[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]

From |
Joseph Coveney <[email protected]> |

To |
Statalist <[email protected]> |

Subject |
Re: st: tests of sphericity |

Date |
Thu, 02 Oct 2003 19:13:38 +0900 |

David Airey wrote in response to a posting by Ricardo Ovaldia: ---------------------------------------------------------------------------- [excerpted] > My understanding is that the epsilon corrects for the > sphericity in the data but is not necessary to use it > if the data meets the sphericity assumption (i.e. > passes Mauchly's test). In which case we can use the > uncorrected F test. I do not like adjusting the df > unless it is necessary. > > Thank you, > Ricardo. I think you are right and that nobody has written a program for Mauchley's test of sphericity. The test is available in other statistical packages. In searching a little I did not find a readable account on what Mauchly's test actually does or how I might program it myself. Do you know the original reference? [excerpted] ---------------------------------------------------------------------------- The original reference is J. W. Mauchley, Significance test of sphericity of a normal n-variate distribution. Annals of Mathematical Statistics 11:204-9, 1940. The formula for Mauchly's chi-square test statistic and an ad hoc SAS IML macro for a particular dataset are provided in N. H. Timm and T. A. Mieczkowski, _Univariate & Multivariate General Linear Models: Theory and Applications using SAS Software_ (Cary, North Carolina: SAS Institute, 1997), pp. 110-15. This source gives a "locally best invariant" test for sphericity that is supposed to be more powerful than Mauchly's for small samples. It also describes a test for the multisample circularity assumption. All of the tests use matrix manipulations, but nothing more involved than what Stata can do readily (determinants, traces, transposes, multiplications). Nearly everything that I've ever read about the matter, however, advises against Mauchly's test as a precondition. I have a follow-up question in this vein: if the assumptions for a statistical test are plausable (are reasonably expected to be satisfied on the basis of prior knowledge or on the basis of information independent of the data under evaluation), especially for assumptions that a test is sensitive to, does the test statistic that results from a statistical test that is performed in one way conditional upon passing such a pretest (and performed in another way conditional upon failing) follow the distribution of the test statistic that is found in the back of the textbooks? In other words, given that I don't have any particular reason to suspect that the assumption of circularity would be violated for a dataset, if I commit to use epsilon-based degree-of-freedom adjustments if the p-value associated with Mauchly's chi-square is 0.05 (or some other threshold) or less, and commit not to use such adjustments if the Mauchly test gives a p-value greater than 0.05, then will the subsequent repeated-measures ANOVA's resulting F-statistic follow an F distribution? It doesn't have to be Mauchly/ANOVA; it could be Levene (Bartlett, Brown-Forsythe)/Student t test with / without Welch (Satterthwaite) adjustment, and so on for other analogous pretest/test pairs where there is a test statistic that is in some sense conditional on the outcome of a pretest on the same data. Joseph Coveney * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

- Prev by Date:
**st: RE: RE: RE: ci, return lists, and statsby commands** - Next by Date:
**RE: st: tests of sphericity** - Previous by thread:
**RE: st: tests of sphericity** - Next by thread:
**re: st: tests of sphericity** - Index(es):

© Copyright 1996–2024 StataCorp LLC | Terms of use | Privacy | Contact us | What's new | Site index |