contingency_table: Contingency table analyses

In statsExpressions: Tidy Dataframes and Expressions with Statistical Details

Contingency table analyses

Description

Parametric and Bayesian one-way and two-way contingency table analyses.

Usage

contingency_table(
  data,
  x,
  y = NULL,
  paired = FALSE,
  type = "parametric",
  counts = NULL,
  ratio = NULL,
  alternative = "two.sided",
  digits = 2L,
  conf.level = 0.95,
  sampling.plan = "indepMulti",
  fixed.margin = "rows",
  prior.concentration = 1,
  ...
)

Arguments

data	A data frame (or a tibble) from which variables specified are to be taken. Other data types (e.g., matrix, table, array, etc.) will not be accepted. Additionally, grouped data frames from {dplyr} should be ungrouped before they are entered as data.
x	The variable to use as the rows in the contingency table.
y	The variable to use as the columns in the contingency table. Default is NULL. If NULL, one-sample proportion test (a goodness of fit test) will be run for the x variable.
paired	Logical indicating whether data came from a within-subjects or repeated measures design study (Default: FALSE). Only relevant for two-way tables (i.e., when y is supplied), and paired designs are only supported for frequentist tests (McNemar's test). For a two-way table with type = "bayes", paired is ignored and the Bayesian test of independence for unpaired data is run instead. For one-way tables (y = NULL), paired has no effect.
type	A character specifying the type of statistical approach: "parametric" "nonparametric" "robust" "bayes" You can specify just the initial letter (e.g. "np" or "bf"). Matching is on the initial lowercase letter only, so any other value (including capitalized values such as "Bayes") falls back to "parametric" without a warning.
counts	The variable in data containing counts, or NULL if each row represents a single observation.
ratio	A vector of proportions: the expected proportions for the proportion test (should sum to 1). Default is NULL, which means the null is equal theoretical proportions across the levels of the nominal variable. E.g., ratio = c(0.5, 0.5) for two levels, ratio = c(0.25, 0.25, 0.25, 0.25) for four levels, etc.
alternative	A character string specifying the alternative hypothesis; Controls the type of CI returned: "two.sided" (default, two-sided CI), "greater" or "less" (one-sided CI). Partial matching is allowed (e.g., "g", "l", "two"...). See section One-Sided CIs in the effectsize_CIs vignette.
digits	Number of digits for rounding or significant figures. May also be "signif" to return significant figures or "scientific" to return scientific notation. Control the number of digits by adding the value as suffix, e.g. digits = "scientific4" to have scientific notation with 4 decimal places, or digits = "signif5" for 5 significant figures (see also signif()).
conf.level	Scalar between 0 and 1 (default: ⁠95%⁠ confidence/credible intervals, 0.95).
sampling.plan	Character describing the sampling plan. Possible options: "indepMulti" (independent multinomial; default) "poisson" "jointMulti" (joint multinomial) "hypergeom" (hypergeometric). Only used for Bayesian two-way tables. For more, see BayesFactor::contingencyTableBF().
fixed.margin	For the independent multinomial sampling plan, which margin is fixed ("rows" or "cols"). Defaults to "rows". Only used for Bayesian two-way tables.
prior.concentration	Specifies the prior concentration parameter, set to 1 by default. It indexes the expected deviation from the null hypothesis under the alternative, and corresponds to Gunel and Dickey's (1974) "a" parameter. Only used for Bayesian analyses.
...	Additional arguments (currently ignored).

Value

The returned object is a tibble data frame with the additional class "statsExpressions". The exact set of columns depends on the test and, for functions that accept a type argument, on the chosen analysis (parametric, non-parametric, robust, or Bayesian). Any given call therefore returns some (not all) of the columns below.

Hypothesis testing

• statistic: the numeric value of a statistic

• df: the numeric value of a parameter being modeled (often degrees of freedom for the test)

• df.error and df: relevant only if the statistic in question has two degrees of freedom (e.g. anova)

• p.value: the p-value associated with the observed statistic (two-sided unless a one-sided alternative is requested, where supported)

• method: the name of the inferential statistical test

Effect size estimation

• effectsize: the name of the effect size

• estimate: estimated value of the effect size

• conf.level: the coverage level of the confidence/credible interval (e.g. 0.95); the interval itself spans conf.low to conf.high

• conf.low: lower bound for the effect size estimate

• conf.high: upper bound for the effect size estimate

• conf.method: method used to compute the confidence/credible interval

• conf.distribution: statistical distribution for the effect

Bayesian analysis (only when type = "bayes")

