How To Do Paired T-test In R : The Best Tutorial You Will Love

HomeT-Test Essentials: Definition, Formula and CalculationHow to Do Paired T-test in R

How to Do Paired T-test in R

T-Test Essentials: Definition, Formula and Calculation

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This article describes how to do a paired t-test in R (or in Rstudio). Note that the paired t-test is also referred as dependent t-test, related samples t-test, matched pairs t test or paired sample t test.

You will learn how to:

• Perform the paired t-test in R using the following functions :
  • t_test() [rstatix package]: the result is a data frame for easy plotting using the ggpubr package.
  • t.test() [stats package]: R base function.
• Interpret and report the paired t-test
• Add p-values and significance levels to a plot
• Calculate and report the paired t-test effect size using Cohen’s d. The d statistic redefines the difference in means as the number of standard deviations that separates those means. T-test conventional effect sizes, proposed by Cohen, are: 0.2 (small effect), 0.5 (moderate effect) and 0.8 (large effect) (Cohen 1998).

Contents:

• Prerequisites
• Demo data
• Summary statistics
• Calculation
  • Using the R base function
  • Using the rstatix package
• Interpretation
• Effect size
• Report
• Summary
• References

Related Book

Practical Statistics in R II - Comparing Groups: Numerical Variables

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

We want to know, if there is any significant difference in the mean weights after treatment?

Summary statistics

Compute some summary statistics (mean and sd) by groups:

mice2.long %>% group_by(group) %>% get_summary_stats(weight, type = "mean_sd") ## # A tibble: 2 x 5 ## group variable n mean sd ## <chr> <chr> <dbl> <dbl> <dbl> ## 1 after weight 10 400. 30.1 ## 2 before weight 10 201. 20.0

Calculation

Using the R base function

There are two options for computing the independent t-test depending whether the two groups data are saved either in two different vectors or in a data frame.

Option 1. The data are saved in two different numeric vectors:

# Save the data in two different vector before <- mice2$before after <- mice2$after # Compute t-test res <- t.test(before, after, paired = TRUE) res ## ## Paired t-test ## ## data: before and after ## t = -30, df = 9, p-value = 1e-09 ## alternative hypothesis: true difference in means is not equal to 0 ## 95 percent confidence interval: ## -217 -182 ## sample estimates: ## mean of the differences ## -199

Option 2. The data are saved in a data frame.

# Compute t-test res <- t.test(weight ~ group, data = mice2.long, paired = TRUE) res

As you can see, the two methods give the same results.

In the result above :

• t is the t-test statistic value (t = -25.55),
• df is the degrees of freedom (df= 9),
• p-value is the significance level of the t-test (p-value = 1.03910^{-9}).
• conf.int is the confidence interval of the mean of the differences at 95% (conf.int = [-217.1442, -181.8158]);
• sample estimates is the mean of the differences (mean = -199.48).

Using the rstatix package

We’ll use the pipe-friendly t_test() function [rstatix package], a wrapper around the R base function t.test(). The results can be easily added to a plot using the ggpubr R package.

stat.test <- mice2.long %>% t_test(weight ~ group, paired = TRUE) %>% add_significance() stat.test ## # A tibble: 1 x 9 ## .y. group1 group2 n1 n2 statistic df p p.signif ## <chr> <chr> <chr> <int> <int> <dbl> <dbl> <dbl> <chr> ## 1 weight after before 10 10 25.5 9 0.00000000104 ****

The results above show the following components:

• .y.: the y variable used in the test.
• group1,group2: the compared groups in the pairwise tests.
• statistic: Test statistic used to compute the p-value.
• df: degrees of freedom.
• p: p-value.

Note that, you can obtain a detailed result by specifying the option detailed = TRUE.

mice2.long %>% t_test(weight ~ group, paired = TRUE, detailed = TRUE) %>% add_significance() ## # A tibble: 1 x 14 ## estimate .y. group1 group2 n1 n2 statistic p df conf.low conf.high method alternative p.signif ## <dbl> <chr> <chr> <chr> <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <chr> <chr> <chr> ## 1 199. weight after before 10 10 25.5 0.00000000104 9 182. 217. T-test two.sided ****

Interpretation

The p-value of the test is 1.0410^{-9}, which is less than the significance level alpha = 0.05. We can then reject null hypothesis and conclude that the average weight of the mice before treatment is significantly different from the average weight after treatment with a p-value = 1.0410^{-9}.

Effect size

The effect size for a paired-samples t-test can be calculated by dividing the mean difference by the standard deviation of the difference, as shown below.

Cohen’s d formula:

\[ d = \frac{mean_D}{SD_D} \]

Where D is the differences of the paired samples values.

Calculation:

mice2.long %>% cohens_d(weight ~ group, paired = TRUE) ## # A tibble: 1 x 7 ## .y. group1 group2 effsize n1 n2 magnitude ## * <chr> <chr> <chr> <dbl> <int> <int> <ord> ## 1 weight after before 8.08 10 10 large

There is a large effect size, Cohen’s d = 8.07.

Report

We could report the result as follow: The average weight of mice was significantly increased after treatment, t(9) = 25.5, p < 0.0001, d = 8.07.

Visualize the results:

# Create a box plot bxp <- ggpaired(mice2.long, x = "group", y = "weight", order = c("before", "after"), ylab = "Weight", xlab = "Groups") # Add p-value and significance levels stat.test <- stat.test %>% add_xy_position(x = "group") bxp + stat_pvalue_manual(stat.test, tip.length = 0) + labs(subtitle = get_test_label(stat.test, detailed= TRUE))

Summary

This article shows how to perform the paired t-test in R/Rstudio using two different ways: the R base function t.test() and the t_test() function in the rstatix package. We also describe how to interpret and report the t-test results.

References

Cohen, J. 1998. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Hillsdale, NJ: Lawrence Erlbaum Associates.

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How To Do Two-Sample T-test in R (Prev Lesson) (Next Lesson) T-test Effect Size using Cohen’s d Measure Back to T-Test Essentials: Definition, Formula and Calculation

Comments ( 2 )

• Ezequiel 16 May 2022

  This package has made my life easier several times. I was wondering how would you run a paired t-test if you had before and after but for 2 datasets

  Reply
• Ezequiel 12 Aug 2022

  And is it possible to do it when you have 2 subgroups?

  Reply

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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

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Alboukadel Kassambara

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