`pairwiseComparisons`: Multiple Pairwise Comparison Tests

Package	Status	Usage	GitHub	References

Introduction

pairwiseComparisons provides a tidy data friendly way to carry out pairwise comparison tests.

It currently supports post hoc multiple pairwise comparisons tests for both between-subjects and within-subjects one-way analysis of variance designs. For both of these designs, parametric, non-parametric, robust, and Bayes Factor statistical tests are available.

Installation

To get the latest, stable CRAN release:

install.packages("pairwiseComparisons")

You can get the development version of the package from GitHub. To see what new changes (and bug fixes) have been made to the package since the last release on CRAN, you can check the detailed log of changes here: https://indrajeetpatil.github.io/pairwiseComparisons/news/index.html

If you are in hurry and want to reduce the time of installation, prefer-

# needed package to download from GitHub repo
install.packages("remotes")

# downloading the package from GitHub
remotes::install_github(
  repo = "IndrajeetPatil/pairwiseComparisons", # package path on GitHub
  dependencies = FALSE, # assumes you have already installed needed packages
  quick = TRUE # skips docs, demos, and vignettes
)

If time is not a constraint-

remotes::install_github(
  repo = "IndrajeetPatil/pairwiseComparisons", # package path on GitHub
  dependencies = TRUE, # installs packages which pairwiseComparisons depends on
  upgrade_dependencies = TRUE # updates any out of date dependencies
)

Summary of types of statistical analyses

Following table contains a brief summary of the currently supported pairwise comparison tests-

Between-subjects design

Type	Equal variance?	Test	p-value adjustment?	Function used
Parametric	No	Games-Howell test	Yes	`stats::pairwise.t.test`
Parametric	Yes	Student’s t-test	Yes	`PMCMRplus::gamesHowellTest`
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`

Within-subjects design

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`

Examples

Here we will see specific examples of how to use this function for different types of

designs (between or within subjects)
statistics (parametric, non-parametric, robust, Bayes Factor)
p-value adjustment methods

Between-subjects design

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

# parametric
# if `var.equal = TRUE`, then Student's *t*-test will be run
pairwise_comparisons(
  data = ggplot2::msleep,
  x = vore,
  y = brainwt,
  type = "parametric",
  var.equal = TRUE,
  paired = FALSE,
  p.adjust.method = "bonferroni"
)
#> # A tibble: 6 x 6
#>   group1  group2  p.value test.details     p.value.adjustment
#>   <chr>   <chr>     <dbl> <chr>            <chr>             
#> 1 carni   herbi     1     Student's t-test Bonferroni        
#> 2 carni   insecti   1     Student's t-test Bonferroni        
#> 3 carni   omni      1     Student's t-test Bonferroni        
#> 4 herbi   insecti   1     Student's t-test Bonferroni        
#> 5 herbi   omni      0.979 Student's t-test Bonferroni        
#> 6 insecti omni      1     Student's t-test Bonferroni        
#>   label                                        
#>   <chr>                                        
#> 1 list(~italic(p)[Bonferroni-corrected]==1.000)
#> 2 list(~italic(p)[Bonferroni-corrected]==1.000)
#> 3 list(~italic(p)[Bonferroni-corrected]==1.000)
#> 4 list(~italic(p)[Bonferroni-corrected]==1.000)
#> 5 list(~italic(p)[Bonferroni-corrected]==0.979)
#> 6 list(~italic(p)[Bonferroni-corrected]==1.000)

