Two-sample Hotelling test
Theorem taught in Estimation and inference for the multivariate normal, part of Statistical learning
Two-sample Hotelling test
| Type | Theorem |
| Taught in | Estimation and inference for the multivariate normal |
| Part | Statistical learning |
Under the common-covariance normal model above, reject H_0:\boldsymbol{\mu}_1=\boldsymbol{\mu}_2 at level \alpha when
\frac{n_1+n_2-p-1}{(n_1+n_2-2)\,p}\,T^2 >F_{\alpha;\,p,\,n_1+n_2-p-1}.
The second degree of freedom is n_1+n_2-p-1. It is the Wishart degrees of freedom n_1+n_2-2, reduced by the dimension in the same way that n-1 became n-p in the one-sample F.
Used in
- Taught in Estimation and inference for the multivariate normal, where the derivation and examples are.
- All 9 questions on Estimation and inference for the multivariate normal
See also
Two-sample t test · Two-sample Hotelling T² test · Degrees of freedom · Wishart distribution · Invariance of the maximum likelihood estimator · Sampling law of the normal mean and scatter · Multivariate central limit theorem · The limit of Hotelling’s statistic