A paired t-test is a form of hypothesis testing where the subject is held constant and an analysis is done for two different conditions. This would be useful in comparing whether two machines are different by having the same operator do the test.

## Overview: What is a paired t-test?

First a little background. A two-sample t-test is a hypothesis test in which you might want to determine if there is a statistically significant difference in the population mean for two independent data sets. For this test, you can select two independent random samples where the machines or people of the two data sets can be different. The sample size can also be different.

For example, if you wanted to determine whether your process improvement project reduced processing time, you would take a random sample before the change, and then another sample after the change. The data may have come from different people in your before and after experiment.

One downside to this test is that if you saw an improvement, you might not be sure if it was due to your change or due to the skill of the different people used in the before and after experiments.

One way to overcome that dilemma is to keep the people the same, thereby eliminating the variation attributable to different people. The challenge is the availability of the same people for your before and after tests. This is where the concept of a paired test comes from. You are pairing your subjects in a before and after format using a pair of measurements for each.

## An industry example of a paired t-test

The training manager was interested in whether his training class was actually helping improve the knowledge of the operators. He decided to test this using a paired t-test.

Prior to starting the class, he asked each of the 15 operators to do a pre-test to determine their baseline level of knowledge. After eight weeks of training, he had the same group of people do a post-test.

After doing the statistical analysis, he rejected his null hypothesis that the difference was zero. The results of the post-test showed a statistically significant improvement in operator knowledge.

### 1. What is the difference between a two-sample t-test and a paired t-test?

A two-sample t-test will look for a difference in population means of independent samples, while the paired t-test uses matched pairs of data for the same subjects.

### 2. What is the null hypothesis for a paired t-test?

In reality, a paired t-test is really a one-sample t-test with the null hypothesis testing whether the difference between the two scenarios is zero.

### 3. How do I know if my data is paired?

Two data sets are considered paired when each data set has the same number of data points and each data point in one data set is related to only one data point in the other data set.