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distribution of PR

Posted By: Timothy Chow
Date: Friday, 29 June 2012, at 6:06 p.m.

In Response To: distribution of PR (Bill)

These are good questions, and the answers depend on what question you're trying to address.

You don't necessarily need to figure out exactly what the shape of the distribution is, if your only concern is (for example) to determine whether some new set of numbers is or is not likely to be drawn from the same distribution.

For example, if you're just trying to test the hypothesis that Stick is Mochy in disguise, one reasonable approach is to use a (two-sample) Kolmogorov–Smirnov test. This is a nonparametric test, meaning that you don't have to come up with a precise model of the shape of the distributions in question in order to apply the test.

This might not be what you're really interested in. After all, even if (say) Mochy and Falafel have similar PR's, their styles may differ enough that you may be able to distinguish their PR distributions. The K-S test will pick up on that if this is true. So if you're just wondering whether Stick plays better than Mochy (where "better" means lower PR for the purposes of this discussion), then the K-S may be "too sensitive" for your purposes.

So, an alternative test you might use is a Mann–Whitney U test, which will test whether Stick's PR's tend to be lower than Mochy's PR's. This is also a nonparametric test, and perhaps gets closer to what Phipps is asking about.

The U test, however, will still only tell you something like, "Yes, I'm very very confident that Stick's PR is lower than Mochy's PR." It doesn't let you say that you're very confident that Stick's PR is a lot lower than Mochy's PR, or even that it's at least half a point lower. For this, you'd probably have to cook up your own home-grown test. Of course, you don't want to pick the threshold of 0.5 by looking at your data first, and then using that same data to execute your test...

Anyway, the point is that there are ways to test these kinds of hypotheses without modeling the distributions.

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