What is the appropriate statistical test to assess position within a distribution?

Question

I am doing a bioinformatics analysis, where I am scoring every protein-coding gene in the human genome (~19,000) for some genomic property ("interestingness"), then plotting the distribution of scores from lowest to highest. I am then marking, within this distribution, the position of specific subsets of genes - in the figures below, gene set 1 is labeled A-Y, and gene set 2 is labeled a-x. Some genes are marked in red and/or larger text, according to whether their individual "interestingness" score is statistically significant. The red dotted line indicates the cutoff point between "positively interesting" and "negatively interesting."

What would be appropriate statistical tests for the "biasedness" of each gene set within the distribution - visually, it looks like group 1 is non-randomly biased toward the "positively interesting" end, while group 2 looks pretty random, but I'd like to be able to quantify this with a statistic and p-value. I can do, for example, a binomial test for membership in the positively vs negatively interesting groups, which confirms my suspicions, but this seems like a very underpowered and uninformative approach. In the genomics world, people frequently use an approach called "Gene Set Enrichment Analysis" (GSEA) for problems like this, but I think there are assumptions built into that (rather opaque) approach that might not be valid for my interestingness metric. I'm using R for my actual analysis, so if you can recommend a specific package or function that works for your recommended test, that would be great. Thanks!

Answer 1

As all the genes are included in a single rank-ordering, this could be handled very simply by a Wilcoxon–Mann–Whitney (WMW) test. That tests whether a randomly sampled member of Group 1 tends significantly to be higher (or lower) than a randomly sampled member of Group 2.

The test itself requires few assumptions. It requires that the observations are independent of each other, which is probably OK here (perhaps depending on your measure of "interestingness"). A frequent interpretation of the WMW test, that the median values differ between groups, does require an assumption that the distributions within the two groups have the same shape.

In R you can use the two-sample version of the standard Wilcox.test() function.