A 2-sample t-test is one of the most common hypothesis tests used in Six Sigma. This test is used to determine if the difference in average success rates between two groups is significant or random chance. This helps answer questions such as whether the average success rate after implementing a sales tool is higher than before, or whether test results for patients who have received a drug are superior to those of patients who had a placebo.

This example shows the basics of the 2-sample t-test hypothesis. It is being asked whether there is a significant difference (or only random) in the average delivery time for a pizza from Pizza Company C vs. Pizza Company D. These data were gathered from a sampling of delivery orders of Company A and Company.

### Using the 2-sample *t*-test

These sections will discuss how to conduct the test, and check our data and other statistical details.

#### What are we looking for?

Two variables are required for the 2-sample *t*-test. The two groups are defined by one variable. The measurement of interest is the second variable.

Also, we have a hypothesis that the means of both groups’ underlying populations are different. Here are some examples:

- There are students who can speak English and those who don’t. All students must pass a reading test. The native English speakers and non-native speakers are divided into two groups. The test scores are our measurements. We believe that the test scores of the different populations of native English speakers and non-native English speakers may differ. We would like to find out if the average score for native English speakers differs from those who have learned English as a second or third language.
- Two brands of energy bars have different amounts of protein. We use two methods to measure it. These are the brands we have divided into two groups. We measure the grams of protein per energy bar. We believe that the average grams of protein for both brands could be different. We would like to see evidence of whether the mean grams protein for both brands of energy bars are different.

#### 2-sample *and*-test assumptions

To administer a valid test:

- Data must be independently derived. Measuring one observation does not affect the measurement of another observation.
- Each group data must be obtained from a random sample of the population.
- The data in each group are usually distributed.
- Continuous data values
- The variances between the two groups are equal.

It can be difficult to test requirements for small data sets. We’ll show you how to use software to verify requirements and what to do if a requirement is not met.