# Kruskal-Wallis Test for Multiple Samples Help

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The Kruskal-Wallis test determines if there is a difference between the medians of different samples. The median is used in this test since it is a better measure of the central tendency of the data than the average for non-normal data. In addition, pairwise comparisons are given to determine which medians are significantly different. The example below shows how to do this test using the SPC for Excel software.

**Example** (from Statistics and Data Analysis, by Ajit Tamhane and Dorothy Dunlop, Prentice-Hall, 2000)

An experiment was done to compare four different methods of teaching the concept of percentages to sixth graders. 28 classes were randomly assigned to the four methods. A 45 item test was given to all classes. The average test scores are given below. We want to use the Kruskal-Wallis test to determine if there are significant differences in the four methods.

- 1. Enter the results into an Excel worksheet as shown below. The data can be downloaded at this link.

- 2. Select the data and the headings.
- 3. Select “NonParametric” from the “Statistical Tools” panel on the SPC for Excel ribbon.
- 4. Select the “Kruskal-Wallis Test for Multiple Samples” option and then OK.

- Enter Data Range with Headings: the default entry is the range selected on the worksheet.
- Alpha: this is the confidence level; 1-alpha is the confidence interval. Default is 0.05 for 95% confidence.
- Select OK to generate the results.
- Select Cancel to end the program.

#### Kruskal-Wallis Test for Multiple Samples Output

The output from the Kruskal-Wallis test is shown below.

The data are reprinted at the top of the output.

- Median: Calculated median for each method.
- Rank Sum: Calculated sum of the ranks.
- Count: Number of results in each method.
- Average Rank: Calculated average rank.
- Alpha: Alpha entered by the user.
- kw Statistic: Calculated Kruskal-Wallis statistics.
- p value: Calculated p value (will be red if ? alpha).

If p value ? alpha, then there are differences between the pairs.

The pairwise comparisons using the studentized range distribution are listed at the bottom of the output. If there is a significant difference, Yes is printed in red.

Note:

Uses the chi-square distribution to determine the p value.