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Mood's Median, Kruskal-Wallis, and Friedman.xlsx10.6 KB Mood's Median, Kruskal-Wallis, and Friedman - Solution.docx

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## Quick reference

### Mood's Median, Kruskal-Wallis, and Friedman

When multiple non-normal data samples are compared in a hypothesis test, there are several potential tests that can be used. The Mood’s Median, Kruskal-Wallis, and Friedman tests are typical tests used and each is best suited to different characteristics of the data.

### When to use

Many Lean Six Sigma projects requiring hypothesis tests are based upon non-normal data sets. The Mood’s Median Test, Kruskal-Wallis Test, and Friedman Test are used with multiple data sets. The specific test to be used will depend upon the characteristics of the data.

### Instructions

#### Mood’s Median Test

The Mood’s Median Test is appropriate for use with multiple data samples whose non-normal data sets have a similar shape – such as skewed left, skewed right, or bathtub. The test will work with multiple data samples. This test is particularly robust with respect to outliers. The test cannot be accomplished with Excel.

- Minitab:
- All the data must be combined into one column. Use the Data > Stack > Column command to merge multiple data samples into one column.
- Stat > Nonparametrics > Mood’s Mediam Test
- Select the data column for the Response field
- Select the data identified column for the Factor field

#### Kruskal-Wallis Test

The Kruskal-Wallis Test is appropriate for use with multiple non-normal data samples. This test is essentially an ANOVA test for non-normal data. The data items should be continuous (not discrete). The data samples do not need to have similar shapes as with the Mood’s Median Test. This test is sensitive to outliers. This test cannot be accomplished with Excel.

- Minitab:
- All the data must be combined into one column. Use the Data > Stack > Column command to merge multiple data samples into one column.
- Stat > Nonparametrics > Kruskal-Wallis
- Select the data column for the Response field
- Select the data identified column for the Factor field

Friedman Test

The Friedman Test is the most complex of the non-normal data hypothesis tests that we use with multiple data samples. The Friedman Test works with large blocks of data. It essentially compares the data within the blocks and then between the blocks. In this regard it is a hybrid of the Paired T Test and an ANOVA or Kruskal-Wallis Test. The minimum sample size you should use in the Friedman Test is 30 data items. This test cannot be accomplished with Excel.

- Minitab:
- All the data must be combined into one column. Use the Data > Stack > Column command to merge multiple data samples into one column.
- Stat > Nonparametrics > Friedman
- Select the data column for the Response field
- Select the data identified column for the Factor field

### Hints & tips

- Stacking data in one column is very easy in Minitab using the stack command. I load my data into Minitab with a separate column for each sample then stack once everything is in. With the Friedman test, the stacked column can easily have hundreds of entries. Loading the data first by sample columns allows me to easily find and fix data problems.
- Run a normality check to see if your data is non-normal.
- Create a histogram of the data in each sample to see the shape of the data set.

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