Manuals/calci/KRUSKALWALLISTEST

KRUSKALWALLISTEST (SampleDataByGroup,ConfidenceLevel,NewTableFlag)

• $SampleDataByGroup$ is the set of values to find the test statistic.
• $Confidencelevel$ is the value between 0 and 1.
• $NewTableFlag$ 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 $\chi$ is greater than the critical value then reject the null hypothesis
  • 5.Calculate the Test Statistic:$H={\frac {12}{N(N+1)}}\sum _{i=1}^{k}{\frac {T_{i}^{2}}{n_{i}}}-3(N+1)$
  • 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

Spreadsheet

	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)

TEST RESULTS

Regression Statistics
Multiple R	0.9989241524588297
R Square	0.9978494623655914
ADJUSTEDRSQUARE	0.996774193548387
STANDARDERROR	0.7071067811865526
OBSERVATIONS	4

ANOVA

	DF	SS	MS	F	SIGNIFICANCE F
REGRESSION	1	464	464	927.9999999999868	0.001075847541170237
RESIDUAL	2	1.0000000000000142	0.5000000000000071
TOTAL	3	465

	COEFFICIENTS	STANDARD ERROR	T STAT	P-VALUE	LOWER 95%	UPPER 95%
INTERCEPT	86.5	0.6885767430246896	125.62143708199342	0.00006336233990811291	83.53729339698282	89.46270660301718
INDEP1	-4.000000000000007	0.1313064328597235	-30.46309242345547	0.0010758475411701829	-4.564965981777561	-3.4350340182224532

Related Videos

Kruskal Wallis Test

See Also

• LEVENESTEST
• MOODSMEDIANTEST
• RIEMANNZETA

References

• Kruskal-Wallis test documentation on Wikipedia
• Kruskal-Wallis test in SPSS

• List of Main Z Functions

• Z3 home