# if `var.equal = FALSE`, then Games-Howell test will be run
pairwise_comparisons(
  data = ggplot2::msleep,
  x = vore,
  y = brainwt,
  type = "parametric",
  var.equal = FALSE,
  paired = FALSE,
  p.adjust.method = "bonferroni"
)
#> # A tibble: 6 x 11
#>   group1  group2  statistic p.value alternative method            distribution
#>   <chr>   <chr>       <dbl>   <dbl> <chr>       <chr>             <chr>       
#> 1 carni   herbi        2.17       1 two.sided   Games-Howell test q           
#> 2 carni   insecti     -2.17       1 two.sided   Games-Howell test q           
#> 3 carni   omni         1.10       1 two.sided   Games-Howell test q           
#> 4 herbi   insecti     -2.41       1 two.sided   Games-Howell test q           
#> 5 herbi   omni        -1.87       1 two.sided   Games-Howell test q           
#> 6 insecti omni         2.19       1 two.sided   Games-Howell test q           
#>   p.adjustment test.details      p.value.adjustment
#>   <chr>        <chr>             <chr>             
#> 1 none         Games-Howell test Bonferroni        
#> 2 none         Games-Howell test Bonferroni        
#> 3 none         Games-Howell test Bonferroni        
#> 4 none         Games-Howell test Bonferroni        
#> 5 none         Games-Howell test Bonferroni        
#> 6 none         Games-Howell test Bonferroni        
#>   label                                        
#>   <chr>                                        
#> 1 list(~italic(p)[Bonferroni-corrected]==1.000)
#> 2 list(~italic(p)[Bonferroni-corrected]==1.000)
#> 3 list(~italic(p)[Bonferroni-corrected]==1.000)
#> 4 list(~italic(p)[Bonferroni-corrected]==1.000)
#> 5 list(~italic(p)[Bonferroni-corrected]==1.000)
#> 6 list(~italic(p)[Bonferroni-corrected]==1.000)

# non-parametric
pairwise_comparisons(
  data = ggplot2::msleep,
  x = vore,
  y = brainwt,
  type = "nonparametric",
  paired = FALSE,
  p.adjust.method = "none"
)
#> # A tibble: 6 x 11
#>   group1  group2  statistic p.value alternative method               
#>   <chr>   <chr>       <dbl>   <dbl> <chr>       <chr>                
#> 1 carni   herbi       0.582  0.561  two.sided   Dunn's all-pairs test
#> 2 carni   insecti     1.88   0.0595 two.sided   Dunn's all-pairs test
#> 3 carni   omni        1.14   0.254  two.sided   Dunn's all-pairs test
#> 4 herbi   insecti     1.63   0.102  two.sided   Dunn's all-pairs test
#> 5 herbi   omni        0.717  0.474  two.sided   Dunn's all-pairs test
#> 6 insecti omni        1.14   0.254  two.sided   Dunn's all-pairs test
#>   distribution p.adjustment test.details p.value.adjustment
#>   <chr>        <chr>        <chr>        <chr>             
#> 1 z            none         Dunn test    None              
#> 2 z            none         Dunn test    None              
#> 3 z            none         Dunn test    None              
#> 4 z            none         Dunn test    None              
#> 5 z            none         Dunn test    None              
#> 6 z            none         Dunn test    None              
#>   label                               
#>   <chr>                               
#> 1 list(~italic(p)[uncorrected]==0.561)
#> 2 list(~italic(p)[uncorrected]==0.060)
#> 3 list(~italic(p)[uncorrected]==0.254)
#> 4 list(~italic(p)[uncorrected]==0.102)
#> 5 list(~italic(p)[uncorrected]==0.474)
#> 6 list(~italic(p)[uncorrected]==0.254)

# robust
pairwise_comparisons(
  data = ggplot2::msleep,
  x = vore,
  y = brainwt,
  type = "robust",
  paired = FALSE,
  p.adjust.method = "fdr"
)
#> # A tibble: 6 x 9
#>   group1  group2  estimate conf.low conf.high p.value test.details             
#>   <chr>   <chr>      <dbl>    <dbl>     <dbl>   <dbl> <chr>                    
#> 1 carni   herbi   -0.0530   -0.274     0.168    0.969 Yuen's trimmed means test
#> 2 carni   insecti  0.0577   -0.0609    0.176    0.969 Yuen's trimmed means test
#> 3 carni   omni     0.00210  -0.151     0.155    0.969 Yuen's trimmed means test
#> 4 herbi   insecti  0.111    -0.0983    0.320    0.969 Yuen's trimmed means test
#> 5 herbi   omni     0.0551   -0.173     0.283    0.969 Yuen's trimmed means test
#> 6 insecti omni    -0.0556   -0.184     0.0728   0.969 Yuen's trimmed means test
#>   p.value.adjustment label                                 
#>   <chr>              <chr>                                 
#> 1 FDR                list(~italic(p)[FDR-corrected]==0.969)
#> 2 FDR                list(~italic(p)[FDR-corrected]==0.969)
#> 3 FDR                list(~italic(p)[FDR-corrected]==0.969)
#> 4 FDR                list(~italic(p)[FDR-corrected]==0.969)
#> 5 FDR                list(~italic(p)[FDR-corrected]==0.969)
#> 6 FDR                list(~italic(p)[FDR-corrected]==0.969)

