Talk:Mauchly's sphericity test

Namesake?
Who or what is this test named after? Robert K S 21:02, 11 October 2007 (UTC)
 * As I suspected, it's after John Mauchly. I'll add this information to the entry. Robert K S 22:05, 11 October 2007 (UTC)



SPSS
I see no reason to mention SPSS at all on this page - not to mention three. I do, however, see reasons not to, at least in the present manner. So, I will remove it unless anyone gives me a good reason not to. GeneralPortion (talk) 23:19, 5 May 2008 (UTC)

Interpreting the Mauchly test
I don't think that the assertion "When the significance level of the Mauchly’s test is < 0.05 then sphericity cannot be assumed", can be justified. There is nothing magical about a value of 0.05 as the criterion value and a researcher could quite reasonably not reject the assumption of sphericity even if p<0.05 or, indeed, were it less than any arbitrary value. Similarly, in some circumstances one might reject the assumption of sphericity if p<0.25, or perhaps 0.2384. Whether, and when, to reject the assumption of sphericity will depend on the the alpha level that the researcher determines for their particular application of Mauchly's test, taking account of what the costs of making a Type I or Type II error (with regard to the Mauchly test) are. — Preceding unsigned comment added by 210.10.243.86 (talk • contribs) 2009-09-26T09:14:42

There should be a change in the recommendation of the Greenhouse-Geisser. Stevens (1999) recommends the Huynh-Feldt correction because simulations have shown the HF adjustment to have a tangible decrease in bias when compared to the GG correction. — Preceding unsigned comment added by 108.202.32.176 (talk) 19:12, 19 October 2011 (UTC)

H1 doesn't seem exactly correct. It isn't that none of them are equal, only that at least one pair (or subset) of differences does not have equal variance. — Preceding unsigned comment added by 130.113.219.88 (talk) 22:06, 20 March 2014 (UTC)

Stevens (1999) might suggest the HF, Kieffer (2002) suggest to use GG. Kieffer, K. M. (2002). On analyzing repeated measures designs with both univariate and multivariate methods: A primer with examples. Multiple Linear Regression Viewpoints, 28(1), 1–17.

Stevens, J. P. (1999) Intermediate statistics: A modern approach (2nd ed.). Mahwah, NJ: Lawrence Erlbaum Associates. — Preceding unsigned comment added by Stikpet (talk • contribs) 09:24, 30 June 2019 (UTC)

Formula for sphericity
In the formula for sphericity graphic - is that really the correct alternative hypothesis? It seems to me that the correct alternative would be something more like "at least one of the equalities in the null doesn't hold" or something equivalent to it... Dasonk (talk) 03:04, 27 March 2013 (UTC)

That seems accurate to me, it doesn't have to be all of them, just one at least. — Preceding unsigned comment added by 169.234.77.211 (talk) 23:51, 2 November 2015 (UTC)

... Exactly. But the graphic implies that all of the comparisons need to be "not equal" https://wikimedia.org/api/rest_v1/media/math/render/svg/f27c6614b359fcab763077462bcb5799c8db5017 That's what I take issue with. --Dasonk (talk) 21:20, 6 December 2017 (UTC)

Alternative Hypothesis Incorrect
Shouldn't the alternative hypothesis for this test be that at least one of the variances doesn't equal at least one of the others (i.e., that not all of them are equal)? As currently written, it states that each sequential pair must be unequal. In other words, instead of "A<>B<>C," it should be of the form, "A,B,C not all equal to each other." As currently written, the null hypothesis and alternative hypothesis are not completely exhaustive conditions, which is also a violation. For example, assuming 3 terms, suppose that the variances between A and C are significantly different, but neither of them are significantly different than B. As currently written, both the null and alternative hypotheses would be rejected. I propose updating the alternative hypothesis to capture the weaker condition that only one of the terms must not equal at least one of the others. 70.174.128.14 (talk) 18:13, 11 April 2015 (UTC)

Worked example of Mauchly's sphericity test required
This article would be improved if Mauchly's sphericity test could be conducted for the example data. Robert P. O&#39;Shea (talk)

Reason for name "sphericity"?
Why is the property called "sphericity"? Does it have to do with the variances being considered all being equal? Jimw338 (talk) 23:26, 31 December 2018 (UTC)