_test.

Value

return a data frame with some the following columns:

  • n: the number of participants.

  • group, group1, group2: the categories or groups being compared.

  • statistic: the value of Pearson's chi-squared test statistic.

  • df: the degrees of freedom of the approximate chi-squared distribution of the test statistic. NA if the p-value is computed by Monte Carlo simulation.

  • p: p-value.

  • p.adj: the adjusted p-value.

  • method: the used statistical test.

  • p.signif, p.adj.signif: the significance level of p-values and adjusted p-values, respectively.

  • observed: observed counts.

  • expected: the expected counts under the null hypothesis.

The returned object has an attribute called args, which is a list holding the test arguments.

Functions

  • chisq_test: performs chi-square tests including goodness-of-fit, homogeneity and independence tests.

  • pairwise_chisq_gof_test: perform pairwise comparisons between groups following a global chi-square goodness of fit test.

  • pairwise_chisq_test_against_p: perform pairwise comparisons after a global chi-squared test for given probabilities. For each group, the observed and the expected proportions are shown. Each group is compared to the sum of all others.

  • chisq_descriptives: returns the descriptive statistics of the chi-square test. These include, observed and expected frequencies, proportions, residuals and standardized residuals.

  • expected_freq: returns the expected counts from the chi-square test result.

  • observed_freq: returns the observed counts from the chi-square test result.

  • pearson_residuals: returns the Pearson residuals, (observed - expected) / sqrt(expected).

  • std_residuals: returns the standardized residuals

Examples

# Chi-square goodness of fit test #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% tulip <- c(red = 81, yellow = 50, white = 27) # Q1: Are the colors equally common? chisq_test(tulip)
#> # A tibble: 1 x 6 #> n statistic p df method p.signif #> * <int> <dbl> <dbl> <dbl> <chr> <chr> #> 1 3 27.9 0.00000088 2 Chi-square test ****
pairwise_chisq_gof_test(tulip)
#> # A tibble: 3 x 8 #> n group1 group2 statistic p df p.adj p.adj.signif #> * <int> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <chr> #> 1 2 red yellow 7.34 0.00676 1 0.0135 * #> 2 2 red white 27 0.000000203 1 0.000000609 **** #> 3 2 yellow white 6.87 0.00876 1 0.0135 *
# Q2: comparing observed to expected proportions chisq_test(tulip, p = c(1/2, 1/3, 1/6))
#> # A tibble: 1 x 6 #> n statistic p df method p.signif #> * <int> <dbl> <dbl> <dbl> <chr> <chr> #> 1 3 0.203 0.904 2 Chi-square test ns
pairwise_chisq_test_against_p(tulip, p = c(1/2, 1/3, 1/6))
#> # A tibble: 3 x 9 #> group observed expected n statistic p df p.adj p.adj.signif #> * <chr> <dbl> <dbl> <int> <dbl> <dbl> <dbl> <dbl> <chr> #> 1 red 81 79 2 0.101 0.75 1 1 ns #> 2 yellow 50 52.7 2 0.203 0.653 1 1 ns #> 3 white 27 26.3 2 0.0203 0.887 1 1 ns
# Homogeneity of proportions between groups #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% # Data: Titanic xtab <- as.table(rbind( c(203, 118, 178, 212), c(122, 167, 528, 673) )) dimnames(xtab) <- list( Survived = c("Yes", "No"), Class = c("1st", "2nd", "3rd", "Crew") ) xtab
#> Class #> Survived 1st 2nd 3rd Crew #> Yes 203 118 178 212 #> No 122 167 528 673
# Chi-square test chisq_test(xtab)
#> # A tibble: 1 x 6 #> n statistic p df method p.signif #> * <dbl> <dbl> <dbl> <int> <chr> <chr> #> 1 2201 190. 5.00e-41 3 Chi-square test ****
# Compare the proportion of survived between groups pairwise_prop_test(xtab)
#> # A tibble: 6 x 5 #> group1 group2 p p.adj p.adj.signif #> * <chr> <chr> <dbl> <dbl> <chr> #> 1 1st 2nd 3.13e- 7 9.38e- 7 **** #> 2 1st 3rd 2.55e-30 1.27e-29 **** #> 3 1st Crew 1.62e-35 9.73e-35 **** #> 4 2nd 3rd 6.90e- 7 1.38e- 6 **** #> 5 2nd Crew 1.94e- 8 7.75e- 8 **** #> 6 3rd Crew 6.03e- 1 6.03e- 1 ns