Within each sample, the values are independent, and identically
distributed.
(The Kruskal-Wallis test
is a nonparametric
test. We need not specify or know what the
distribution is,
only that all the values in each sample follow the same
continuous distribution.)
The populations from which the different samples were taken
differ only in location.
That is, the populations may differ in their means or medians,
but not in their dispersions
or distributional shape (such as skewness).
For multiple comparisons
to be meaningful,
the treatment effect is viewed as fixed,
so that the populations (treatment groups)
in the experiment include all those of interest.
Because the test statistic for the Kruskal-Wallis test
is based only on the ranks
of the data values, the test can
be performed when the only data available are those relative ranks.
Guidance:
Ways to detect before performing the
Kruskal-Wallis test whether your data violate any
assumptions.
Ways to examine
Kruskal-Wallis test results to detect
assumption violations.
Possible alternatives if your data or
Kruskal-Wallis test results indicate assumption violations.
To properly analyze and interpret
results of the Kruskal-Wallis test, you should be familiar with the
following terms and concepts:
If you are not familiar with these terms and concepts, you are advised to
consult with a statistician. Failure to understand and properly apply the
Kruskal-Wallis test may result in drawing erroneous conclusions from your data.
Additionally, you may want to consult the following references:
Brownlee, K. A. 1965. Statistical Theory and Methodology
in Science and Engineering. New York: John Wiley & Sons.
Conover, W. J. 1980. Practical Nonparametric Statistics. 2nd ed.
New York: John Wiley & Sons.
Daniel, Wayne W. 1978. Applied Nonparametric Statistics.
Boston: Houghton Mifflin.
Daniel, Wayne W. 1995. Biostatistics. 6th ed.
New York: John Wiley & Sons.
Hollander, M. and Wolfe, D. A. 1973. Nonparametric Statistical Methods.
New York: John Wiley & Sons.
Lehmann, E. L. 1975. Nonparametrics: Statistical Methods Based on
Ranks. San Francisco: Holden-Day.
Miller, Rupert G. Jr. 1996. Beyond ANOVA, Basics of Applied
Statistics. 2nd. ed.
London: Chapman & Hall.
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