# How to Distinguish Between Paired Sample T-Test and Independent Sample T-Test

The t-test is one of the associative tests researchers frequently use to examine the difference in mean values between variables. This test is applicable only when dealing with two groups of samples. If the tested variables differ among more than two sample groups, then the t-test cannot be utilized.

Certain assumptions must be met to employ the t-test. One of these assumptions is that the data being tested should follow a normal distribution. Consequently, researchers need to assess the normality of the variables under investigation.

As the title of this article – “How to Distinguish Between Paired Sample T-Test and Independent Sample T-Test” – in this time, I will elaborate on their distinctions more clearly and comprehensively.

## Assumptions of T-Test

The t-test is designed to observe the difference in mean values between variables. Assumptions for the t-test include the requirement for data to follow a normal distribution, and the comparison is performed between two sample groups.

Once both of these assumptions are met, the next step is to determine whether to use a paired sample t-test or an independent sample t-test.

If the assumption of normality is not satisfied, researchers need not force the use of the t-test. There are alternative methods for analyzing differences in non-normally distributed data or non-parametric variables, such as the Mann-Whitney and Wilcoxon tests.

## Paired Sample T-test

In a paired sample t-test, the number and characteristics of the samples used are the same. To better understand the application of the paired sample t-test, let’s consider the case of a researcher as follows.

A researcher intends to examine the difference in rice production among farmers in the ABC region. Using proportional random sampling, the researcher selects a sample of 250 farmers.

Next, the researcher conducts an experiment by introducing a new variety of rice cultivation. To assess the effectiveness of this new rice variety on production, the researcher records rice yields before and after the experiment.

Before implementing the new rice variety experiment, the researcher collects production data from the last harvest of the 250 farmers. This data is referred to as the pre-test.

Following this, the researcher replaces the existing rice variety with the new one, believed to have production advantages. During the experiment, farmers continued their usual planting and cultivation practices.

After harvesting the new rice variety, the researcher gathers post-experiment production data. This post-experiment production data is referred to as the post-test.

Subsequently, the researcher conducts a comparison between the pre-test and post-test values. This comparison is known as a paired t-test. Essentially, the same set of farmers is analyzed both before and after the experiment.

## Independent Sample T-Test

For the independent sample t-test, there is no requirement for the tested samples to be paired or identical. In fact, the sample sizes between the two groups being compared can differ.

Let’s align this with the example case discussed earlier to provide a deeper understanding. In the previous example, how would we apply the independent sample t-test?

When using the independent sample t-test, researchers need to identify a comparative location. Let’s say a researcher wants to observe the difference in rice production between the ABC and XYZ regions.

Rice production data from 145 farmers in the ABC region is collected as a sample. In the XYZ region, a sample of 127 farmers is gathered.

The researcher then compiles rice production data for the 145 samples from the ABC region and the 127 samples from the XYZ region. The comparison of rice production differences can be conducted using the independent sample t-test.

Based on these examples, we hope the distinction between the paired sample t-test and independent samples t-test is now clearer.

However, researchers need to note whether they’re using the paired sample t-test or independent samples t-test; both methods must satisfy two main assumptions. These assumptions involve the data following a normal distribution and the testing performed on two separate sample groups.

It’s time to conclude. The t-test is carried out to test the difference in mean values between two sample groups. The t-test can be applied to paired samples t-test and independent samples t-test. The variables being compared must adhere to the assumption of a normal distribution.

Well, this concludes the article I can write for now. Hopefully, this article proves helpful and contributes to the educational value for those in need. Stay tuned for the next week’s article update from Kanda Data. Thank you.