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,
digits = 2L,
...
)

## 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. In case of a repeated measures or within-subjects design, if subject.id argument is not available or not explicitly specified, the function assumes that the data has already been sorted by such an id by the user and creates an internal identifier. So if your data is not sorted, the results can be inaccurate when there are more than two levels in x and there are NAs present. The data is expected to be sorted by user in subject-1,subject-2, ..., pattern.

y

The response (or outcome or dependent) variable from data.

subject.id

Relevant in case of a repeated measures or within-subjects design (paired = TRUE, i.e.), it specifies the subject or repeated measures identifier. Important: Note that if this argument is NULL (which is the default), the function assumes that the data has already been sorted by such an id by the user and creates an internal identifier. So if your data is not sorted and you leave this argument unspecified, the results can be inaccurate when there are more than two levels in x and there are NAs present.

type

A character specifying the type of statistical approach:

• "parametric"

• "nonparametric"

• "robust"

• "bayes"

You can specify just the initial letter.

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.

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()).

...

Additional arguments passed to other methods.

## 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.

## 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

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.

## 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,
)
#> # A tibble: 3 × 6
#>   group1 group2     p.value p.adjust.method test        expression
#>   <chr>  <chr>        <dbl> <chr>           <chr>       <list>
#> 1 4      6      0.0106      None            Student's t <language>
#> 2 4      8      0.000000207 None            Student's t <language>
#> 3 6      8      0.00516     None            Student's t <language>

# 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,
)
#> # A tibble: 3 × 9
#>   group1 group2 statistic   p.value alternative distribution p.adjust.method
#>   <chr>  <chr>      <dbl>     <dbl> <chr>       <chr>        <chr>
#> 1 4      6           5.39 0.0125    two.sided   q            Bonferroni
#> 2 4      8           9.11 0.0000124 two.sided   q            Bonferroni
#> 3 6      8           5.12 0.0148    two.sided   q            Bonferroni
#>   test         expression
#>   <chr>        <list>
#> 1 Games-Howell <language>
#> 2 Games-Howell <language>
#> 3 Games-Howell <language>

# non-parametric (Dunn test)
pairwise_comparisons(
data            = mtcars,
x               = cyl,
y               = wt,
type            = "nonparametric",
paired          = FALSE,
)
#> # A tibble: 3 × 9
#>   group1 group2 statistic    p.value alternative distribution p.adjust.method
#>   <chr>  <chr>      <dbl>      <dbl> <chr>       <chr>        <chr>
#> 1 4      6           1.84 0.0663     two.sided   z            None
#> 2 4      8           4.76 0.00000198 two.sided   z            None
#> 3 6      8           2.22 0.0263     two.sided   z            None
#>   test  expression
#>   <chr> <list>
#> 1 Dunn  <language>
#> 2 Dunn  <language>
#> 3 Dunn  <language>

# robust (Yuen's trimmed means *t*-test)
pairwise_comparisons(
data            = mtcars,
x               = cyl,
y               = wt,
type            = "robust",
paired          = FALSE,
)
#> # A tibble: 3 × 10
#>   group1 group2 estimate conf.level conf.low conf.high  p.value p.adjust.method
#>   <chr>  <chr>     <dbl>      <dbl>    <dbl>     <dbl>    <dbl> <chr>
#> 1 4      6        -0.909       0.95    -1.64    -0.173 0.00872  FDR
#> 2 4      8        -1.62        0.95    -2.50    -0.746 0.000549 FDR
#> 3 6      8        -0.713       0.95    -1.58     0.155 0.0438   FDR
#>   test                 expression
#>   <chr>                <list>
#> 1 Yuen's trimmed means <language>
#> 2 Yuen's trimmed means <language>
#> 3 Yuen's trimmed means <language>

# Bayes Factor (Student's *t*-test)
pairwise_comparisons(
data   = mtcars,
x      = cyl,
y      = wt,
type   = "bayes",
paired = FALSE
)
#> # A tibble: 3 × 18
#>   group1 group2 term       effectsize      estimate conf.level conf.low
#>   <chr>  <chr>  <chr>      <chr>              <dbl>      <dbl>    <dbl>
#> 1 4      6      Difference Bayesian t-test   -0.686       0.95    -1.22
#> 2 4      8      Difference Bayesian t-test   -1.63        0.95    -2.21
#> 3 6      8      Difference Bayesian t-test   -0.715       0.95    -1.36
#>   conf.high    pd prior.distribution prior.location prior.scale    bf10
#>       <dbl> <dbl> <chr>                       <dbl>       <dbl>   <dbl>
#> 1   -0.157  0.992 cauchy                          0       0.707   11.4
#> 2   -1.01   1     cauchy                          0       0.707 5222.
#> 3   -0.0910 0.987 cauchy                          0       0.707    5.36
#>   conf.method log_e_bf10 n.obs expression test
#>   <chr>            <dbl> <int> <list>     <chr>
#> 1 ETI               2.44    18 <language> Student's t
#> 2 ETI               8.56    25 <language> Student's t
#> 3 ETI               1.68    21 <language> Student's t

