Nonparametric generalization of ANOVA
On Mar 5, 2010, at 8:19 AM, blue sky wrote:
My interpretation of the relation between 1-way ANOVA and Wilcoxon's test (wilcox.test() in R) is the following. 1-way ANOVA is to test if two or multiple distributions are the same, assuming all the distributions are normal and have equal variances. Wilcoxon's test is to test two distributions are the same without assuming what their distributions are. In this sense, I'm wondering what is the generalization of Wilcoxon's test to more than two distributions. And, more general, what is the generalization of Wilcoxon's test to multi-way ANOVA with arbitrary complex model formula? What are the equivalent F statistics and t statistics in the generalization of Wilcoxon's test? Note that I'm not interested in looking for a specific nonparametric test for a particular dataset right now, although this is important in practice. What I'm interested the general nonparametric statistical framework that parallels ANOVA. Could somebody give some hints on what references I should look for? I have google searched this topic, but don't find a page that exactly answered my question.
This is your first of three postings in the last hour and they are all in a category that could well be described as requests for tutoring in basic statistical topics. I am of the impression you have been requested not to engage in such behavior on this list. For this question for instance there is an entire CRAN Task View available and you have been in particular asked to sue such resource before posting. It's not the described role of the r-help list to remediate your lack of statistical background, but rather to deal with difficulties in applying the R-language to particular, discrete and exemplified problems.
David Winsemius, MD West Hartford, CT