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 the Hotelling T2 test and I would like to use the Hotelling package available in R. However, in the documentation of the hotelling.test function in R, I do not see any assumption on the covariance matrices of the two samples. It is implicitly assumed that the two samples must have equal covariance matrices or does that mean that I can use this test even if the two samples do not have equal covariance matrices?

  • $\begingroup$ Almost any two samples will have different covariance matrices. There is no reason to be concerned about that, because sample covariances are subject to random variation. One thing to ask about is whether the null hypothesis assumes that the two populations have the same covariance matrix. If this is not obvious, then please consult any reference. The one interesting question remaining concerns the power of the test under alternatives with two different covariance matrices. Is this what you mean by "use this test"? $\endgroup$ – whuber Dec 17 '14 at 16:15

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