## About this lesson

One of the most commonly used tests in Lean Six Sigma analysis is the T Test. This lesson discusses the One-Sample T Test, Two-Sample T Test, and the Paired T Test. Each of these can be easily accomplished using both Excel and Minitab.

## Exercise files

Download this lessonâ€™s related exercise files.

T Tests.xlsx10.4 KB T Tests - Solution.docx

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## Quick reference

### T Tests

T Tests compare the mean of a data sample to either a target value or the mean of another sample of data.

### When to use

T Tests are used to show differences between data sets. When the means are different it can indicate cause and effect relationships. Also, the tests are often used in a before/after analysis to demonstrate the effectiveness of an improvement.

### Instructions

T Tests are among the easiest hypothesis tests to perform. The test determines the mean of the sample and compares it to a target. There are three types of T Tests used in Lean Six Sigma projects:

- One-sample T Tests compares the mean to a specified target value.
- Excel cannot do this test.
- Minitab:
- Stat > Basic Stats > 1-sample T
- Enter the column containing the data
- Enter the target value
- Check the box for Hypothesis test

- Two-sample T Tests compares the means between two data samples. Before that test is done, a test for equal variances should be done using the F Test and the correct variant of the Two-sample T Test used.
- Excel:
- Data Analysis > T Test: Two Sample Assuming Equal Variance (or unequal based upon the result of the F Test)
- Enter the data range for each sample

- Minitab:
- Stat > Basic Stats > 2-sample T
- Indicate the format of the data
- Select the data column(s)
- Select the Option button to indicate equal variances (default is unequal variances) and to change the relationship to greater than or less than

- Excel:
- Paired T Tests compares the means of two data sets, but these data sets have identical number of data points and the points are linked or paired between the data sets. This pairing is based upon the order of the data items in each set.
- Excel:
- Data Analysis > T Test: Paired Two Samples for Means
- Enter the data range for each sample.

- Minitab:
- Stat > Basic Stats > Paired T
- Select the data columns
- Select the Option button to change the relationship to greater than or less than

- Excel:

There are several reasons for pairing the data. One reason is to do before/after testing with process resources to show levels of improvement. Another reason is to conduct a controlled test where paired items are exposed to the same conditions. The items are identical except for the feature being investigated. The third reason is when two different items are linked or paired together and then both are simultaneously exposed to identify conditions to determine the different types of reactions

### Hints & tips

- When using a greater than or less than Alternative Hypothesis, be sure to enter the data ranges in the correct order for the P Value to be correctly stated.
- Use the F Test to determine if there are equal variances in order to do the correct T Test.

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