# 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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### Hotelling's $T^2$ test VS dendrogram

When i perform a Hotelling's $T^2$ test on a dataset, it stated that there is strong evidence that the mean vectors of the two groups differ. However, when I create a dendrogram, I got: where number ...
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### Hotelling's T for Matrix Normal Distribution

Suppose you observe matrix normal $\mathbf{X}_i \sim \mathcal{MN}_{m,p}\left(\mathbf{M},\mathbf{U},\mathbf{V}\right)$, for $i=1,2,\ldots,n$. That is $\mathbf{X}_i$ is an $m\times p$ matrix which is ...
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### 95% confidence ellipse using Hotelling T-squared in a score plot (R)

I am trying to draw a 95% confidence ellipse using Hotelling T-squared in a score plot of two principal components from a PCA. I have checked that: https://stackoverflow.com/questions/42637860/pca-...
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### Hotelling T-squared: Degrees of Fredom for confidence interval

I am trying to define a confidence interval for a multivariate data set (data[n_samples, n_comp]) to detect outliers with the mahalanobis distance. The distances of ...
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### What is “Discriminant hotelling”?

Recently I have encountered the term Discriminant hotelling. And I have no idea what this term means. All I know is that this is in context with multivariable data analysis. I tried googling but in ...
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### Alternative distribution of $T^2$ statistic without Gaussian assumption

Background Let $p(x)$ be an arbitrary distribution defined on $\mathbb{R}^d$. Define $\mu = \mathbb{E}[x]$. Given an i.i.d. sample $x_1, \ldots, x_n \sim p(x)$, consider the following $T^2$ statistic ...
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### Show that distribution of $\small(n-1)\overline{X}'(S^{-1}-\frac{S^{-1}\mu_0\mu_0'S^{-1}}{\mu_0'S^{-1}\mu_0})\overline{X}$ is $\small T^2(p-1,n-1)$

Show that the distribution of $(n-1)\overline{X}'\left(S^{-1}-\dfrac{S^{-1}\mu_0\mu_0'S^{-1}}{\mu_0'S^{-1}\mu_0}\right)\overline{X}$ is $T^2(p-1,n-1)$ where $X_i\sim N_p(\mu,\Sigma)$, where $\Sigma$ ...
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### distribution of $T^2$ statistic without Gaussian assumption

I would like to know if the Gaussian assumption is needed on $x_i$ in deriving the asymptotic distribution of the $T^2$ statistic. Here is the presentation sequence I got from the Wiki page on ...
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### Paired Hypothesis Test in TWO Linear Regressions

I am wondering how to perform a paired hypothesis test in a panel regression. I have been looking in many stats books but I have not found anything. The question goes: assume for $i=1,2,\cdots, N$ ...
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### Hotelling's one-sample T2 statistic

I wanted to determine if a new sample is within reasonable bounds of the mean of an approximately normally distributed sample of points. I want to use Hotelling's $T^2$ statistic to obtain a $p$-...
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### Which is right? Individual variable t test or multivariate Hotelling t test?

So, lets say a hypothetical example. You have data of women aged 25-50 on their nutrition activity and measured for 737 such women(n,sample size) on 5 variables(Calcium, Protein, Vitamin A, Vitamin ...
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### Using the Hotelling package in R

I have two samples of data in $\mathbb{R}^2$, assumed drawn from a gaussian distribution, and I would like to test whether the two samples have the same mean. I know that the right test to do this is ...
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### Violation of the assumption of equal covariance matrices for two-sample Hotelling's test

I would like to compare nutrient intake of men and women. But the assumption of the same variance-covariance matrix is violated and therefore two-sample Hotelling's $T^2$ test cannot be applied. How ...
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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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### 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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### 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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### 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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