[nerdponx]

It's their point, and it's a good one, but I think they're somewhat overstating how common power-law data is; it probably varies a lot by field of study. And at least the logarithm of a power-law variable can help bring it back closer to the world of sanity. Plus, there are plenty of fields where nonparametric tests of medians are accepted standard practice.

[mjburgess]

You can turn most issues into powerlaws by recursing a reasonable risk distribution over it.

So suppose we ask, what is our confidence in X? (rather than X); and then, what is our confidence in the model by which we give confidences in X (ie., the model risk); and so on...

In practice, what we want to model is the appropriate confidence, not an actual prediction (bunk). So we are very often screwed.

Statistics is an illusion.