Re: [Maxima-discuss] "distrib" package

[Soegtrop, M. <mic...@in...>]

Dear Henry,

are we talking about distributions with known parameters, or are we talking about two samples from two different distributions with unknown parameters, but known distribution (e.g. normal)?

In the first case, you can follow the path outlined by Robert Dodier. In the second case you could first estimate the distribution parameters from the samples and then follow the same path, but unless the samples are very large, there is the problem that the estimated parameters themselves have very large errors. This means that probabilities you get from comparing these distributions are themselves just a single sample of a random distribution, with potentially very large errors (the smaller then sample, the larger the error). When the samples are so small that the error of estimated parameters cannot be neglected any more, it become quite tricky, and you need more advanced methods to get a usefull result. This is the difference between the Behrens-Fisher problem and what Robert Dodier outlined.

If you are just looking into tails, it is also a good question whether this is still sufficiently normal distributed. The capabilities of humans might be normal distributed, but if you take training and the like into account, which essentially streteches the capabilities of the top quite a bit, I have my doubts. I think you might be better of with a paremeter free method.

I am a bit out of this and would have to think about what method can be applied here. The Mann Whitney Wilcoxon test would e.g. answer the question if one team is significantly better than the other or if both look the same. This goes a bit in your direction, but it is not exactly what you want. But it doesn't make assumptions about what distribution your data has, so the results are trustworthy.

See http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U

Best regards,

Michael