# Bayes Factor
pairwise_comparisons(
  data = ggplot2::msleep,
  x = vore,
  y = brainwt,
  type = "bayes",
  paired = FALSE
)
#> # A tibble: 6 x 16
#>   group1  group2  term       estimate conf.low conf.high    pd rope.percentage
#>   <chr>   <chr>   <chr>         <dbl>    <dbl>     <dbl> <dbl>           <dbl>
#> 1 carni   herbi   Difference   0.376   -0.349     1.15   0.800           0.183
#> 2 carni   insecti Difference  -0.0348  -0.105     0.0272 0.818           0.143
#> 3 carni   omni    Difference   0.0440  -0.0962    0.208  0.693           0.252
#> 4 herbi   insecti Difference  -0.394   -1.34      0.596  0.758           0.177
#> 5 herbi   omni    Difference  -0.362   -0.938     0.191  0.859           0.172
#> 6 insecti omni    Difference   0.0762  -0.141     0.261  0.732           0.172
#>   prior.distribution prior.location prior.scale  bf10 method          log_e_bf10
#>   <chr>                       <dbl>       <dbl> <dbl> <chr>                <dbl>
#> 1 cauchy                          0       0.707 0.540 Bayesian t-test     -0.617
#> 2 cauchy                          0       0.707 0.718 Bayesian t-test     -0.332
#> 3 cauchy                          0       0.707 0.427 Bayesian t-test     -0.851
#> 4 cauchy                          0       0.707 0.540 Bayesian t-test     -0.616
#> 5 cauchy                          0       0.707 0.571 Bayesian t-test     -0.560
#> 6 cauchy                          0       0.707 0.545 Bayesian t-test     -0.606
#>   label                         test.details    
#>   <chr>                         <chr>           
#> 1 list(~log[e](BF['01'])==0.62) Student's t-test
#> 2 list(~log[e](BF['01'])==0.33) Student's t-test
#> 3 list(~log[e](BF['01'])==0.85) Student's t-test
#> 4 list(~log[e](BF['01'])==0.62) Student's t-test
#> 5 list(~log[e](BF['01'])==0.56) Student's t-test
#> 6 list(~log[e](BF['01'])==0.61) Student's t-test

Within-subjects design

# for reproducibility
set.seed(123)

# parametric
pairwise_comparisons(
  data = bugs_long,
  x = condition,
  y = desire,
  subject.id = subject,
  type = "parametric",
  paired = TRUE,
  p.adjust.method = "BH"
)
#> # A tibble: 6 x 6
#>   group1 group2  p.value test.details     p.value.adjustment
#>   <chr>  <chr>     <dbl> <chr>            <chr>             
#> 1 HDHF   HDLF   1.06e- 3 Student's t-test FDR               
#> 2 HDHF   LDHF   7.02e- 2 Student's t-test FDR               
#> 3 HDHF   LDLF   3.95e-12 Student's t-test FDR               
#> 4 HDLF   LDHF   6.74e- 2 Student's t-test FDR               
#> 5 HDLF   LDLF   1.99e- 3 Student's t-test FDR               
#> 6 LDHF   LDLF   6.66e- 9 Student's t-test FDR               
#>   label                                    
#>   <chr>                                    
#> 1 list(~italic(p)[FDR-corrected]==0.001)   
#> 2 list(~italic(p)[FDR-corrected]==0.070)   
#> 3 list(~italic(p)[FDR-corrected]==3.95e-12)
#> 4 list(~italic(p)[FDR-corrected]==0.067)   
#> 5 list(~italic(p)[FDR-corrected]==0.002)   
#> 6 list(~italic(p)[FDR-corrected]==6.66e-09)

