Homogeneity of variance & non-parametric tests

[#1]

Is homogeneity of variance required for running a Wilcoxon or Kruskal-wallis test? If so, what test can I run if my data fails this assumption?

My objective is to see if there is a statistically significant difference between "seasons" (7 levels, i.e. - May 2011, August 2011, etc.) in terms of standardized abundance (n/m^3). We sampled the same location each month and year.

[#2 · Accepted solution]

Just to be clear, the non-parametric tests address any difference in populations without reference to a specific parameter, such as the location, shape, or scale. So there is no assumption of homoscedasticity.

[#3]

Perfect, thank you!

[#4]

Hey Mark,

Does this stand true for the Hodges-Lehmann estimate and its corresponding confidence interval that is produced using the Wilcoxon Each Pair test? 

Thanks,

[#5]

It bothered me that I did not know how the confidence interval is formulated, so I looked at the documentation. It is not in one of the JMP guides, but it is in the SAS/STAT documentation. The asymptotic method is probably what JMP uses. It does not assume anything about the distribution of the response variables. It assumes that the pair-wise differences are normally distributed for large N. The other method (exact limits) does not assume a distribution model for the response.