How to Perform Paired t-Test for Multiple Columns in R

In statistics, a paired t-test is used to compare two related groups, determining if their means are significantly different from each other. It’s commonly applied in cases like "before and after" measurements. In R, we can perform a paired t-test on individual pairs of columns or multiple pairs of columns simultaneously. In this article, we'll explore the theory behind the paired t-test, the syntax for performing it in R, and provide examples that demonstrate how to execute it on multiple columns at once.

Paired t-Test

The paired t-test is a statistical method used when you have two related samples, where each observation in one group is paired with a unique observation in the other group. This could occur, for example, when you measure the same subjects under different conditions. Assumptions of the Paired t-Test:

1. Paired samples: Each data point in one sample has a corresponding data point in the other sample.
2. Normality: The differences between the paired observations are normally distributed.
3. Continuous variables: The paired measurements should be on an interval or ratio scale.

Now we will discuss step by step implementation of How to Perform Paired t-Test for Multiple Columns in R Programming Language.

Step 1: Data Preparation

Let’s say you have a dataset with multiple columns representing measurements taken before and after an intervention, and you want to perform a paired t-test for each pair of columns (before vs. after).

# Load necessary library
library(dplyr)

# Create sample data
set.seed(123)
data <- data.frame(
  before_1 = rnorm(30, mean = 100, sd = 10),
  after_1 = rnorm(30, mean = 102, sd = 10),
  before_2 = rnorm(30, mean = 90, sd = 15),
  after_2 = rnorm(30, mean = 88, sd = 15)
)

# Preview data
head(data)

Output:

   before_1   after_1 before_2   after_2
1  94.39524 106.26464 95.69459 102.90256
2  97.69823  99.04929 82.46515  96.22595
3 115.58708 110.95126 85.00189  91.58098
4 100.70508 110.78133 74.72137  78.58141
5 101.29288 110.21581 73.92313 108.40979
6 117.15065 108.88640 94.55293  78.99611

Step 2: Running Paired t-Test for Multiple Pairs

You can automate the process of running paired t-tests for multiple columns using a loop or apply functions. Below is an approach using dplyr and purrr to iterate over paired columns.

# Load the purrr library for iteration
library(purrr)

# Define a function to perform paired t-test between pairs of columns
paired_t_test <- function(before, after) {
  t.test(before, after, paired = TRUE)
}

# Apply paired t-test to each pair of columns
results <- map2(data[grepl("before", names(data))], 
                data[grepl("after", names(data))], 
                paired_t_test)

# Print the results
results

Output:

$before_1

	Paired t-test

data:  before and after
t = -1.6826, df = 29, p-value = 0.1032
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
 -9.425597  0.916755
sample estimates:
mean difference 
      -4.254421 


$before_2

	Paired t-test

data:  before and after
t = 1.0962, df = 29, p-value = 0.282
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
 -3.267613 10.816893
sample estimates:
mean difference 
        3.77464 

• t-statistic: A value that measures the difference between the sample means in terms of standard error.
• Degrees of freedom (df): Represents the number of independent values that can vary.
• p-value: If the p-value is less than the significance level (usually 0.05), you reject the null hypothesis.
• Confidence interval: A range of values that is likely to contain the true difference in means.

Conclusion

In this article, we explored how to perform paired t-tests for multiple columns in R. We discussed the theory behind paired t-tests, created a dataset with multiple paired columns, and automated the t-test process using R's purrr package. The ability to handle multiple tests efficiently is crucial for large datasets, and the methods provided allow for flexible and scalable analysis. By interpreting the results and visualizing the data, you gain a better understanding of how groups differ under different conditions.