# Rank transformed 2-way ANOVA

I know I'm asking a lot of questions these days! Sorry about that, but I'm trying to work through my grad thesis data collected over the last 4 years, and am repeatedly tripping on my beginner's grasp on stats.

The background: My basic question is the same as described in another question on this site. In brief, I'm trying to sort out a reasonable way to compare good years vs. poor between 2 sites for a bunch of variables (breeding metrics of birds). I'm only interested in comparing good years between sites and poor years between sites. I'm not interested (much) in whether good years at one site are better than poor years at the other site (so I guess that means I'm not interested in interactions? Although what I want to get at is whether Site within Year-type is sig. different, so perhaps interactions are important?). Though the metrics are related in that they're all from the same 2 populations, the variables I'm looking at are independent otherwise.

This question is about comparing nest initiation date (converted to ordinal day and is therefore ordinal data) between these 2 sites and 2 year-types. The data are skewed and the variances heterogeneous from a glance at a histogram and boxplots. My sample size ranges (for good within-site and poor within-site) from n= 69 to 864. I thought I should use a non-parametric 2-way ANOVAs and did some searching on those. I've seen Friedmans' test offered up as a non-parametric alternative to 2-way ANOVAs, but from what I gather, it's only for repeated measures data. I found some who recommended that you can rank-transform data and run the 2-way ANOVA on that.

To do this, I just converted the days within each site and within each year-type to ranks by making the first day (say, 154) = 1, day 155 = 2 etc. , but this really doesn't change anything in my data since I have ordinal dates anyway.

So, what can I do? I've run the 2-way ANOVA on ranks and on the original centred data. While the numbers aren't the same from each test, the ultimate result is: the Holm-Sidak mulitple comparisons show that within each year-type of good and poor, the sites are significantly different (p<0.001). Can I accept these results? Or is there a better way of analyzing these data?

I'm currently using Sigmaplot 11 (with built-in Sigmastat functionality) for the basic stuff, and turning to R whenever it can't handle what I need to do.

Thanks for reading, and for any tips you can provide! Mog

EDIT: I'm also interested in what I can do with continuous data that is non-normal (skewed) and has unequal variances. Is rank-transforming inappropriate for that as well?

One of many computational tools for the PO model is the lrm function in the R rms package. The rms package's contrast, anova, summary, plot, and nomogram functions can help.