# 2-Sample t

## Summary

Analyzes the difference between the observed process mean at two settings of an input. To use a 2-sample t-test, you must collect a sample of data at both levels of the input variable.

• If I change an input from one level to another level, does the process mean stay the same or does it change?
• Is the process mean the same before and after a change has been made to the process?
When to Use Purpose
Mid-project Fixing an input at two different settings (levels) helps determine which inputs have significant influence on the mean of the output.
End of project Verify a significant difference exists between the means of the pre-project process and the post-project improved process. Of course, this assumes that one of the goals of the project was to shift the location of the process (change the process mean).

### Data

Continuous Y (output), a single 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 data’s precision; how to record the data, and so on).
3. You can use one of three methods to enter data in Minitab:
• Enter data in two columns, one for each factor level.
• Enter Y data in one column with the factor level (X) in a second column.
• Use summarized data by entering the sample size, mean, and standard deviation for both factor levels directly into the dialog box.
4. Determine the hypotheses. The alternative hypothesis (Ha) is what you are trying to prove with the data. For the 2-sample t-test, the alternative hypothesis states either the two means are not equal or one mean is greater than the other mean. The null hypothesis (Ho) is the opposite of the alternative hypothesis. For the 2-sample t-test, the null hypothesis states the two means are equal. First, develop a sound data collection strategy to ensure that your conclusions are based on truly representative data.

## Guidelines

• Develop a sound data collection strategy to ensure that your conclusions are based on truly representative data.
• Use Minitab’s Power and Sample Size command to determine the sample size necessary to detect the smallest difference of interest with sufficient power.
• The data must be continuous and reasonably normal, and the samples must be independent.
• The 2-sample t-test is very robust to violations of the normality assumption, especially if the sample sizes are large (n > 25).
• You should always graph your data when you use a statistical test. For the 2-sample t-test, use histograms or normal probability plots to evaluate reasonable normality and to check for outliers.
• By default, the 2-sample t-test does not assume equal variances for the two samples; however, you can check Assume equal variances for a slightly more powerful test. Use the 2 Variances procedure to determine if the variances are equal. The test is also quite robust to unequal variances if the sample sizes are approximately equal.
• 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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