# Questions tagged [hotelling-t2]

Hotelling's T-squared test (one-sample or two-sample) is a generalization of a t-test for the multivariate case. It relies on Hotelling's T-squared distribution.

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### What is a generalisation of t-test to the case of multivariate distribution?

When we have a sample of numbers, one of the most basic tests is the t-test, in which we check the null hypothesis that the population mean is equal to zero. I am interested in a generalisation of ...
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### Intuition for Hotelling's T^2 Test

I have been learning about Hotelling's $T^2$ test from Multivariate Statistics: Old School. The test is given by $T^2 = \nu\cdot\text{trace}(\bf{W}^{-1}\bf{B})$. The author shows that in the case of ...
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### Hotelling T squared seemingly useless at detecting a mean shift

I am trying to develop a single-sample Hotelling $T^2$ test in order to implement a multivariate control chart, as described in Montgomery, D. C. (2009) Introduction To Statistical Quality Control, ...
0answers
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### Finding the probability density function of Hotelling's T-squared distribution

The following image is seen on wikipedia when searching for Hotelling's T-squared distribution This is apparently the pdf of the Hotelling T-squared distribution at different parameters. However, I ...
0answers
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1answer
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### Relation between Two Sample Hotelling's T-test and Mahalanobis Distance?

Mahalanobis distance is a measure of distance between a point and distribution. So if we want to check if a point belongs to a particular distribution or not, we can use Hotelling's T-test, which is ...
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1answer
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### Hotelling T^2 test derivation question

I am reading about the Hotelling $T^2$ test (A primer of multivariate statistic s by Richard J. Harris). It says here that the test can be seen as creating a linear combination of your variables and ...
0answers
102 views

### What is the distribution of this nearly-Hotelling statistic?

Let $X$ be an $n \times l$ matrix, and $F$ an $n \times p$ matrix, with the rows of $X$ and $F$ drawn i.i.d. from multivariate Gaussians. (The independence applies to rows: the $X$ and $F$ may be ...
0answers
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### Tutorial for performing Contrasts for MANOVA

Context I have a multivariate dataset with a test group and three control groups. I was thinking that the best way to determine if and how the test group differed from all of the control groups would ...
2answers
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### How exactly does Wilks' Lambda distribution generalize the Hotelling distribution?

According to Wikipedia, Wilks' Lambda distribution generalizes Hotelling's distribution. I am having some problems seeing how this works. I can see how Hotelling's distribution generalizes Student's t-...