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

# parametric (Student's *t*-test)
pairwise_comparisons(
data            = bugs_long,
x               = condition,
y               = desire,
subject.id      = subject,
type            = "parametric",
paired          = TRUE,
)
#> # A tibble: 6 × 6
#>   group1 group2  p.value p.adjust.method test        expression
#>   <chr>  <chr>     <dbl> <chr>           <chr>       <list>
#> 1 HDHF   HDLF   1.06e- 3 FDR             Student's t <language>
#> 2 HDHF   LDHF   7.02e- 2 FDR             Student's t <language>
#> 3 HDHF   LDLF   3.95e-12 FDR             Student's t <language>
#> 4 HDLF   LDHF   6.74e- 2 FDR             Student's t <language>
#> 5 HDLF   LDLF   1.99e- 3 FDR             Student's t <language>
#> 6 LDHF   LDLF   6.66e- 9 FDR             Student's t <language>

# non-parametric (Durbin-Conover test)
pairwise_comparisons(
data            = bugs_long,
x               = condition,
y               = desire,
subject.id      = subject,
type            = "nonparametric",
paired          = TRUE,
)
#> # A tibble: 6 × 9
#>   group1 group2 statistic  p.value alternative distribution p.adjust.method
#>   <chr>  <chr>      <dbl>    <dbl> <chr>       <chr>        <chr>
#> 1 HDHF   HDLF        4.78 1.44e- 5 two.sided   t            BY
#> 2 HDHF   LDHF        2.44 4.47e- 2 two.sided   t            BY
#> 3 HDHF   LDLF        8.01 5.45e-13 two.sided   t            BY
#> 4 HDLF   LDHF        2.34 4.96e- 2 two.sided   t            BY
#> 5 HDLF   LDLF        3.23 5.05e- 3 two.sided   t            BY
#> 6 LDHF   LDLF        5.57 4.64e- 7 two.sided   t            BY
#>   test           expression
#>   <chr>          <list>
#> 1 Durbin-Conover <language>
#> 2 Durbin-Conover <language>
#> 3 Durbin-Conover <language>
#> 4 Durbin-Conover <language>
#> 5 Durbin-Conover <language>
#> 6 Durbin-Conover <language>

# robust (Yuen's trimmed means t-test)
pairwise_comparisons(
data            = bugs_long,
x               = condition,
y               = desire,
subject.id      = subject,
type            = "robust",
paired          = TRUE,
)
#> # A tibble: 6 × 11
#>   group1 group2 estimate conf.level conf.low conf.high     p.value  p.crit
#>   <chr>  <chr>     <dbl>      <dbl>    <dbl>     <dbl>       <dbl>   <dbl>
#> 1 HDHF   HDLF      1.03        0.95   0.140      1.92  0.00999     0.0127
#> 2 HDHF   LDHF      0.454       0.95  -0.104      1.01  0.0520      0.025
#> 3 HDHF   LDLF      1.95        0.95   1.09       2.82  0.000000564 0.00851
#> 4 HDLF   LDHF     -0.676       0.95  -1.61       0.256 0.0520      0.05
#> 5 HDLF   LDLF      0.889       0.95   0.0244     1.75  0.0203      0.0169
#> 6 LDHF   LDLF      1.35        0.95   0.560      2.14  0.000102    0.0102
#>   p.adjust.method test                 expression
#>   <chr>           <chr>                <list>
#> 1 Hommel          Yuen's trimmed means <language>
#> 2 Hommel          Yuen's trimmed means <language>
#> 3 Hommel          Yuen's trimmed means <language>
#> 4 Hommel          Yuen's trimmed means <language>
#> 5 Hommel          Yuen's trimmed means <language>
#> 6 Hommel          Yuen's trimmed means <language>

# Bayes Factor (Student's *t*-test)
pairwise_comparisons(
data       = bugs_long,
x          = condition,
y          = desire,
subject.id = subject,
type       = "bayes",
paired     = TRUE
)
#> # A tibble: 6 × 18
#>   group1 group2 term       effectsize      estimate conf.level conf.low
#>   <chr>  <chr>  <chr>      <chr>              <dbl>      <dbl>    <dbl>
#> 1 HDHF   HDLF   Difference Bayesian t-test    1.10        0.95   0.491
#> 2 HDHF   LDHF   Difference Bayesian t-test    0.455       0.95  -0.0483
#> 3 HDHF   LDLF   Difference Bayesian t-test    2.13        0.95   1.62
#> 4 HDLF   LDHF   Difference Bayesian t-test   -0.661       0.95  -1.32
#> 5 HDLF   LDLF   Difference Bayesian t-test    0.991       0.95   0.369
#> 6 LDHF   LDLF   Difference Bayesian t-test    1.65        0.95   1.14
#>   conf.high    pd prior.distribution prior.location prior.scale     bf10
#>       <dbl> <dbl> <chr>                       <dbl>       <dbl>    <dbl>
#> 1    1.76   1.00  cauchy                          0       0.707 4.16e+ 1
#> 2    0.955  0.962 cauchy                          0       0.707 5.83e- 1
#> 3    2.63   1     cauchy                          0       0.707 1.20e+10
#> 4    0.0315 0.97  cauchy                          0       0.707 6.98e- 1
#> 5    1.57   0.999 cauchy                          0       0.707 1.81e+ 1
#> 6    2.15   1     cauchy                          0       0.707 4.81e+ 6
#>   conf.method log_e_bf10 n.obs expression test
#>   <chr>            <dbl> <int> <list>     <chr>
#> 1 ETI              3.73     88 <language> Student's t
#> 2 ETI             -0.539    88 <language> Student's t
#> 3 ETI             23.2      88 <language> Student's t
#> 4 ETI             -0.359    88 <language> Student's t
#> 5 ETI              2.90     88 <language> Student's t
#> 6 ETI             15.4      88 <language> Student's t