T-Test Essentials: Definition, Formula and Calculation

Prerequisites

Make sure you have installed 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.

Start by loading the following required packages:

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

Demo data

Here, we’ll use a demo dataset mice2 [datarium package], which contains the weight of 10 mice before and after the treatment.

# Wide format
data("mice2", package = "datarium")
head(mice2, 3)

##   id before after
## 1  1    187   430
## 2  2    194   404
## 3  3    232   406

# Transform into long data: 
# gather the before and after values in the same column
mice2.long <- mice2 %>%
  gather(key = "group", value = "weight", before, after)
head(mice2.long, 3)

##   id  group weight
## 1  1 before    187
## 2  2 before    194
## 3  3 before    232

First, start by computing the difference between groups:

mice2 <- mice2 %>% mutate(differences = before - after)
head(mice2, 3)

##   id before after differences
## 1  1    187   430        -242
## 2  2    194   404        -210
## 3  3    232   406        -174

Identify outliers

Outliers can be easily identified using boxplot methods, implemented in the R function identify_outliers() [rstatix package].

mice2 %>% identify_outliers(differences)

## [1] id          before      after       differences is.outlier  is.extreme 
## <0 rows> (or 0-length row.names)

Check normality by groups

The normality assumption can be checked by computing the Shapiro-Wilk test for each group. If the data is normally distributed, the p-value should be greater than 0.05.

mice2 %>% shapiro_test(differences) 

## # A tibble: 1 x 3
##   variable    statistic     p
##   <chr>           <dbl> <dbl>
## 1 differences     0.968 0.867

You can also create QQ plots for each group. QQ plot draws the correlation between a given data and the normal distribution.

ggqqplot(mice2, "differences")