What is Paired T Test, Formula and Table?

For a group of random samples whose deviations are almost normally distributed, the paired t-test offers a hypothesis analysis of the distinction between population means. In a before-after example or with subjects as close as possible, subjects are also tested. The paired t-test is a test demonstrating that there are zero discrepancies between the two observations. 

Let us consider some Paired Sample T Test examples:

1. Suppose a doctor records every patients' blood pressure. Then gives a new medicine. After a month, the doctor again measures the blood test of those same patients. The before and after blood pressure measurements of patients create a new pair.
2. You measure the grip strength of every volunteer in left and right hands to determine if there is a consistent difference.
3. A lab weighs same set of 10 samples on old balance and then on a newly calibrated balance to assess whether the new machine reads higher or lower.

1. What is a paired sample t test used for? 

Solution: Two populations mean that you have two experiments in which findings in one sample can be combined with observations in the other sample and correlated with a paired t test. 

2. How do you know if data is paired or unpaired data? 

Solution: A paired t test is designed to measure the means in two different cases with the same category or entity. The definitions of two separate or incompatible classes are contrasted by an unpaired t test. The difference between groups is presumed to be equal in an unpaired t test. The variation is not considered to be equal in a paired t test.

For convenience of students t test table has been given below. CBSE board exam students must go through this to solve problems based on statistics chapter:

 In the t-test table, different terms mean the following:

• df means degrees of freedom (df = n -1): Number of independent pieces of information which is available for estimating a parameter. This is calculated as sample size minus number of estimated parameters. Here n is number of paired differences
• α means significance level: This refers to the total probability to make type 1 error split equally between two tails

• A paired t test is used when each data point comes in pairs. Say, you have taken before and after measurements for a group of people. Even a crossover trial where the volunteers are taking drug A in the first week and drug B in the second week. Since you are subtracting one value from its pair, noise from person-to-person variability will drop, and the difference will approximately behave like a bell curve. Say, you have taken before and after measurements for a group of people. Even a crossover trial where the volunteers are taking drug A in the first week and drug B in the second week. Since you are subtracting one value from its pair, noise from person-to-person variability will drop, and the difference will approximately behave like a bell curve. Paired sample t test should not be used when you have 2 independent groups. For instance, a paired t test will not be used for different patients in placebo arms or when you are tracking more than 2 time points. IIT JAM and JEE Main ask questions based on the use of paired t-test.
• Paired t test should not be used when you have 2 independent groups. For instance, a paired t test will not be used for different patients in placebo arms or when you are tracking more than 2 time points. 

The following table explains the difference between paired p-test and ANOVA analysis of variance test:

The following table differentiates paired vs unpaired t test on the mentioned parameters: