Thanks to some help from my friend (and Google), I was able to find the answer to this question. Basically, it's because there are only 2 levels of repeated measures. As such, there is only one set of difference scores and nothing to compare those difference scores against to indicate a violation of sphericity. I'm glad it was an easy answer.

In general, don't use repeated measures ANOVA. There are better ways nowadays of analysing repeated data by using robust variance adjustment to account for clustering. It's most unlikely in real life that your data will pass a test for sphericity, and with small N the test has little power.

With 2 levels of repeated measures, there is no need to conduct the Mauchly's test of sphericity . the assumption of Mauchly's sphericity will be met under this situation!@

Thank you for the responses. Dr. Conroy, for future reference, what techniques do you recommend for repeated measures? Do you have any recommended texts so that I could learn more about them? Thank you for your time!

If you use Stata, you can simply adjust for clustering by participant, and this additionally allows you to use participants with incomplete data, in contrast to repeated measures where only participants with complete data are used. What package are you using?

I currently have access to SPSS, SAS, and R. I have heard of Stata, but I have never used it. Is that your preferred software package?

Stata has a very powerful implementation of robust variance estimation that applies to virtually every model you can run. It's also one of the packages of choice in my area, health research. A recent paper on statistical software used on published papers in healh research gave SAS and Stata 47% each in terms of frequency of citation, with SPSS way down at just 4%.

See http://www.biomedcentral.com/content/pdf/1472-6963-11-252.pdf

Thank you for the information and your time; I appreciate it! I'll definitely look into Stata.

Hi Thomas and Others,

I have had the same problem with Sphericity values coming out p=  .  in a 2x2 design ANOVA.

You said that its because there were only 2 levels of repeated measures in your analysis - this is also true of mine.  My queries are thus:

a)I am still a little unclear of why that makes a difference - shouldn't it be comparing the variances across those 2 (within)sets of scores anyway - why does it need a third?

And b) do you therefore use the Assumed sphericity or the Greenhau-Geisser p-value?

Many Thanks in advance

Hi Rachael,

I'm not sure if you were able to find the answer to your question (and sorry I haven't responded until now; I have been so swamped and haven't been on this site in a while!), but I think of it spatially when looking at sphericity.  At the end of the day, I think that the reason why sphericity isn't what you look at when there are two measurements is because all you have to do is look at general homogeneity of variance.  The sphericity part is when you have more than 2 measurements that need to be taken into account when looking at multiple (more than 2) difference scores.  So, just look at your normal assessments of homogeneity of variance tests (e.g., Levene's test and looking for outliers).  I hope this helps!  Please let me know if it doesn't :)

Thanks!

 Hi Thomas,

I don't know whether it is too late to involve this question. I faced the same problem, and I tried some simple tests to figure out the problem. In fact, the test results shows that this problem is not caused by the number of the repeat measures. For example, in my case I have 16 repeat measures, but also has the same problem. It seem like that  this problem is caused by the rank of the repeat measures. I did a simple test to verify this point. First I downloaded a example of SPSS which include 3 repeat measures, and everything is going well when I did the repeat measure ANOVA following by the procedure shown in the tutorial. However, if I add some new repeat measures simply by copying the the existing repeat measures (i.e. I copied the columns and pasted them in the table), the Mauchly's test would give nothing just as your case. But when I modified the data slightly to make them be a little different, the Mauchly's test can give something out. Anyway, I don't know the essential reason of the problem, I hope someone can give the mathematical explanation. Thanks!    

NO MAUCHLEY TEST RESULTS WHEN REPEATED MEASUREMENT > 2.

Hello All,

I have a sample size of 12 and a repeated measures of 20. My Mauchley test's value results are as 'p=.' (just a dot) and chi square values = '.' (just a dot; no number is displayed).

I observed that:

(1) If my repeated measurement is greater than sample size (eg. Repeated measurement = 15 and sample size  = 9), the Mauchley's test fails to give a value for chi-squared and p-value, and displays only a '".". However, I could see a value for Greenhouse-Geisser and Huynh-Feldt.

(2) if I include only 5 repeated measurement in my analysis (i.e repeated measurements < sample size),  Mauchley;s test gives a value for both chi square and p-value.

I have attached the mauchley test results for the first case.

In this case, should I assume that the sphericity has been violated and go for a correction?

Thanks

Hello everybody,

I am having exactly the same problem. I have a 2x2x2 mixed design in which the first two factors are measured involving the same participants, meaning that there are 4 situations included in the repeated measures (within subjects) and other two levels of the last factor across groups (between subjects).

So when I try to use repeated measures ANOVA, and I run the two factors separately (but obviously I get 4 different situations), nothing happens and the test of sphericity gives me no value for significance. 

Interestingly, when I run the test with 4 different situations and all the situations are included in the same factor, it gives me some output for the test. The data is the same but I only get output for the test if I run the 4  situations in the same factor instead of using different factors.

Anybody an idea?

Now that I've been investigating a bit on what does my data tell me, I found out something interesting...

I read that if you have one variable with only 2 conditions, does not matter if you have two variables, so 2x2 design, as long as you  have only 2 conditions for every variable. That is because the df of every variable would be 1 and we can assume sphericity on that. Some people may not agree on that, but that is what I came up with by reading.

Hi all,

Yes, I think that what you're saying is right Arnau (and others). I think the key is that assessing sphericity has to do with determining if the "variances of the DIFFERENCES between conditions are equal." So, if you only have 2 repeated measures (e.g., Time 1 vs. Time 2), you only have 1 difference score. So, you can't compare the variance of multiple difference scores in this case because there is only 1 difference score. There's nothing to compare it to :). So, you would need to worry about sphericity if you have more than 2 repeated measures. In Field they give an example of this: 3 measures (A, B, and C) in which to compare variances. You compare A vs. B (get variance 1), A vs. C (get variance 2), and B vs. C (get variance 3). Sphericity (based on my understanding) would be seeing if those variances (1, 2, and 3) aren't significant different.

Does that make sense? Maybe I'm missing something, but that seems to make sense to me :)

For your situations, Zuheng Ming and Tom Shuttleworth, assuming that everything is set up correctly in columns and rows as repeated measures (which I'm sure it is), then it could be this other point that Field brings up. If you have local circularity (which means that two [or more?] of the variances of differences are identical, which seems like your case Zuheng), then "the sphericity assumption has been met for any multiple comparisons involving these conditions" (Field, 2009, p. 460). Field then references an article on local circularity (Rouanet & Lepine, 1970).  So maybe this explains why there was no Mauchly's test when you used similar data but it would appear with slight changes? I'm just guessing, but this makes sense in my head :)

And I'm really sorry for the super late replies. I have been swamped with internship and working on my dissertation! :)

 Hi Thomas, 

I have the same issue....no p value results for Mauchly's....so my question is what did you focus on in your test of within-subject effects (greenhouse, huynh-fedlt, etc)? 

 Hi Thomas, 

I have the same issue....no p value results for Mauchly's....so my question is what did you focus on in your test of within-subject effects (greenhouse, huynh-fedlt, etc)? 

 Hi Thomas, 

I have the same issue....no p value results for Mauchly's....so my question is what did you focus on in your test of within-subject effects (greenhouse, huynh-fedlt, etc)? 

Hi LeNessa,

Was your situation the same (2 repeated measures)? If so, then you don't need to worry about sphericity but instead just look at normal homogeneity of variance statistics (and normality etc while you're at it). If those are violated, then it'll all depend on things like sample size and the degree of violation.

Also, I took a look at my output from various studies with 2 repeated measures, and all of my Greenhouse-Geisser, Huynh-Feldt, sphericity assumed, and Lower-bound results are the same. I'm assuming this is somehow related; maybe because adjustments are made only if there are multiple repeated measures? If you don't have Field's (2009) book, then I recommend getting it because he gives a lot of great justification for why to use one of these over another in the chapter on repeated measures. It's also really funny, helpful, and engaging :). When making the decision (which you would only do if sphericity is violated), I remember you have to look at which statistic is closest to 1 and go with that (e.g., if Greenhouse-Geisser correction epsilon is closer to 1 than the lower limit of epsilon, then that is the preferred statistic per Field).

Hope this helps! Take care!

Tom

Hi, you don't have Mauchly test stasts because you have only 2 within-subject repeated measures. Isn't it?

Yup!

Just had the same problem, and this was really helpful! Just curious whether having uneven sample sizes between groups will affect this much you think? And are there any solutions around that? My study has one between- and two within-subject factors

Jenkin, How much unequal is your sample sizes? Generaly, ANOVA is qiute resilent to sample sizes disturbances.

My sample size for the primary two groups I want to compare would be about 30 in one group to 10 in the other group approximately. If I were to include two additional levels for the Between-subject Group comparison (So 4 groups instead of the two I just mentioned all with unqueal sample sizes), would you suppose that makes it problematic as well? Thank you for your help!

The rule I learned to maximize robustness of ANOVA to violations of assumptions (and improve interpretability is to ensure your largest group is no more than 1.5 times the size of your smallest group. Perhaps randomly remove some folks from the larger group? Or, equalize them on some important factor that is unrelated to your research question (e.g., SES or IQ)?

Good point, Thomas! Thanks for sharing that! We may need to test more individuals in the larger group to match them more closely with the smaller group anyway. This might be a good time to reinforce the 1.5x rule!

NO MAUCHLEY'S TEST RESULTS DISPLAYED FOR REPEATED MEASUREMENT > 2.

Hello All,

I have a sample size of 19 and a repeated measures of 22. My Mauchley test's value results are as 'p=.' (just a dot) and chi square values = '.' (just a dot; no number is displayed).

In SPSS,  I observed that:

(1) If my repeated measurement is greater than sample size (eg. Repeated measurement = 22 and sample size  = 19), the Mauchley's test fails to give a value for chi-squared and p-value, and displays only a '".". However, I could see a value for Greenhouse-Geisser and Huynh-Feldt.

(2) if I include only 5 repeated measurement in my analysis for sample size = 19 (i.e repeated measurements < sample size),  Mauchley;s test gives a value for both chi square and p-value.

I have attached the mauchley test results for the first case.

In my first case, should I assume that the sphericity has been violated and go for a correction?

Thanks

I have 18 subjects. And I am getting dots even at Greenhouse-Geisser and Huynh-Feldt levels. What do I do. 

Hello, I have the same issue, there no result for Mauchly's test of sphericity. Can I ignore this issue, and use the corrected result of Greenhouse-Geisser?

Thanks for this thread :)

Thank you so much for these information Mr Daniel,

Daniel Pientka

so please how do we test for sphericity if its a 2x2 design? or don't we need to?

Thanks for the thread! It helped me in 2021 :-)

So I have one final questions about this topic: How do we report this (APA-format)? Facing the same issue in 2021 and almost going insane :-)