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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?

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  • $\begingroup$ 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
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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.

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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 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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    $\begingroup$ @toto_tico, you need to use clmm() in the ordinal package for that. The vignettes are good; also brief tutorial here. $\endgroup$ – gung Nov 13 '15 at 23:14
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    $\begingroup$ @toto_tico, they're not quite the same as the documentation; they're more supplemental. Not all packages have them (but all packages must be documented). They're more tutorial-style introductions to the statistical ideas & how to use the functions in the package to implement those ideas. The documentation is just a set of standardized help files for the functions. $\endgroup$ – gung Nov 13 '15 at 23:41
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    $\begingroup$ @toto_tico, if you go to the webpage for the package on CRAN (linked above), you can see the vignettes listed & can download them as pdfs from there. I have them in a separate folder on my machine. $\endgroup$ – gung Nov 14 '15 at 0:44

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