# Mann-Whitney

## Summary

Analyzes the observed differences in the process median between two input settings. This test is similar to the 2-sampe t-test, and is an alternative for cases where the data from the two samples are not reasonably normal.

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

### Data

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

## How-To

1. Verify the measurement system for the Y data is 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. Enter Y data in one column and the factor levels (X) in a second column.
4. Determine your hypothesis. The alternative hypothesis (Ha) is what you are trying to prove with the data. The alternative hypothesis for a Mann-Whitney test can be whether the first process median is greater than, less than, or not equal to the second process median. The null hypothesis (H0) is the opposite of the alternative hypothesis.

## Guidelines

• Develop a sound data collection strategy to ensure that your conclusions are based on truly representative data.
• The Mann-Whitney test is from a category called nonparametric statistics. It is meant to be an alternative to the parametric test (2-sample t-test) for cases where the normality assumption fails badly. Such cases do not occur frequently because parametric tests are robust; therefore, the parametric tests are recommended for the majority of cases.
• While the Mann-Whitney test does not assume normality, it does assume equal variances. In the majority of cases, the 2-sample t-test is more powerful.
• For these reasons, it is usually recommended that you use the t-test whenever the data are reasonably normal (or the sample sizes are large), and use the Mann-Whitney test as a last resort.
• You should always graph your data whenever you use a statistical test. For the Mann-Whitney test, histograms or dotplots of the two samples, or a side-by-side boxplot, show the relative locations of the samples. The histograms and boxplots also identify 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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