Paired T-Test Assumptions : The Best Tutorial You Will Love

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Paired T-Test Assumptions

T-Test Essentials: Definition, Formula and Calculation

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Assumptions

The paired samples t-test assume the following characteristics about the data:

the two groups are paired.
No significant outliers in the difference between the two related groups
Normality. the difference of pairs follow a normal distribution.

In this section, we’ll perform some preliminary tests to check whether these assumptions are met.

Check paired t-test assumptions in R

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 formatdata("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 columnmice2.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)

There were no extreme outliers.

Note that, in the situation where you have extreme outliers, this can be due to: 1) data entry errors, measurement errors or unusual values.

You can include the outlier in the analysis anyway if you do not believe the result will be substantially affected. This can be evaluated by comparing the result of the t-test with and without the outlier.

It’s also possible to keep the outliers in the data and perform Wilcoxon test or robust t-test using the WRS2 package.

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

From the output, the two p-values are greater than the significance level 0.05 indicating that the distribution of the data are not significantly different from the normal distribution. In other words, we can assume the normality.

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")

All the points fall approximately along the (45-degree) reference line, for each group. So we can assume normality of the data.

Note that, if your sample size is greater than 50, the normal QQ plot is preferred because at larger sample sizes the Shapiro-Wilk test becomes very sensitive even to a minor deviation from normality.

In the situation where the data are not normally distributed, it’s recommended to use the non parametric Wilcoxon test.

T-test in R

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Course Curriculum

Types of T-Test
3 mins
- One Sample T-Test
  10 mins
- Unpaired T-Test
  10 mins
  - Student's T-Test
    5 mins
  - Welch T-Test
    5 mins
- Paired T-Test
  5 mins
Pairwise T-Test
5 mins
T-Test Formula
3 mins
- One Sample T-Test Formula
  3 mins
- Independent T-Test Formula
  3 mins
- Paired T-Test Formula
  3 mins
T-Test Assumptions
- One Sample T-Test Assumptions
- Independent T-Test Assumptions
- Paired T-Test Assumptions
How to Do a T-test in R: Calculation and Reporting
- How To Do a One-Sample T-test in R
- How To Do Two-Sample T-test in R
- How to Do Paired T-test in R
T-test Effect Size using Cohen's d Measure

Teacher

Alboukadel Kassambara

Role : Founder of Datanovia

Website : https://www.datanovia.com/en
Experience : >10 years
Specialist in : Bioinformatics and Cancer Biology

Paired T-Test Assumptions : The Best Tutorial You Will Love - Datanovia (2024)