Paired vs Unpaired Test

The t-statistics were developed in 1908 by chemist William Sealy Gosset in Ireland. He used it to monitor the quality of a dark beer called stout while he was working in the Guinness Brewery. He published it in the Biometrika using the pen name “Student.”
There are several types of t-tests, the most commonly used are:

One sample location test wherein the mean of a population has value in a null hypothesis.
A test wherein the slope of a regression line differs notably from 0.
Two sample location tests for a difference in mean which can either be paired or unpaired.

In a paired test, the data is collected from subjects measured at two different points wherein each subject has two measurements which are done before and after the treatment. Subjects must be paired or matched before collecting data. This is also known as the repeated samples t-test.
An example is when comparing the weight loss of a group of people who are being given a special diet. These people are tested before they are started with the new diet and are again tested after they have been on the new diet for a few weeks. The results of both tests which are given to the same set group of people determine how much weight they have lost while on the special diet.

Unpaired tests, on the other hand, is when data is collected from two different and independent subjects or patients. The size between the two samples may be equal or not, and it assumes that data gathered is from a normal distribution and that the standard deviation is the same for both samples.
An example is the test that is applied to two groups of patients or subjects, those that have cancer and those that don’t. Tests such as this are also called Student’s t-tests wherein variances between the two subject populations are equal.
A paired test, therefore, is a test of the null hypothesis that the means of two groups of subjects that are normally distributed are equal while an unpaired test is the test of the null hypothesis that two responses which are measured in the same unit have a difference with a mean value of zero.

Both tests assume that all data that have been analyzed are normally distributed. Paired t-tests are more comprehensive and compelling than unpaired t-tests because they are done with subjects that have similar characteristics.

Summary:

1.A paired test is the test of the null hypothesis that the means of two subjects are equal while an unpaired test is the test of the null hypothesis that the difference between subjects has the mean value of zero.
2.A paired test is also known as a repeated samples t-test while an unpaired test is also known as a Student’s t-test.
3.A paired test is done on subjects that are similar or paired before data is collected and two tests are done before and after a treatment while an unpaired test is done on two independent subjects.

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