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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Why does the Hotellings T-Squared Statistic scale by a factor of n?
According to the NIST: https://www.itl.nist.gov/div898/handbook/pmc/section5/pmc543.htm the equation for a T-Squared statistic has a scaling factor of n (Interestingly, the Wikipedia page for this ...
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Hotelling's $T^2$ chart for subgroups with unequal size
I have been reading about Hotelling's $T^2$ control charts and I'm unsure on how to deal with the case where the mean observations come from unequal-sized subgroups.
Consider $m$ observations $\mathbf{...
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Joint testing of proportions, analogous to the Hotelling $T^2$ test?
Hotelling's $T^2$ test examine if two multivariate Gaussian distributions with the same covariance matrix have the same mean vector. Assuming the two distributions to have the same covariance matrix ...
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Confidence regions for multivariate normal distributions
From this post, Confidence regions on bivariate normal distributions using $\hat{\Sigma}_{MLE}$ or $\mathbf{S}$, the equation
$(\mathbf{x} - \boldsymbol{\mu})^{T} \mathbf{\Sigma}^{-1} (\mathbf{x} - \...
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Testing that a multivariate mean approximately equals a vector of constants
Suppose we have a $p$-variate random vector that has a multivariate Normal distribution, $\boldsymbol{X}\sim MVN(\boldsymbol{\mu},\Sigma)$. My hypothesis is that the mean vector contains only zeros, $\...
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Should I favor the results of a Hotelling's $T^2$ or Bonferroni confidence interval?
I am trying to understand if my reasoning is correct about these two methods. Faced with a situation where it is impossible to get both methods to fail to reject the null hypothesis, which should I ...
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Hotelling t at 0.95 interval
Suppose I want to test the hypothesis that the lengths of head size for first borns and seconds borns are $x = (182, 182)$ by using the Hotelling-T test.
So given our data:
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Why "multivariate test takes advantage of the correlations between the marginal distributions?
It is claimed (in a comment here) that "The advantage of the multivariate test is that it takes advantage of the correlations between the marginal distributions". Why this is the case for ...
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Why Hotelling's $T^2$ is taught in the book but it is not used anywhere so far?
I have seen various multivariate statistics book covering Hotelling $T^2$ statistics. However, when reading medical journals and papers, it does not show up anywhere.
Q1:Is this test of any practical ...
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How to compare multiple Two-Sample Hotelling's T-squared tests performed on different sample sizes
It's my first question, so please be patient with me.
I'm working on the comparison of multiple datasets of different lengths (60 to ~10000). They share a set of 9 features which I would like to use ...
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Trying to understand how to calculate a hotelling's T2 Confidence Ellipse
I have read probably too many things and maybe confused myself along the way :)
Anyway, let's say I had a data set that I have performed PCA analysis on.
Let's say a spectral dataset 100 observations ...
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Moments of the Hotelling Lawley Trace under the alternative
The Hotelling Lawley trace is used in multivariate ANOVA, or for tests of the Multivariate General Linear Hypothesis (regression coefficient testing in many-to-many linear regression). For our ...
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In Hotelling's theory, why create a statistic and calculate the likelihood instead of using the maximum likelihood estimated normal distribution?
In Hotelling's theory, when data is assumed to be generated from a normal distribution, a statistic based on the Mahalanobis distance is calculated, and the degree of anomaly of the data is calculated ...
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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 [closed]
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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