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A Nonparametric Test for Interactions of Any Order

Summary: A new procedure is presented for testing interactions of any order without requiring any elaborate assumptions about the shapes or variances of the sampled populations. Its principal limitations are that there must be equal numbers of observations per cell and that measurement must not be so gross as to yield many cited observations. The test procedure involves three steps. First, the data are collapsed over all variables except replicates and those variables whose interaction is to be tested. Then, by a series of subtractions, the resulting data table is reduced to one in which all lower-order effects have been eliminated and which now contains only as many cells as there are degrees of freedom for the interaction of interest. At this point, a test for main effects applied tot he cells of the reduced table is equivalent to a test for interaction in the original data table. So the final step is to apply the appropriate nonparametric test for main effects to the data in the reduced table.

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  • Topics:
  • Keywords: Interactions,Statistical tests
  • Author: Bradley, James V.
  • Journal: Journal of Quality Technology