The Kruskal Wallis test can be applied in the one factor ANOVA case. It is a non-parametric test for the situation where the ANOVA normality assumptions may not apply.
Let ni (i = 1, 2, ..., k) represent the sample sizes for each of the k groups (i.e., samples) in the data. Next, rank the combined sample. Then compute Ri = the sum of the ranks for group i. Then the Kruskal Wallis test statistic is:
This statistic approximates a chi-square distribution with k-1 degrees of freedom if the null hypothesis of equal populations is true. Each of the ni should be at least 5 for the approximation to be valid.
We reject the null hypothesis of equal population means if the test statistic H is greater than CHIPPF(ALPHA,K-1) where CHIPPF is the chi-square percent point function
where <y> is the response (= dependent) variable;
<x> is the factor (= independent) variable;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
KRUSKAL WALLIS Y X SUBSET X = 1 TO 4
READ SPLETT2.DAT Y MACHINE
KRUSKAL WALLIS Y MACHINE
The following output is generated.
KRUSKALL-WALLIS TEST FOR ONE-WAY ANOVA 1. STATISTICS NUMBER OF OBSERVATIONS = 99 NUMBER OF GROUPS = 4 KRUSKALL-WALLIS TEST STATISTIC = 41.06223 2. PERCENT POINTS OF THE CHI-SQUARE REFERENCE DISTRIBUTION FOR KRUSKALL-WALLIS TEST STATISTIC 0 % POINT = .0000000 50 % POINT = 2.365974 75 % POINT = 4.108345 90 % POINT = 6.251388 95 % POINT = 7.814727 99 % POINT = 11.34487 99.9 % POINT = 16.26626 100.0000 % Point: 41.06223 3. CONCLUSION (AT THE 5% LEVEL): THE 4 SAMPLES DO NOT COME FROM IDENTICAL POPULATIONS.
Date created: 6/5/2001