# non-parametric
pairwise_comparisons(
  data = bugs_long,
  x = condition,
  y = desire,
  subject.id = subject,
  type = "nonparametric",
  paired = TRUE,
  p.adjust.method = "BY"
)
#> # A tibble: 6 x 11
#>   group1 group2 statistic  p.value alternative
#>   <chr>  <chr>      <dbl>    <dbl> <chr>      
#> 1 HDHF   HDLF        4.78 1.44e- 5 two.sided  
#> 2 HDHF   LDHF        2.44 4.47e- 2 two.sided  
#> 3 HDHF   LDLF        8.01 5.45e-13 two.sided  
#> 4 HDLF   LDHF        2.34 4.96e- 2 two.sided  
#> 5 HDLF   LDLF        3.23 5.05e- 3 two.sided  
#> 6 LDHF   LDLF        5.57 4.64e- 7 two.sided  
#>   method                                                                
#>   <chr>                                                                 
#> 1 Durbin's all-pairs test for a two-way balanced incomplete block design
#> 2 Durbin's all-pairs test for a two-way balanced incomplete block design
#> 3 Durbin's all-pairs test for a two-way balanced incomplete block design
#> 4 Durbin's all-pairs test for a two-way balanced incomplete block design
#> 5 Durbin's all-pairs test for a two-way balanced incomplete block design
#> 6 Durbin's all-pairs test for a two-way balanced incomplete block design
#>   distribution p.adjustment test.details        p.value.adjustment
#>   <chr>        <chr>        <chr>               <chr>             
#> 1 t            none         Durbin-Conover test BY                
#> 2 t            none         Durbin-Conover test BY                
#> 3 t            none         Durbin-Conover test BY                
#> 4 t            none         Durbin-Conover test BY                
#> 5 t            none         Durbin-Conover test BY                
#> 6 t            none         Durbin-Conover test BY                
#>   label                                   
#>   <chr>                                   
#> 1 list(~italic(p)[BY-corrected]==1.44e-05)
#> 2 list(~italic(p)[BY-corrected]==0.045)   
#> 3 list(~italic(p)[BY-corrected]==5.45e-13)
#> 4 list(~italic(p)[BY-corrected]==0.050)   
#> 5 list(~italic(p)[BY-corrected]==0.005)   
#> 6 list(~italic(p)[BY-corrected]==4.64e-07)

# robust
pairwise_comparisons(
  data = bugs_long,
  x = condition,
  y = desire,
  subject.id = subject,
  type = "robust",
  paired = TRUE,
  p.adjust.method = "hommel"
)
#> # A tibble: 6 x 10
#>   group1 group2 estimate conf.low conf.high  p.value  p.crit
#>   <chr>  <chr>     <dbl>    <dbl>     <dbl>    <dbl>   <dbl>
#> 1 HDHF   HDLF      1.16    0.318      2.00  1.49e- 3 0.0127 
#> 2 HDHF   LDHF      0.5    -0.188      1.19  6.20e- 2 0.025  
#> 3 HDHF   LDLF      2.10    1.37       2.82  1.79e-10 0.00851
#> 4 HDLF   LDHF     -0.701  -1.71       0.303 6.20e- 2 0.05   
#> 5 HDLF   LDLF      0.938   0.0694     1.81  1.36e- 2 0.0169 
#> 6 LDHF   LDLF      1.54    0.810      2.27  1.16e- 6 0.0102 
#>   test.details              p.value.adjustment
#>   <chr>                     <chr>             
#> 1 Yuen's trimmed means test Hommel            
#> 2 Yuen's trimmed means test Hommel            
#> 3 Yuen's trimmed means test Hommel            
#> 4 Yuen's trimmed means test Hommel            
#> 5 Yuen's trimmed means test Hommel            
#> 6 Yuen's trimmed means test Hommel            
#>   label                                       
#>   <chr>                                       
#> 1 list(~italic(p)[Hommel-corrected]==0.001)   
#> 2 list(~italic(p)[Hommel-corrected]==0.062)   
#> 3 list(~italic(p)[Hommel-corrected]==1.79e-10)
#> 4 list(~italic(p)[Hommel-corrected]==0.062)   
#> 5 list(~italic(p)[Hommel-corrected]==0.014)   
#> 6 list(~italic(p)[Hommel-corrected]==1.16e-06)

