Performs Kruskal-Wallis H-Rank Sum Test for Independent-Samples.
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.
•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.
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.
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.
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.
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.
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)
Type of Test Two-sided
Distribution Chi-Square Approximation
Kruskal-Wallis H 13.6904
Degree of freedom 3
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.