SPSSX Discussion - Re: Undefined Mauchly's Test

Re: Undefined Mauchly's Test

Posted by Rudobeck, Emil (LLU) on Oct 07, 2016; 5:27pm
URL: http://spssx-discussion.165.s1.nabble.com/Undefined-Mauchly-s-Test-tp5733212p5733219.html

When it comes to reporting the findings, despite the shortcomings, Mauchly's test is widely used and understood. I haven't come across running t-tests on variances. Where can I read more about that approach?

The measurement is time - brain responses are sampled from each subject for a period of time (e.g., 72 samples during an hour) after a "learning" stimulus is applied. So change over time is expected biologically. This is essentially a nonlinear growth curve and I know that there are more advanced approaches (LMM, SEM, etc) which I use as well, but my concern here is with sphericity in GLM. Transformation is not going to address the issue, nor will larger N be feasible. It is possible to perhaps average adjacent time points, but this would introduce its own problems. This is a mixed design since subjects are grouped into different treatments and it's the differences in treatment that's important.

Your question is more about design than stats. Certainly, if you have any suggestions, I would be interested. The current method is well established and has been used for decades. Whether the individual repeated measures are different or not does not matter too much in this case. It's more important whether the curves themselves between treatment groups are different (the between factor). Using repeated measures overcomes the issue of correlations, since there is no other way around it.

From: Rich Ulrich [[hidden email]]
Sent: Thursday, October 06, 2016 8:06 PM
To: [hidden email]; Rudobeck, Emil (LLU)
Subject: Re: Undefined Mauchly's Test

For small and moderate samples, a non-significant Mauchly's test does not mean much at all. That is

why many people will recommend, wisely, that followup test be performed as paired t-tests instead of

using some pooled variance term.

What are you measuring? Is it a good measure, with good scaling expected and no outliers observed?

I don't like analyses where those corrections are made, unless I have a decent understanding of why

they are required, such as, the presence of excess zeroes.

Would some transformation be thought of, by anyone? Analyzing with unnecessarily-unequal variances

is a way to get into unneeded trouble. If the "levels" represent time, it might be appropriate and proper

to test a much more powerful hypothesis that makes use of contrasts (linear for growth, etc.) in order to

overcome the inevitable decline in correlations across time.

You say: more levels than subjects -- Is this because you have very small N or because you have moderate N

but also have too many levels to test a sensible hypothesis across them all?

State your hypotheses. What tests them? A single-d.f. test is what gives best power, whenever one of those

can be used. I favor constructing contrasts -- sometimes in the form of separate variables -- over tests that

include multiple d.f. and multiple hypotheses, all at once. And I would rather remove the causes of

heterogeneity (variances or correlations) beforehand, than have to hope that I have suitably corrected for it.

--
Rich Ulrich

From: SPSSX(r) Discussion <[hidden email]> on behalf of Rudobeck, Emil (LLU) <[hidden email]>
Sent: Thursday, October 6, 2016 2:20 PM
To: [hidden email]
Subject: Undefined Mauchly's Test

Given the paucity of information online, I was wondering if anyone knows the procedural approach to the evaluation of sphericity when Mauchly's test is undefined, which is the case when the number of repeated levels is larger than the number of subjects (insufficient df). I am not sure if sphericity can still be assumed based on the reported values of epsilon larger than 0.75, whether based on Greenhouse-Geisser or Huynh-Feldt. In one particular dataset, epsilon is less than 0.1. Presumably it can be assumed that sphericity is violated when epsilon is that low.

I am aware of using mixed models to overcome the assumptions of sphericity. My concern is with GLM in this case.

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