# Bayes Factor
pairwise_comparisons(
  data = bugs_long,
  x = condition,
  y = desire,
  subject.id = subject,
  type = "bayes",
  paired = TRUE,
  bf.prior = 0.77
)
#> # A tibble: 6 x 16
#>   group1 group2 term       estimate conf.low conf.high    pd rope.percentage
#>   <chr>  <chr>  <chr>         <dbl>    <dbl>     <dbl> <dbl>           <dbl>
#> 1 HDHF   HDLF   Difference   -1.10    -1.62    -0.621  1               0    
#> 2 HDHF   LDHF   Difference   -0.465   -0.868   -0.0521 0.962           0.151
#> 3 HDHF   LDLF   Difference   -2.13    -2.57    -1.74   1               0    
#> 4 HDLF   LDHF   Difference    0.652    0.105    1.21   0.971           0.135
#> 5 HDLF   LDLF   Difference   -0.983   -1.46    -0.506  0.999           0    
#> 6 LDHF   LDLF   Difference   -1.67    -2.10    -1.27   1               0    
#>   prior.distribution prior.location prior.scale     bf10 method         
#>   <chr>                       <dbl>       <dbl>    <dbl> <chr>          
#> 1 cauchy                          0        0.77 3.95e+ 1 Bayesian t-test
#> 2 cauchy                          0        0.77 5.42e- 1 Bayesian t-test
#> 3 cauchy                          0        0.77 1.22e+10 Bayesian t-test
#> 4 cauchy                          0        0.77 6.50e- 1 Bayesian t-test
#> 5 cauchy                          0        0.77 1.72e+ 1 Bayesian t-test
#> 6 cauchy                          0        0.77 4.78e+ 6 Bayesian t-test
#>   log_e_bf10 label                           test.details    
#>        <dbl> <chr>                           <chr>           
#> 1      3.68  list(~log[e](BF['01'])==-3.68)  Student's t-test
#> 2     -0.612 list(~log[e](BF['01'])==0.61)   Student's t-test
#> 3     23.2   list(~log[e](BF['01'])==-23.22) Student's t-test
#> 4     -0.430 list(~log[e](BF['01'])==0.43)   Student's t-test
#> 5      2.84  list(~log[e](BF['01'])==-2.84)  Student's t-test
#> 6     15.4   list(~log[e](BF['01'])==-15.38) Student's t-test

Using `pairwiseComparisons` with `ggsignif`

Example-1: between-subjects

# needed libraries
set.seed(123)
library(ggplot2)
library(pairwiseComparisons)
library(ggsignif)

# converting to factor
mtcars$cyl <- as.factor(mtcars$cyl)

# creating a basic plot
p <- ggplot(mtcars, aes(cyl, wt)) +
  geom_boxplot()

# using `pairwiseComparisons` package to create a dataframe with results
set.seed(123)
(df <-
  pairwise_comparisons(mtcars, cyl, wt) %>%
  dplyr::mutate(.data = ., groups = purrr::pmap(.l = list(group1, group2), .f = c)) %>%
  dplyr::arrange(.data = ., group1))
#> # A tibble: 3 x 12
#>   group1 group2 statistic   p.value alternative method            distribution
#>   <chr>  <chr>      <dbl>     <dbl> <chr>       <chr>             <chr>       
#> 1 4      6           5.39 0.00831   two.sided   Games-Howell test q           
#> 2 4      8           9.11 0.0000124 two.sided   Games-Howell test q           
#> 3 6      8           5.12 0.00831   two.sided   Games-Howell test q           
#>   p.adjustment test.details      p.value.adjustment
#>   <chr>        <chr>             <chr>             
#> 1 none         Games-Howell test Holm              
#> 2 none         Games-Howell test Holm              
#> 3 none         Games-Howell test Holm              
#>   label                                      groups   
#>   <chr>                                      <list>   
#> 1 list(~italic(p)[Holm-corrected]==0.008)    <chr [2]>
#> 2 list(~italic(p)[Holm-corrected]==1.24e-05) <chr [2]>
#> 3 list(~italic(p)[Holm-corrected]==0.008)    <chr [2]>

