I am wondering which test in JMP to run for my data. I am comparing different groups of birds and have different sample sizes for the groups. My understanding is that the Wilcoxon test compares medians and Steel Dwass compares means? In creating graphs, would I use the mean and standard error or medians and confidence intervals?
These are both non-parametric tests so I think they will both work with rank calculations and hence are comparing medians not means. The distinction between the two is that the Wilcoxin test performs pairwise comparisons (it is the non-parametric equivalent of performing a Student's t test on each pair); the alpha level is fixed and takes no account of the number of comparisons being performed. The Steel Dwaas method performs the multiple comparisons whilst controlling the overall experiment-wise error rate (it is the non-parametric equivalent to the Tukey All-Pairs method). If you don't take account of the number of comparisons then your overall Type I error rate will grow quickly as illustrated below: