GLM Repeated measures Mauchly's test undefined
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I'm doing a two-way mixed ANOVA in SPSS. I have two groups with 9 subjects each (so total = 18), and 24 levels of one measure.
I understand why Mauchly's test of Sphericity has no meaning when there are are only 2 levels of a repeated measures factor, but I notice (using GLM.....repeated measures in SPSS) that Mauchly's test of Sphericity also appears to be undefined (or gives the useless output of Mauchly's W = '.0' , p = '.') when the number of levels of a repeated measure is equal to or greater than the number of cases (subjects). In these instances, even though Mauchly's statistic is not calculated, Greenhouse-Geisser, Huynh-Feldt, and Lower-Bound Epsilon values are calculated. I would be really happy if someone could provide some insight on why Mauchly's statistic is not calculated in these cases and what should be done to assess sphericity in the absence of Mauchly's statistic. Thank you |
Re: GLM Repeated measures Mauchly's test undefined
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I'm pretty sure that Mauchly's is not calculated for the usual reason
that other stats get omitted in various analyses -- It can't be computed because you run out of degrees of freedom. Here's a comment from the Wikip article on Mauchly's test: While Mauchly’s test is one of the most commonly used to evaluate sphericity, the test fails to detect departures from sphericity in small samples and over-detects departures from sphericity in large samples. Consequently, the sample size has an influence on the interpretation of the results. I don't know how large the N has to be before you run into "over-detection". That is kind of a standard problem, at some level, for every sort of test that tries to "protect" another test. I do remember seeing gross distortion in my own data with what seemed like moderately big N, and I eventually found the advice (which seemed sound) that, in order to feel secure about tests, you like to see the Mauchley test at p> 0.5 rather than the conventional p>0.05 ... So, how different are your variances at different levels? How different are the correlations between (say) period 1 vs 2 and period 1 vs 24? - You do need to understand the nature of the problem, which is that the error term is not going to be very accurate if-and-when you pool "pieces" of error that are vastly different. Thus: Two adjacent "periods" may have very high correlation, and thus a very small standard error for their comparison, where two distant periods have smaller r and larger SE for a test. I can point out, with some relevance, that the appropriate post-hoc tests for repeated measures are often taken as the simple, paired t-tests between the elements that you want to test. Similarly, the safe way to test something like the linear trend (which is what I would test, for 24 periods,assuming they are periods) is for the program to compute the actual contrast, and also compute the actual, observed error of that contrast. (BMDP repeated measures has that option. I am not aware that SPSS does. I always retreated to BMDP for my RM testing.) Twenty-four levels? - You are looking at a *trememdous" lack of power for an overall comparison between 24 levels. When you compute particular contrasts and test them, you gain a lot of power. "Linear trend" is the simple, most obvious contrast, to someone who does not know your design. If you have an intervention along the way, you may want to design your contrasts and move to a regression program for testing them. That's enough to consider, for now. -- Rich Ulrich > Date: Tue, 26 Mar 2013 19:47:38 -0700 > From: [hidden email] > Subject: GLM Repeated measures Mauchly's test undefined > To: [hidden email] > > I'm doing a two-way mixed ANOVA in SPSS. I have two groups with 9 subjects > each (so total = 18), and 24 levels of one measure. > > I understand why Mauchly's test of Sphericity has no meaning when there are > are only 2 levels of a repeated measures factor, but I notice (using > GLM.....repeated measures in SPSS) that Mauchly's test of Sphericity also > appears to be undefined (or gives the useless output of Mauchly's W = '.0' , > p = '.') when the number of levels of a repeated measure is equal to or > greater than the number of cases (subjects). In these instances, even though > Mauchly's statistic is not calculated, Greenhouse-Geisser, Huynh-Feldt, and > Lower-Bound Epsilon values are calculated. > > I would be really happy if someone could provide some insight on why > Mauchly's statistic is not calculated in these cases and what should be done > to assess sphericity in the absence of Mauchly's statistic. > > Thank you > ... |
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In reply to this post by praznin
WHAT are you measuring 24 times. Please describe the time intervals between the measurements. I am assuming you are not comparing 24 commensurate scales, are you? If so, to what end? Whatever it is you are doing, we need more information to provide much of anything above and beyond what the other poster said. If you do not want to discuss the details, then you have received your answer. If want to discuss further, we must get more information. Also, would be nice to know the value of GG-epsilon.
Ryan On Tue, Mar 26, 2013 at 10:47 PM, praznin <[hidden email]> wrote: I'm doing a two-way mixed ANOVA in SPSS. I have two groups with 9 subjects |
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