Talk:Behrens–Fisher problem

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 Field: Probability and statistics

Solved?[edit]

The statement "The Behrens–Fisher Problem has been solved" neddssome clarification, not least because the problem to be solved has not been accurately specified. Even the meaning of "solved" is open ... is this an exact mathematical solution, a solution good enough for practical purposes, something only valid in a Bayesian framework or ...? Melcombe (talk) 10:01, 15 February 2010 (UTC)

Indeed. The Behrens–Fisher problem is not a math problem. One can model it as a math problem in any of various ways, and there are essentially philosophical disputes about which, if any, is the right one, and each of those separately is a math problem. Michael Hardy (talk) 17:02, 15 February 2010 (UTC)
I've looked into the cited article by Dudewicz et al. (doi:10.1016/j.jspi.2006.09.007), and the authors indeed use the word “solved” to describe their findings :). The major disadvantage of their “exact” solution is that it is formalized in terms of the power of the test, β. That is, if you want a test which achieves a specific power β for a specific value of |μ1μ2|, the authors’ procedure will tell you how many observations n1 and n2 you have to collect to achieve that power. An uncommon, but not unfeasible approach of course. However in practice we more frequently encounter situations where the sample sizes are given beforehand, and we’d want a test which would be “most powerful” in certain respect.  // stpasha »  07:40, 16 February 2010 (UTC)

I have removed the claim and revamped the article to reflect the above, adequately I hope. Melcombe (talk) 17:12, 16 February 2010 (UTC)

approximation?[edit]

Currently this article states:

Fisher approximated the distribution of this by ignoring the random variation of the relative sizes of the standard deviations

But based on some comments in Fisher's book I doubt that this is true. I think Fisher thought one should be using the conditional probability distribution given the ratio of sizes of sample SDs.

(Actually, I have lots of qualms about this article.) Michael Hardy (talk) 17:37, 26 August 2012 (UTC)