# Talk:Hotelling's T-squared distribution

Hi Michael

that was a good edit!

I suppose if the observations are rank deficient, that would be equivalent to them all lying in a (p − 1)-dimensional hyperplane. I can't quite visualize the effect on ${\displaystyle W^{-1}}$. Any ideas as to how to "see" what's going on in this case?

best

Robinh 22:07, 26 Feb 2005 (UTC)

I'll think about that one. But notice that if the sample size is smaller than p, then you would necessarily have a rank deficiency. Michael Hardy 23:13, 26 Feb 2005 (UTC)

## Confusing

Hello,

Could someone add a brief, common-sense explanation of what the T-square statistic actually is for? I have a somewhat vague idea, but nothing certain. Such an addition would be a much appreciated preface to the mathematical details. Thanks, 65.183.135.231 (talk) 04:58, 26 August 2008 (UTC)

Hi. The T-square statistic is a generalization of Student's t statistic that is used in multivariate hypothesis testing (cut-and-pasted from the article). In what way does this fall short of what you ask for? Best wishes, Robinh (talk) 07:10, 26 August 2008 (UTC)

## Relation to Mahalanobis distance

The only difference is the factor of N. I have been trying to compare the results from some statistical software but I do not quite see their results to show this relationship. Shyamal (talk) 07:12, 26 December 2008 (UTC)

## Results

Hello, How do you view your data set? as a set of n vectors of p samples each, or p samples of a single vector of n dimensions? So long as you are consistent, the results are consistent withe 'cov()' function in 'R'. I've checked my own function against the returns of cov(). —Preceding unsigned comment added by 129.198.241.62 (talk) 19:33, 22 June 2010 (UTC)

## Rename to Hotelling's T-squared Statistics

The Hotelling's T-squared distribution is essentially the F-distribution, and has been noted on the F-distribution article. This article, as the edit history shows, is clearly more concerned with the Hotelling's T-squared statistics.

Do remember to sign comments. The edit history doesn't show this as there are essdentailly no comments there. There are some related comments above on the Talk page. Any change should follow the usual convention on capitals. And there would be merit in following the general set-up of related articles that exist in pairs such as F-test and F-distribution ... this would suggest having "Hotelling's T-squared test" as a name, rarther than "...statistic". Having a pair would leave some room for expansion of distributional properties but, given the link to the F distribution, there is not much need for this ...unless there are important uses in the published literature that use the T-squared explicitly. Melcombe (talk) 09:57, 13 December 2010 (UTC)

## Positive Definite vs. Positive Semidefinite

Am I correct in think that we should change "It can be shown that ${\displaystyle \mathbf {W} }$ is positive-definite and follows..." to "It can be shown that ${\displaystyle \mathbf {W} }$ is positive-semidefinite and follows..." Monsterman222 (talk) 20:55, 12 March 2013 (UTC)

## M's Wishart distribution

Hello, There is a good chance I have misunderstood, but (in the first line of the `distribution' section) isn't there a problem with ${\displaystyle M}$ being an ${\displaystyle m\times p}$ matrix then a ${\displaystyle p\times p}$ matrix that is inverted? Should it be that ${\displaystyle (_{m}M_{p})^{T}(_{m}M_{p})=_{p}M_{p}}$ is Wishart distributed?Benedict.powell (talk) 16:55, 7 September 2013 (UTC)