On 27 May 2004 08:56:55 -0700, [EMAIL PROTECTED] (Richard Hindmarsh) wrote:
> I have a physically-based model which turns some data into esimates of > of a set of parameters, together with their non-diagonal covariance > matrix. I now want to test whether these parameters are different from > say zero. By analogy with linear regression, where I can test whether > the slope or intercept are different from zero using the t-test, I > have looked for a multi-variate t-test, and come across the Hotelling > T^2 test. > > Q. Am I right to think that the Hotelling Test is a fairly general > recipe for my problem, given that I have a non-diagonal covariance > matrix? Yes, the Hotelling's T-squared for one sample sounds right. > > Q. Presumably there is more devil in the detail regarding the precise > formulation of the hypothesis; for example, if I have three > parameters, do I have to formulate a hypothesis for all three e.g. > they are all different from zero, or can I do it for just one? It would be a big waste of power and test the wrong hypothesis. If it failed to reject, you would know that a weak test did not reject the null. If it rejected, you would not know how much your given hypothesis was responsible. > > Q. Is there a decent reference to describe the above? Mathematical is > fine. What I have mentioned is only basic inference. You should read some more and run some examples. Googling on < test "hotelling's T" one-sample tutorial > gives a 82 hits, and the initial ones look interesting. > > Q. Are there any alternatives to the Hotelling procedure? > That is the one-sample test that I know of, which includes "any combination of the variables." You could use Bonferroni correction to test three univariate hypotheses. You could use repeated measures and look at the test for the constant, if your variables are all scaled the same and will differ in the same direction. If your hypothesis is about one variable in three, there's a different test. One-sample t-test? -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html . . ================================================================ This list will soon be replaced by the new list EDSTAT-L at Penn State. Please subscribe to the new list using the web interface at http://lists.psu.edu/archives/edstat-l.html. ================================================================
