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Pairwise contingency table analyses

Source: R/pairwise-contingency-table.R
pairwise_contingency_table.Rd

Pairwise Fisher's exact tests as post hoc tests for contingency table analyses, with effect sizes (Cramer's V) and p-value adjustment for multiple comparisons.

Usage

pairwise_contingency_table(
  data,
  x,
  y,
  counts = NULL,
  p.adjust.method = "holm",
  digits = 2L,
  conf.level = 0.95,
  alternative = "two.sided",
  ...
)

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.

counts

The variable in data containing counts, or NULL if each row represents a single observation.

p.adjust.method

Adjustment method for p-values for multiple comparisons. Possible methods are: "holm" (default), "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr", "none".

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.

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.

...

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 two-sided p-value associated with the observed statistic

  • 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.

Pairwise contingency table tests

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

Hypothesis testing

Testp-value adjustment?Function used
Fisher's exact testYesstats::fisher.test()

Effect size estimation

Effect sizeCI available?Function used
Cramer's VYeseffectsize::cramers_v()

Citation

Patil, I., (2021). statsExpressions: R Package for Tidy Dataframes and Expressions with Statistical Details. Journal of Open Source Software, 6(61), 3236, https://doi.org/10.21105/joss.03236

Examples

# for reproducibility
set.seed(123)
library(statsExpressions)

# pairwise Fisher's exact tests with Holm adjustment
pairwise_contingency_table(
  data = mtcars,
  x = cyl,
  y = am,
  p.adjust.method = "holm"
)
#> # A tibble: 3 × 14
#>   group1 group2 p.value p.value.adj estimate conf.level conf.low conf.high
#>   <chr>  <chr>    <dbl>       <dbl>    <dbl>      <dbl>    <dbl>     <dbl>
#> 1 4      6      0.332        0.560     0.180       0.95        0     0.743
#> 2 4      8      0.00514      0.0154    0.568       0.95        0     0.983
#> 3 6      8      0.280        0.560     0.229       0.95        0     0.728
#>   effectsize        conf.method conf.distribution p.adjust.method
#>   <chr>             <chr>       <chr>             <chr>          
#> 1 Cramer's V (adj.) ncp         chisq             Holm           
#> 2 Cramer's V (adj.) ncp         chisq             Holm           
#> 3 Cramer's V (adj.) ncp         chisq             Holm           
#>   test                expression
#>   <chr>               <list>    
#> 1 Fisher's exact test <language>
#> 2 Fisher's exact test <language>
#> 3 Fisher's exact test <language>

# with counts data and Bonferroni adjustment
pairwise_contingency_table(
  data = as.data.frame(Titanic),
  x = Class,
  y = Survived,
  counts = Freq,
  p.adjust.method = "bonferroni"
)
#> # A tibble: 6 × 14
#>   group1 group2  p.value p.value.adj estimate conf.level conf.low conf.high
#>   <chr>  <chr>     <dbl>       <dbl>    <dbl>      <dbl>    <dbl>     <dbl>
#> 1 1st    2nd    2.78e- 7    1.67e- 6    0.207       0.95   0.125     0.287 
#> 2 1st    3rd    3.68e-30    2.21e-29    0.357       0.95   0.296     0.419 
#> 3 1st    Crew   1.81e-34    1.09e-33    0.359       0.95   0.302     0.415 
#> 4 2nd    3rd    8.19e- 7    4.91e- 6    0.157       0.95   0.0926    0.220 
#> 5 2nd    Crew   2.77e- 8    1.66e- 7    0.164       0.95   0.105     0.222 
#> 6 3rd    Crew   5.98e- 1    1   e+ 0    0           0.95   0         0.0581
#>   effectsize        conf.method conf.distribution p.adjust.method
#>   <chr>             <chr>       <chr>             <chr>          
#> 1 Cramer's V (adj.) ncp         chisq             Bonferroni     
#> 2 Cramer's V (adj.) ncp         chisq             Bonferroni     
#> 3 Cramer's V (adj.) ncp         chisq             Bonferroni     
#> 4 Cramer's V (adj.) ncp         chisq             Bonferroni     
#> 5 Cramer's V (adj.) ncp         chisq             Bonferroni     
#> 6 Cramer's V (adj.) ncp         chisq             Bonferroni     
#>   test                expression
#>   <chr>               <list>    
#> 1 Fisher's exact test <language>
#> 2 Fisher's exact test <language>
#> 3 Fisher's exact test <language>
#> 4 Fisher's exact test <language>
#> 5 Fisher's exact test <language>
#> 6 Fisher's exact test <language>

# no p-value adjustment
pairwise_contingency_table(
  data = mtcars,
  x = cyl,
  y = am,
  p.adjust.method = "none"
)
#> # A tibble: 3 × 14
#>   group1 group2 p.value p.value.adj estimate conf.level conf.low conf.high
#>   <chr>  <chr>    <dbl>       <dbl>    <dbl>      <dbl>    <dbl>     <dbl>
#> 1 4      6      0.332       0.332      0.180       0.95        0     0.743
#> 2 4      8      0.00514     0.00514    0.568       0.95        0     0.983
#> 3 6      8      0.280       0.280      0.229       0.95        0     0.728
#>   effectsize        conf.method conf.distribution p.adjust.method
#>   <chr>             <chr>       <chr>             <chr>          
#> 1 Cramer's V (adj.) ncp         chisq             None           
#> 2 Cramer's V (adj.) ncp         chisq             None           
#> 3 Cramer's V (adj.) ncp         chisq             None           
#>   test                expression
#>   <chr>               <list>    
#> 1 Fisher's exact test <language>
#> 2 Fisher's exact test <language>
#> 3 Fisher's exact test <language>