Manuals/calci/KRUSKALWALLISTEST
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KRUSKALWALLISTEST (SampleDataByGroup,ConfidenceLevel,NewTableFlag)
- is the set of values to find the test statistic.
- is the value between 0 and 1.
- is either TRUE or FALSE.
Description
- This function gives the test statistic value of the Kruskal Wallis test.
- It is one type of Non parametric test.
- It is a logical extension of the Wilcoxon-Mann-Whitney Test.
- The parametric equivalent of the Kruskal-Wallis test is the one-way analysis of variance (ANOVA).
- This test is used for comparing more than two sample that are independent or not related.
- It is used to test the null hypothesis that all populations have identical distribution functions against the alternative hypothesis that at least two of the samples differ only with respect to Median.
- Kruskal–Wallis is also used when the examined groups are of unequal size.
- When the Kruskal-Wallis test leads to significant results, then at least one of the samples is different from the other samples.
- The test does not identify where the differences occur or how many differences actually occur.
- Since it is a non-parametric method, the Kruskal–Wallis test does not assume a normal distribution of the residuals, unlike the analogous one-way analysis of variance.
- However, the test does assume an identically shaped and scaled distribution for each group, except for any difference in medians.
- The Kruskal Wallis test data are having the following properties:
- 1.The data points must be independent from each other.
- 2.The distributions do not have to be normal and the variances do not have to be equal.
- 3.The data points must be more than five per sample.
- 4.All individuals must be selected at random from the population.
- 5.All individuals must have equal chance of being selected.
- 6.Sample sizes should be as equal as possible but some differences are allowed.
- Steps for Kruskal Wallis Test:
- 1. Define Null and Alternative Hypotheses:
- Null Hypotheses:There is no difference between the conditions.
- Alternative Hypotheses:There is a difference between the conditions.
- 2.State Alpha:Alpha=0.05.
- 3.Calculate degrees of freedom:df = k – 1, where k = number of groups.
- 4.State Decision Rule:From the Chi squared table calculate the critical value.
- Suppose the is greater than the critical value then reject the null hypothesis
- 5.Calculate the Test Statistic:
- 6.State Results:In this step we have to take a decision of null hypothesis either accept or reject depending on the critical value table.
- 7.State Conclusion:To be significant, our obtained H has to be equal to or LESS than this critical value.
Examples
A | B | C | |
---|---|---|---|
1 | New | Old | Control |
2 | 27 | 22.5 | 3 |
3 | 12.5 | 11 | 24.5 |
4 | 19 | 8 | 14 |
5 | 26 | 5.5 | 4 |
6 | 15 | 9.5 | 7 |
7 | 20 | 9.5 | 2 |
8 | 16 | 12.5 | 22.5 |
9 | 21 | 1 | 5.5 |
10 | 24.5 | 17 | |
11 | 18 |
=KRUSKALWALLISTEST([A2:A11,B2:B10,C2:C9],0.05,0)
A | B | C | |
---|---|---|---|
1 | GROUP-0 | GROUP-1 | GROUP-2 |
2 | 27 | 22.5 | 3 |
3 | 12.5 | 11 | 24.5 |
4 | 19 | 8 | 14 |
5 | 26 | 5.5 | 4 |
6 | 15 | 9.5 | 7 |
7 | 20 | 9.5 | 2 |
8 | 16 | 12.5 | 22.5 |
9 | 21 | 1 | 5.5 |
10 | 24.5 | 17 | undefined |
11 | 18 | undefined | undefined |
GROUP-0 | GROUP-1 | GROUP-2 | |
---|---|---|---|
SUM OF RANKS | 199 | 96.5 | 82.5 |
GROUP SIZE | 10 | 9 | 8 |
R^2/N | 3960.1 | 1034.6944444444443 | 850.78125 |
TOTALRANKSUM | 378 | ||
TOTAL GROUP SIZE | 27 | ||
TOTAL R^2/N | 5845.575694444444 | ||
H | 8.78691578483243 | ||
DF | 2 | ||
P-VALUE | 0.012357922885420258 | ||
A | 0.05 |
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