Hi I am trying to find the non-parametric equivalent of a two-way ANOVA (3x4 design) which is capable of including interactions. From my reading in Zar 1984 "Biostatistical analysis" this is possible using a method put forth in Scheirer, Ray, and Hare (1976), however, according to other posts online it was inferred that this method is no longer appropriate (if it ever was).

Does anyone know what method would be appropriate for doing so, and if so the corresponding functions in R or Stata?

  • $\begingroup$ The best choice (if there is any) depends on the reason why you think classic ANOVA is not appropriate in your case. $\endgroup$ – Michael M Dec 3 '13 at 7:40
  • $\begingroup$ Hi Michael, the classic ANOVA is not appropriate because despite using transformations it is not possible to meet the normality assumption. $\endgroup$ – user35595 Dec 4 '13 at 18:11

When most people think of a non-parametric equivalent of ANOVA, they think of the Kruskal-Wallis test. The Kruskal-Wallis test cannot be applied to a factorial structure, however.

The first workaround to this is to run all of your conditions as a one-way analysis. This does not let you test your factors individually, but you may be able to get what you need from the main test, possibly combined with post-hoc tests.

The Kruskal-Wallis test can be considered a special case of ordinal logistic regression, however. Moreover, OLR can handle a factorial structure, and does not require that your response data are normally distributed, only that they are ordinal. This is likely to be your best option. On UCLA's excellent statistics help website, you can find guides to OLR in both R and Stata.

  • $\begingroup$ The vignettes from the ordinal package provide a good introduction to ordinal logistic regression and clm has far more capabilities than the polr command in the MASS package. $\endgroup$ – John Dec 3 '13 at 0:42
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    $\begingroup$ Hi gung, and thank you for the response. Am I mistaken in that using the Kruskal-Wallis test it is not possible to see interaction effects since it is just the non-parametric equivalent of a one-way ANOVA? I am really interested in seeing the interaction effects, since it is clear that they exist, and would like to be able to properly demonstrate this. In such a case is using OLR appropriate? $\endgroup$ – user35595 Dec 4 '13 at 18:15
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    $\begingroup$ OLR is perfectly appropriate; it is your best option in this case. $\endgroup$ – gung - Reinstate Monica Dec 4 '13 at 18:20
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    $\begingroup$ All continuous data are ordinal as well. It just means that you have N ranks w/ no ties. $\endgroup$ – gung - Reinstate Monica Feb 23 '14 at 13:30
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    $\begingroup$ @gung indeed, I would say that the concept of ordinality is ontologically prior to the concept of quantity. :) $\endgroup$ – Alexis Sep 8 '14 at 18:10

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