I'm reading Subramanian et. al's (2005) original GSEA paper. In the paper, the authors mention the following:
We noticed that the use of weighted steps could cause the distribution of observed ES scores to be asymmetric in cases where many more genes are correlated with one of the two phenotypes. We therefore estimate the significance levels by considering separately the positively and negatively scoring gene sets
I understand what they're saying, but I simply don't understand why it's a problem. Basically, they're saying that in some cases, most genes in the list we're testing could appear mostly at the top or bottom of the list. But I don't understand why having asymmetric distributions is a problem. What is the issue here?
EDIT: Here are some examplesexample GSEA plots I found via a web search with such gene sets. Where is the problem?
One thing I don't get though is why this problem would be introduced through "weighting" of the steps. I feel like it would also be a problem without weighting. The way it is phrased in the paper seems to suggest that it's the weighting that causes an issue.