Talk:Behrens–Fisher problem

Solved?

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 |μ₁−μ₂|, 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?

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)

"Random and Fairly Mixed," Perhaps?

The opening sentence, "In statistics, the Behrens–Fisher problem, named after Walter Behrens and Ronald Fisher, is the problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on two independent samples." is incorrect.

There are no normally distributed populations.

Normal distribution is a hypothetical attribute of some mathematical objects at some limit. "A pair of shoelaces" begins with the letter A, but shoelaces contain no letters of the alphabet at all. Similarly, populations do not necessarily have any of the qualities of their arithmetical denominations.

David Lloyd-Jones (talk) 08:44, 4 May 2020 (UTC)