Contingency table analyses

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).

type

A character specifying the type of statistical approach:

• "parametric"

• "nonparametric"

• "robust"

• "bayes"

You can specify just the initial letter.

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). If NULL, no confidence intervals will be computed.

sampling.plan

Character describing the sampling plan. Possible options are "indepMulti" (independent multinomial; default), "poisson", "jointMulti" (joint multinomial), "hypergeom" (hypergeometric). For more, see ?BayesFactor::contingencyTableBF().

fixed.margin

For the independent multinomial sampling plan, which margin is fixed ("rows" or "cols"). Defaults to "rows".

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.

...

Additional arguments (currently ignored).

Value

The returned tibble data frame can contain some or all of the following columns (the exact columns will depend on the statistical test):

• 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 two-sided p-value associated with the observed statistic

• method: the name of the inferential statistical test

• estimate: estimated value of the effect size

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

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

• conf.level: width of the confidence interval

• conf.method: method used to compute confidence interval

• conf.distribution: statistical distribution for the effect

• effectsize: the name of the effect size

• n.obs: number of observations

• expression: pre-formatted expression containing statistical details

For examples, see 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

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

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

if (identical(Sys.getenv("NOT_CRAN"), "true")) {
  #### -------------------- association test ------------------------ ####

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

  # unpaired

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

  # paired

  paired_data <- 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"
  )
}
#> # A tibble: 1 × 4
#>      bf10 prior.scale method                                      expression
#>     <dbl>       <dbl> <chr>                                       <list>    
#> 1 4.17e55           1 Bayesian one-way contingency table analysis <language>