Comparing Ratios of Sexual Size Dimorphism I am trying to find a test to compare degrees of sexual size dimorphism (SSD) between different populations. SSD is easily calculated as the ratio of the mean male size:mean female size. 
I have four populations, and in each population, the numbers of males and females are different (e.g., pop 1: n(males)=35, n(females)=25; pop 2: n(males)=45, n(females)=28). 
I do a lot of ANOVAs to compare differences in males and females between populations, but because each population only provides a single value/ratio for SSD, I am not sure how to compare these.
A permutation test was suggested by a colleague, but I'm not quite sure how to do this in R or any other package.
Thanks in advance!
 A: I do not think that permutation testing immediately confers an answer to this problem.
If you carefully read the problem, you'll see that an ordinary linear model suffices to test the hypothesis about whether the ratio of average sizes between males and females differs substantially between species.
I would do this analysis by fitting two models. First I would create a transformed logSize variable, so that you are comparing geometric means (e.g. differences in ratios). Then I would create a "full model" by regressing logSize on categorical effects for gender, species, as well as the two way interaction between gender and species. I would fit a "reduced model" which regresses logSize on categorical gender and species as before, but omits the interaction. A likelihood ratio test, or other appropriate structured test of nested linear models, would be correct in assessing the hypothesis. 
This gives a test for whether the interaction effects are significant. Since I assume there's more than one species, this ANCOVA approach is suited to testing multiple simultaneous effects, or a difference in the grand-mean of interaction effects. 
Basically, the interaction allows the male-female ratio to differ between species, whereas the reduced model fits the data under the assumption that average size differs between species but the male-female ratio is constant. Each interaction effect can be interpretted as a discrepancy in male-female ratios for that species compared to the principle species (which is arbitrary).
Very nice question.
