Performs Kruskal-Wallis H-Rank Sum Test for Independent-Samples.

This test is a generalization of the procedure used by the Mann-Whitney test and, like Mood's Median test, offers a nonparametric alternative to the one-way analysis of variance.

The null hypothesis of the test is that all k distribution functions are equal. The alternative hypothesis is that at least one of the populations tends to yield larger values than at least one of the other populations.

Assumptions:

•random samples from populations

•independence within each sample

•mutual independence among samples

•measurement scale is at least ordinal

•either k population distribution functions are identical, or else some of the populations tend to yield larger values than other populations

•Samples in one column:

Choose if the sample data are in a single column, differentiated by factor levels in a second column.

oResponse: Enter the columns containing the sample data.

oFactor: Enter the columns containing the sample factor.

•Samples in different columns:

Choose if you have entered raw data in separate columns.

oSamples: Enter the column containing the samples.

•Report:

The display of outputs of VisualStat.

The response (measurement) data must be stacked in one numeric column. You must also have a column that contains the factor levels or population identifiers. Factor levels can be numeric, or text. Data can also be in separate numeric columns.

•Summary Statistics:

Check to compute summaries for each sample.

•Adjusted for ties:

Check if the statistic is computed with average ranks used in the case of ties.

•Confidence Level:

Enter the level of confidence desired. Enter any number between 0 and 100. Entering 90 will result in a 90% confidence interval. The default is 95%.

The data are from a comparison of four investment firms. The observations represent percentage of growth during a three month period for recommended funds.

1.Open the DataBook nonparam.vstz

2.Select the sheet growth

3.Choose the tab Statistics, the group Nonparametric Tests and the command Kruskal-Wallis

4.Select group Samples in different columns

5.In Samples, select A, B, C and D.

6.Click Options page and check Summary Statistics.

7.Click OK

Report window output

Kruskal-Wallis Rank Sum Test for Independent-Samples

Test of the equality of medians for two or more populations

alternative hypothesis: true Not all the population medians are equal.

Summary Statistics

N Mean Median Std Dev Mean Rank Rank Sum

A 4 4.1750 4.1000 0.2681 16.2500 65.0000

B 5 2.9800 2.8000 0.5075 8.3000 41.5000

C 5 2.1800 2.1000 0.3311 3.5000 17.5000

D 5 3.7600 3.7000 0.4543 13.2000 66.0000

Kruskal-Wallis Rank Sum Test (adjusted for ties)

NB 19

Type of Test Two-sided

Distribution Chi-Square Approximation

Kruskal-Wallis H 13.6904

Degree of freedom 3

p-value 0.0034

alpha-level 0.05

Critical Value 7.8147

Conclusion Accept the Alternative Hypothesis

Interpreting the results

The p-value for a = 0.05 with df = 3 is 0.0285. Since 0.05 > 0.0285, we reject the null hypothesis.

See Also: |

One-Way Analysis of Variance | Mann-Whitney U-test for Independent-Samples | Report | Numeric Formats

Web Resource: NIST e-Handbook of Statistical Methods, 2006 | Probability and statistics EBook | Non-parametric tests (PDF)