﻿ Kruskal-Wallis Rank Sum Test for Independent-Samples

# Kruskal-Wallis Rank Sum Test for Independent-Samples

### Statistics > Nonparametric Tests > Kruskal-Wallis

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

### Dialog box items

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.

### Data

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.

### Options

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%.

### Example

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.

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