This article describes how to compute **pairwise T-test** in R between groups with corrections for multiple testing. The pairwise t-test consists of calculating **multiple t-test** between all possible combinations of groups.

You will learn how to:

- Calculate pairwise t-test for unpaired and paired groups
- Display the p-values on a boxplot.

Contents:

#### Related Book

Practical Statistics in R II - Comparing Groups: Numerical Variables## Prerequisites

Make sure you have the following R packages:

`tidyverse`

for data manipulation and visualization`ggpubr`

for creating easily publication ready plots`rstatix`

provides pipe-friendly R functions for easy statistical analyses`datarium`

: contains required data sets for this chapter

Load required R packages:

```
library(tidyverse)
library(ggpubr)
library(rstatix)
```

## Pairwise t-test for independent groups

This section shows how to perform multiple independent t-tests between groups.

```
# Load and inspect the demo data
data("PlantGrowth")
set.seed(1234)
PlantGrowth %>% sample_n_by(group, size = 2)
```

```
## # A tibble: 6 x 2
## weight group
## <dbl> <fct>
## 1 5.58 ctrl
## 2 4.61 ctrl
## 3 6.03 trt1
## 4 3.83 trt1
## 5 5.8 trt2
## 6 5.29 trt2
```

```
# Pairwise comparisons
pwc <- PlantGrowth %>%
pairwise_t_test(
weight ~ group, pool.sd = FALSE,
p.adjust.method = "bonferroni"
)
pwc
```

```
## # A tibble: 3 x 10
## .y. group1 group2 n1 n2 statistic df p p.adj p.adj.signif
## * <chr> <chr> <chr> <int> <int> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 weight ctrl trt1 10 10 1.19 16.5 0.25 0.75 ns
## 2 weight ctrl trt2 10 10 -2.13 16.8 0.048 0.144 ns
## 3 weight trt1 trt2 10 10 -3.01 14.1 0.009 0.028 *
```

```
# Visualization: box plots with p-values
pwc <- pwc %>% add_xy_position(x = "group", step.increase = 1)
ggboxplot(PlantGrowth, x = "group", y = "weight") +
stat_pvalue_manual(pwc, hide.ns = TRUE)
```

## Pairwise t-test for paired groups

This section shows how to perform multiple paired t-tests between groups. We’ll use the self-esteem score dataset measured over three time points. The data is available in the datarium package.

```
# Data preparation: Wide format
data("selfesteem", package = "datarium")
head(selfesteem, 3)
```

```
## # A tibble: 3 x 4
## id t1 t2 t3
## <int> <dbl> <dbl> <dbl>
## 1 1 4.01 5.18 7.11
## 2 2 2.56 6.91 6.31
## 3 3 3.24 4.44 9.78
```

```
# Gather columns t1, t2 and t3 into long format
# Convert id and time into factor variables
selfesteem <- selfesteem %>%
gather(key = "time", value = "score", t1, t2, t3) %>%
convert_as_factor(id, time)
head(selfesteem, 3)
```

```
## # A tibble: 3 x 3
## id time score
## <fct> <fct> <dbl>
## 1 1 t1 4.01
## 2 2 t1 2.56
## 3 3 t1 3.24
```

```
# Pairwise comparisons
pwc <- selfesteem %>%
pairwise_t_test(
score ~ time, paired = TRUE,
p.adjust.method = "bonferroni"
)
pwc
```

```
## # A tibble: 3 x 10
## .y. group1 group2 n1 n2 statistic df p p.adj p.adj.signif
## * <chr> <chr> <chr> <int> <int> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 score t1 t2 10 10 -4.97 9 0.000772 0.002 **
## 2 score t1 t3 10 10 -13.2 9 0.000000334 0.000001 ****
## 3 score t2 t3 10 10 -4.87 9 0.000886 0.003 **
```

```
# Visualization: box plots with p-values
pwc <- pwc %>% add_xy_position(x = "time")
ggboxplot(selfesteem, x = "time", y = "score", add = "point") +
stat_pvalue_manual(pwc)
```

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what are the assumptions for the pairwise test?