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.
| Null Hypothesis, H0 | Alternate Hypothesis, H1 |
| m1 = m2 = ... = mi | m1 <> m2 <> ... <> mi |
where mi are the medians of population i
At the Excel Menu (For Excel 2007, go to Add-ins first)
Choose ProcessMA > Statistics > Nonparametric > Kruskal-Wallis
For data in single stacked column
In Variable, select the column containing the response data (Numeric)
In Factor, select the column containing factor levels (>=2 levels)
For data in different columns
In Variables, select the columns containing the response data (Numeric, >= 2 variables)
Click OK
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.
Open data worksheet by choosing ProcessMA > Tools > Data
Choose ProcessMA > Statistics > Nonparametric > Kruskal-Wallis
In Variable, select BQ - Cycle Time
In Factor, select BR - Officer
Click OK
For a desired a = 0.05, since p = 0.0002 < a, we will reject H0. Therefore, we conclude that there is significant evidence that the median cycle times for the three officers are different.
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