• bf10: Bayes factor for the alternative hypothesis relative to the null

• log_e_bf10: natural logarithm of the Bayes factor (present for most, but not all, Bayesian analyses)

• prior.distribution, prior.scale, prior.location: prior specification used to compute the Bayes factor and posterior estimates

Pairwise comparisons (for pairwise_comparisons() and pairwise_contingency_table())

• group1, group2: the two levels being compared

• p.adjust.method: the adjustment method used for multiple comparisons

• p.value.adj: the adjusted p-value; returned by pairwise_contingency_table(). Note that pairwise_comparisons() instead folds the adjusted value into p.value (and does not return a separate p.value.adj column)

Common columns

• n.obs: number of observations

• expression: a list-column of pre-formatted plotmath expressions; each element is a language object (not a character string) containing the statistical details, ready to be used in {ggplot2} (e.g. in labs() or annotate())

For a per-function, column-by-column breakdown of the output (and an explanation of the internal add_expression_col() engine that builds the expression column), see the Return value schema article. For more examples, see the data frame output vignette.

Contingency table analyses

The table below provides summary about:

• statistical test carried out for inferential statistics

• type of effect size estimate and a measure of uncertainty for this estimate

• functions used internally to compute these details

There are no dedicated non-parametric or robust contingency table analyses. type = "nonparametric" and type = "robust" are accepted, but run the same frequentist tests as type = "parametric" (the "Parametric/Non-parametric" rows below).

two-way table

Hypothesis testing

Type	Design	Test	Function used
Parametric/Non-parametric	Unpaired	Pearson's chi-squared test	stats::chisq.test()
Bayesian	Unpaired	Bayesian Pearson's chi-squared test	BayesFactor::contingencyTableBF()
Parametric/Non-parametric	Paired	McNemar's chi-squared test	stats::mcnemar.test()
Bayesian	Paired	No	No

Effect size estimation

Type	Design	Effect size	CI available?	Function used
Parametric/Non-parametric	Unpaired	Cramer's V	Yes	effectsize::cramers_v()
Bayesian	Unpaired	Cramer's V	Yes	effectsize::cramers_v()
Parametric/Non-parametric	Paired	Cohen's g	Yes	effectsize::cohens_g()
Bayesian	Paired	No	No	No

Paired Bayesian analysis is not supported: for a two-way table with type = "bayes", the paired argument is ignored and the unpaired Bayesian test is run instead.

one-way table

Hypothesis testing

Type	Test	Function used
Parametric/Non-parametric	Goodness of fit chi-squared test	stats::chisq.test()
Bayesian	Bayesian Goodness of fit chi-squared test	(custom)

Effect size estimation

Type	Effect size	CI available?	Function used
Parametric/Non-parametric	Pearson's C	Yes	effectsize::pearsons_c()
Bayesian	No	No	No

Examples

#### -------------------- association test ------------------------ ####

# ------------------------ frequentist ---------------------------------

# unpaired

set.seed(123)
contingency_table(
  data = mtcars,
  x = am,
  y = vs,
  paired = FALSE
)

# paired

paired_data <- dplyr::tibble(
  response_before = structure(
    c(1L, 2L, 1L, 2L),
    levels = c("no", "yes"),
    class = "factor"
  ),
  response_after = structure(
    c(1L, 1L, 2L, 2L),
    levels = c("no", "yes"),
    class = "factor"
  ),
  Freq = c(65L, 25L, 5L, 5L)
)

set.seed(123)
contingency_table(
  data = paired_data,
  x = response_before,
  y = response_after,
  paired = TRUE,
  counts = Freq
)

# ------------------------ Bayesian -------------------------------------

# unpaired

set.seed(123)
contingency_table(
  data = mtcars,
  x = am,
  y = vs,
  paired = FALSE,
  type = "bayes"
)

# paired

set.seed(123)
contingency_table(
  data = paired_data,
  x = response_before,
  y = response_after,
  paired = TRUE,
  counts = Freq,
  type = "bayes"
)

#### -------------------- goodness-of-fit test -------------------- ####

# ------------------------ frequentist ---------------------------------

set.seed(123)
contingency_table(
  data = as.data.frame(HairEyeColor),
  x = Eye,
  counts = Freq
)

# ------------------------ Bayesian -------------------------------------

set.seed(123)
contingency_table(
  data = as.data.frame(HairEyeColor),
  x = Eye,
  counts = Freq,
  ratio = c(0.2, 0.2, 0.3, 0.3),
  type = "bayes"
)

statsExpressions documentation built on Oct. 9, 2026, 5:06 p.m.