Hi friends! If you are searching for information about the Paired T Test, then you are on the right platform. Today, we will discuss the Paired T Test, which is one of the hypothesis tests in the Analysis phase.
When is the Paired T Test used?
A paired t-test is a statistical method used to compare the means of two related groups. It is specifically designed for situations where the data sets are paired or matched in some way.
Let us understand with some examples.
Before-and-after Studies:
When you have measurements on the same subjects or entities before and after an intervention. For example, measuring the blood pressure of individuals before and after a treatment.
Repeated Measurements: When each subject is measured multiple times under different conditions.
Matched Pairs: When you have pairs of similar or related subjects, and you want to compare the mean difference between the paired observations. This could be siblings, twins, or matched pairs based on certain characteristics.
The paired t-test is suitable when the data can be considered as dependent samples, meaning that there is a natural pairing or connection between the observations in the two groups being compared. The goal is often to determine whether the mean difference between the paired observations is significantly different from zero.
Let us understand with one solved example.
The thickness of a printed circuit board was measured by six individuals, using two different kinds of calipers. The results (in mm) are shown below:
| Subject | Calliper 1 | Calliper 2 |
| 1 | .265 | .264 |
| 2 | .265 | .265 |
| 3 | .266 | .264 |
| 4 | .267 | .266 |
| 5 | .267 | .267 |
| 6 | .265 | .268 |
Is there is significant difference between the mean thicknesses of measurements obtained of two calipers?
Solution:
Step – 1: Hypothesis formulation.
Consider that D = X -Y = 0 (No difference)
D is difference, X is the mean value (6 Nos values) measured by Calliper 1 and Y is the mean value (6 Nos values) measured by Calliper 2.
H0: µD = 0 (Null Hypothesis)
H1: µD ≠ 0 (Alternative Hypothesis)
Now open the Minitab.
Path
Stat>Basic Statistics >Paired T Test. Then select “Each sample is in a column” Afterward, select Sample 1 as “caliper 1” and choose Sample 2 as “caliper 2, as mentioned in below picture.
Then go to the “Options” tab. Select a confidence level of 95, set the hypothesized difference to 0, and choose the alternative hypothesis as “Difference ≠ hypothesized difference.” Finally, click “Ok.”
Conclusion – The paired t-test comparing measurements from two calipers yielded a P-Value of 0.822. With the P-Value exceeding 0.05, we can not reject the null hypothesis (µD =difference = 0). This suggests that the observed difference is likely due to chance, and there isn’t enough evidence to claim a significant distinction between the measurements taken by the two calipers. There is no difference.