pairwise_comparisons: Multiple pairwise comparison for one-way design

In statsExpressions: Tidy Dataframes and Expressions with Statistical Details

Multiple pairwise comparison for one-way design

Description

Calculate parametric, non-parametric, robust, and Bayes Factor pairwise comparisons between group levels with corrections for multiple testing.

Usage

pairwise_comparisons(
  data,
  x,
  y,
  subject.id = NULL,
  type = "parametric",
  paired = FALSE,
  var.equal = FALSE,
  tr = 0.2,
  bf.prior = 0.707,
  p.adjust.method = "holm",
  digits = 2L,
  exact = FALSE,
  ...
)

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 grouping (or independent) variable from data. For repeated measures designs, see the note on ordering in subject.id.
y	The response (or outcome or dependent) variable from data.
subject.id	Relevant in case of a repeated measures or within-subjects design (i.e., paired = TRUE), it specifies the subject or repeated measures identifier. Important: If this argument is NULL (which is the default), observations are paired by their row order within each level of x (i.e., the data is assumed to be sorted in a subject-1, subject-2, ... pattern within every level). If the data is not sorted this way, the paired results will be silently incorrect, so it is safest to always specify subject.id.
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.
paired	Logical that decides whether the experimental design is repeated measures/within-subjects or between-subjects. The default is FALSE.
var.equal	a logical variable indicating whether to treat the two variances as being equal. If TRUE then the pooled variance is used to estimate the variance otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used.
tr	Trim level for the mean when carrying out robust tests. In case of an error, try reducing the value of tr, which is by default set to 0.2. Lowering the value might help.
bf.prior	A number between 0.5 and 2 (default 0.707), the prior width to use in calculating Bayes factors and posterior estimates. In addition to numeric arguments, several named values are also recognized: "medium", "wide", and "ultrawide", corresponding to r scale values of 1/2, sqrt(2)/2, and 1, respectively. In case of an ANOVA, this value corresponds to scale for fixed effects.
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()).
exact	A logical indicating whether you want exact p-values to be computed. Relevant only when type = "nonparametric" (Default: FALSE).
...	Additional arguments passed to the underlying pairwise test function for the parametric and non-parametric tests (see the table below). Ignored for robust tests. For Bayesian tests, they are passed to the frequentist test (stats::pairwise.t.test() or PMCMRplus::gamesHowellTest()) that is run first to enumerate the pairs, so they do not change the Bayes factors, but unsupported arguments can still cause an error.

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.

Pairwise comparison 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

between-subjects

Hypothesis testing

Type	Equal variance?	Test	p-value adjustment?	Function used
Parametric	No	Games-Howell test	Yes	PMCMRplus::gamesHowellTest()
Parametric	Yes	Student's t-test	Yes	stats::pairwise.t.test()
Non-parametric	No	Dunn test	Yes	PMCMRplus::kwAllPairsDunnTest()
Robust	No	Yuen's trimmed means test	Yes	WRS2::lincon()
Bayesian	NA	Student's t-test	NA	BayesFactor::ttestBF()

Effect size estimation

Not supported.

within-subjects

Data requirement: Paired pairwise tests assume exactly one observation per subject per condition. If your data has multiple trials per cell, aggregate first (e.g., take the mean).

Hypothesis testing

Type	Test	p-value adjustment?	Function used
Parametric	Student's t-test	Yes	stats::pairwise.t.test()
Non-parametric	Durbin-Conover test	Yes	PMCMRplus::durbinAllPairsTest()
Robust	Yuen's trimmed means test	Yes	WRS2::rmmcp()
Bayesian	Student's t-test	NA	BayesFactor::ttestBF()

Effect size estimation

Not supported.

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

References

For more, see: https://www.indrapatil.com/ggstatsplot/articles/web_only/pairwise.html

Examples

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

#------------------- between-subjects design ----------------------------

# parametric
# if `var.equal = TRUE`, then Student's t-test will be run
pairwise_comparisons(
  data            = mtcars,
  x               = cyl,
  y               = wt,
  type            = "parametric",
  var.equal       = TRUE,
  paired          = FALSE,
  p.adjust.method = "none"
)

# if `var.equal = FALSE`, then Games-Howell test will be run
pairwise_comparisons(
  data            = mtcars,
  x               = cyl,
  y               = wt,
  type            = "parametric",
  var.equal       = FALSE,
  paired          = FALSE,
  p.adjust.method = "bonferroni"
)

# non-parametric (Dunn test)
pairwise_comparisons(
  data            = mtcars,
  x               = cyl,
  y               = wt,
  type            = "nonparametric",
  paired          = FALSE,
  p.adjust.method = "none"
)

# robust (Yuen's trimmed means *t*-test)
pairwise_comparisons(
  data            = mtcars,
  x               = cyl,
  y               = wt,
  type            = "robust",
  paired          = FALSE,
  p.adjust.method = "fdr"
)

# Bayes Factor (Student's *t*-test)
pairwise_comparisons(
  data   = mtcars,
  x      = cyl,
  y      = wt,
  type   = "bayes",
  paired = FALSE
)

#------------------- within-subjects design ----------------------------

# parametric (Student's *t*-test)
pairwise_comparisons(
  data            = bugs_long,
  x               = condition,
  y               = desire,
  subject.id      = subject,
  type            = "parametric",
  paired          = TRUE,
  p.adjust.method = "BH"
)

# non-parametric (Durbin-Conover test)
pairwise_comparisons(
  data            = bugs_long,
  x               = condition,
  y               = desire,
  subject.id      = subject,
  type            = "nonparametric",
  paired          = TRUE,
  p.adjust.method = "BY"
)

# robust (Yuen's trimmed means t-test)
pairwise_comparisons(
  data            = bugs_long,
  x               = condition,
  y               = desire,
  subject.id      = subject,
  type            = "robust",
  paired          = TRUE,
  p.adjust.method = "hommel"
)

# Bayes Factor (Student's *t*-test)
pairwise_comparisons(
  data       = bugs_long,
  x          = condition,
  y          = desire,
  subject.id = subject,
  type       = "bayes",
  paired     = TRUE
)

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