chisq_test: Chi-squared Test for Count Data

Description

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

chisq_test() also accepts a pipe-friendly data-frame interface for the test of independence between two categorical variables: pass a data frame as x and the two columns either positionally (data %>% chisq_test(var1, var2)) or via vars (data %>% chisq_test(vars = c("var1", "var2"))). The contingency table is built internally. Note that in the positional form the second column occupies the correct argument slot, so use the vars form (or the table interface) if you need to set correct/simulate.p.value.

See the Datanovia tutorial Chi-Square Test of Independence in R for a worked walkthrough.

Usage

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

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.

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 as 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.
vars: optional character vector of length two giving the names of two columns in the data frame x to cross-tabulate for a test of independence. An alternative to passing the two columns positionally.
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.

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. Only available for a single (ungrouped) chisq_test() result.
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

Run this code

# Chi-square goodness of fit test
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
tulip <- c(red = 81, yellow = 50, white = 27)
# Q1: Are the colors equally common?
chisq_test(tulip)
pairwise_chisq_gof_test(tulip)
# Q2: comparing observed to expected proportions
chisq_test(tulip, p = c(1/2, 1/3, 1/6))
pairwise_chisq_test_against_p(tulip, p = c(0.5, 0.33, 0.17))

# 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
# Chi-square test
chisq_test(xtab)
# Compare the proportion of survived between groups
pairwise_prop_test(xtab)

# Test of independence using the data-frame interface
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
df <- data.frame(
  gender = rep(c("M", "F"), each = 100),
  smoker = rep(c("yes", "no", "yes", "no"), times = c(30, 70, 60, 40))
)
# Positional columns
df %>% chisq_test(gender, smoker)
# Equivalent, using vars (keeps `correct` settable)
df %>% chisq_test(vars = c("gender", "smoker"), correct = FALSE)