# Mood's Median Test

## Summary

Analyzes the observed differences in the process median from one input setting to another. This test is similar to the one-way ANOVA, and is an alternative to the one-way ANOVA for cases where the sample data taken at each input level are not reasonably normal. Generally, the Kruskal-Wallis median test is the preferred, more powerful nonparametric alternative to the one-way ANOVA when the normality assumption fails badly. However, Mood's median test may be more appropriate than the Kruskal-Wallis median test when outliers are present.

• If I change an input from one level to another, does the median of the process stay the same or does it change?
When to Use Purpose
Mid-project Test which inputs have significant influence on the output by fixing an input at different settings (levels).

### Data

Continuous Y (output), a single X (input) at two or more 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 the 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 Mood's median test states that the process median at one or more levels is different from the others. The null hypothesis (Ho) is that all the medians are equal.

## Guidelines

• Develop a sound data collection strategy to ensure that your conclusions are based on truly representative data.
• The Mood's median test is from a category called nonparametric statistics. It is meant to be an alternative to the parametric test (one-way ANOVA) for cases where the normality assumption fails badly. Check Minitab Help because certain parametric tests and test conditions are robust to departures from normality.
• While the Mood's median test does not assume normality, it does assume population distributions have the same shape and their variances are equal.
• Because parametric tests are more powerful than their nonparametric alternatives, you should use one-way ANOVA whenever the data are reasonably normal and use the Mood's median test (or Kruskal-Wallis median test) only as a last resort.
• As good practice, you should also graph your data before using a statistical test. For the Mood's median test, a dotplot or boxplot of Y by X is recommended, as these plots show the locations of the Y data for each level of X. The dotplot or boxplot also identifies outliers and allows you to see if the data at each level are distributed with approximately the same shape.
• 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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