# using `geom_signif` to display results
# (note that you can choose not to display all comparisons)
p +
  ggsignif::geom_signif(
    comparisons = list(df$groups[[1]]),
    annotations = df$label[[1]],
    test = NULL,
    na.rm = TRUE,
    parse = TRUE
  )

Example-2: within-subjects

# needed libraries
library(ggplot2)
library(pairwiseComparisons)
library(ggsignif)

# creating a basic plot
p <- ggplot(WRS2::WineTasting, aes(Wine, Taste)) +
  geom_boxplot()

# using `pairwiseComparisons` package to create a dataframe with results
set.seed(123)
(df <-
  pairwise_comparisons(
    WRS2::WineTasting,
    Wine,
    Taste,
    subject.id = Taster,
    type = "bayes",
    paired = TRUE
  ) %>%
  dplyr::mutate(.data = ., groups = purrr::pmap(.l = list(group1, group2), .f = c)) %>%
  dplyr::arrange(.data = ., group1))
#> # A tibble: 3 x 17
#>   group1 group2 term       estimate conf.low conf.high    pd rope.percentage
#>   <chr>  <chr>  <chr>         <dbl>    <dbl>     <dbl> <dbl>           <dbl>
#> 1 Wine A Wine B Difference -0.00721  -0.0473    0.0307 0.624           0.431
#> 2 Wine A Wine C Difference -0.0766   -0.129    -0.0265 0.989           0    
#> 3 Wine B Wine C Difference -0.0696   -0.0991   -0.0368 1.00            0    
#>   prior.distribution prior.location prior.scale   bf10 method         
#>   <chr>                       <dbl>       <dbl>  <dbl> <chr>          
#> 1 cauchy                          0       0.707  0.235 Bayesian t-test
#> 2 cauchy                          0       0.707  3.71  Bayesian t-test
#> 3 cauchy                          0       0.707 50.5   Bayesian t-test
#>   log_e_bf10 label                          test.details     groups   
#>        <dbl> <chr>                          <chr>            <list>   
#> 1      -1.45 list(~log[e](BF['01'])==1.45)  Student's t-test <chr [2]>
#> 2       1.31 list(~log[e](BF['01'])==-1.31) Student's t-test <chr [2]>
#> 3       3.92 list(~log[e](BF['01'])==-3.92) Student's t-test <chr [2]>

# using `geom_signif` to display results
p +
  ggsignif::geom_signif(
    comparisons = df$groups,
    map_signif_level = TRUE,
    tip_length = 0.01,
    y_position = c(6.5, 6.65, 6.8),
    annotations = df$label,
    test = NULL,
    na.rm = TRUE,
    parse = TRUE
  )

Acknowledgments

The hexsticker was generously designed by Sarah Otterstetter (Max Planck Institute for Human Development, Berlin).

Contributing

I’m happy to receive bug reports, suggestions, questions, and (most of all) contributions to fix problems and add features. I personally prefer using the GitHub issues system over trying to reach out to me in other ways (personal e-mail, Twitter, etc.). Pull Requests for contributions are encouraged.

Here are some simple ways in which you can contribute (in the increasing order of commitment):

Read and correct any inconsistencies in the documentation
Raise issues about bugs or wanted features
Review code
Add new functionality

Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.

chencaf / pairwisecomparisons Goto Github PK

pairwisecomparisons's Introduction

`pairwiseComparisons`: Multiple Pairwise Comparison Tests

Introduction

Installation

Summary of types of statistical analyses

Between-subjects design

Within-subjects design

Examples

Between-subjects design

Within-subjects design

Using `pairwiseComparisons` with `ggsignif`

Example-1: between-subjects

Example-2: within-subjects

Acknowledgments

Contributing

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pairwisecomparisons's Introduction

pairwiseComparisons: Multiple Pairwise Comparison Tests

Introduction

Installation

Summary of types of statistical analyses

Between-subjects design

Within-subjects design

Examples

Between-subjects design

Within-subjects design

Using pairwiseComparisons with ggsignif

Example-1: between-subjects

Example-2: within-subjects

Acknowledgments

Contributing

Recommend Projects

Recommend Topics

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`pairwiseComparisons`: Multiple Pairwise Comparison Tests

Using `pairwiseComparisons` with `ggsignif`