# Paired t

## Summary

Analyzes observed differences in sample units that are subjected to two different inputs. To use the paired t-test, you must subject the exact same sample units to both levels of the input variable to remove potential effects due to differences in the sample units themselves, which might mask the effect due to the change in the input. For example, you want to test whether two types of tires result in differences in gas mileage. The variation in gas mileage due to different cars in the sample would be much greater than variation due to different tires. The paired t-test accounts for the differences in cars.

• If I change an input from one level to another, does the process mean stay the same or does it change?
• Is the change in the process mean due to changing the input independent of the items tested?
When to Use Purpose
Mid-project Fixing an input at two different settings (levels) helps to determine which inputs have significant influence on mean of the output.
Mid-project Verify changes to inputs result in significant differences from the pre-project mean, provided you can test on the same units as those in the pre-project sample.

### Data

Continuous Y (output), one X (input) at two levels.

## How-To

1. Verify the measurement systems for the Y data and the input X are adequate.
2. Develop a data collection strategy (who should collect the data, as well as where and when; how many data values are needed; the preciseness of the data; how to record the data, and so on).
3. You can use one of two methods to enter the data in Minitab:
• Enter data in two columns, one for each factor level – the data from each unit must be in the same row of the two columns.
• Use summarized data by entering the sample size, mean, and standard deviation of the differences observed in each sample unit (Y at level 1 minus Y at level 2) directly into the dialog box.
4. Determine your hypotheses. The alternative hypothesis (Ha) is what you are trying to prove with the data; for the paired t test, it is whether the mean of the paired differences (Y at level 1 minus Y at level 2) is not equal to, greater than, or less than zero. The null hypothesis (Ho) is the opposite of the alternative hypothesis.

## Guidelines

• Develop a sound data collection strategy so that you ensure that your conclusions are based on truly representative data.
• The differences (calculated for each sample run at the two levels of X) must be continuous and reasonably normal.
• The paired t-test is very robust to the normality assumption, especially if the sample sizes are large (approximately larger than 25).
• You should always graph your data whenever you use a statistical test. For the paired t-test, use a histogram or normal probability plot of the differences to evaluate reasonable normality and to check for outliers.
• If you have discrete numeric data from which you can obtain every equally spaced value and you have measured at least 10 possible values, you can evaluate these data as if they are continuous.
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