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Generating null distributions by a residual permutation procedure

I am trying to understand the method described in this paper which describes an hypothesis-testing framework for stable isotope ratios. The data are in a bivariate isotopic space and the metrics that ...
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1answer
142 views

Alternative tests for Hotelling's two-sample T-test

I have a bunch of vectors from two groups, $X$ and $Y$, and each vector in either $X$ or $Y$ groups has $m$ elements. Now I have $X_{1},\ldots,X_{8}$ and $Y_{1}, \ldots, Y_{8}$ in each group, and ...
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2answers
218 views

Proof for two-sample Hotelling $T^2$ statistic?

I've been reading "A primer of multivariate statistics" by Richard J. Harris, page 546, which shows how to derive the Hotelling $T^2$ statistic, after seeing this related but different question (I ...
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1answer
142 views

Correlation and Hotelling test

To find a Hotelling $T^2$ score it is necessary to calculate the covariance matrix and then invert it. Now, when the test is a two-sample $T^2$ test, the covariance matrix is a pooled matrix. When ...
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69 views

How do I find the coefficients of a two-sample T2 Hotelling Test?

Hi I am trying to figure out how to obtain the coefficients for the linear combination of variables determined by a Hotelling $T^2$ test. I know that for the one sample case it is $a = S^{-1} \Delta ...
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1answer
195 views

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 ...
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1answer
256 views

Is there a generalization of Pillai trace and the Hotelling-Lawley trace?

In the setting of multivariate multiple regression (vector regressor and regressand), the four major tests for the general hypothesis (Wilk's Lambda, Pillai-Bartlett, Hotelling-Lawley, and Roy's ...
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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 ...
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313 views

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 ...
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2k views

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 ...