The Kruskal-Wallis is a nonparametric test of the equality of medians for two or more populations. Its parametric counterpart is the One-Way Analysis of Variance.
This procedure assumes that the samples are randomly and independently drawn from populations that have the same shape. It is more robust than the Mood's median test for data of many distributions but is less robust for data with outliers.
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Null Hypothesis, H0 |
Alternate Hypothesis, H1 |
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m1 = m2 = . . . = mi |
m1 ¹ m2 ¹ . . . ¹ mi |
where mi are the medians of population i.
1. Choose ProcessMA > Statistics > Nonparametric > Kruskal-Wallis.
2. In Data in, choose how your data is stored.
· If your data in stored in a single column:
- In Variable, select the column containing the response.
- In Category, select the column containing subgroup codes.
· If your data in stored in different columns:
- In Variables, select the columns containing the separate responses.
3. Click OK.
Note To select a column of data into a textbox, double-click on any of the column names shown in the list on the left of the dialog box while in the textbox.
Variable: Numeric.
Category: Text or Numeric; Must have the same number of data points as the variable; Must contain at least 2 distinct categories.
Variables: Numeric.
You are the manager of the mortgage department in a bank. You have three officers processing mortgage applications. You collected data on cycle time to process applications for the last 2 months and you want to assess if the three officers have the same processing speed.
1. Open worksheet ProcessMA > Tools > Data Files > Stat.xls.
2. Choose ProcessMA > Statistics > Nonparametric > Kruskal-Wallis.
3. In Data in, choose a single column.
4. In Variable, select Y – Cycle time.
5. In Category, select Z – Officer.
6. Click OK.
Interpretation
For a desired a = 0.05, since p = 0. 0002 < a, we will reject H0. Therefore, we conclude that there is no significant evidence that the median cycle times for the three officers are different.