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May 4, 2018 1:48 PM
(3989 views)

I have two questions on running a sphericity test for a repeated measures ANOVA if people are willing to hear me out?

Here's a description of my experiment and data: my experiment involved testing different filter media to remove phosphorus from water. I have a total of 12 boxes (my "subjects") that represent 4 filter media in triplicate. In my JMP data table, each row represents a box, and for my columns, I have an "ID" column (basically 1-12 for my filter boxes), one column that's the filter media called "Treatment" (labeled "BF", "NF", "NS", and "WS" and repeated 3 times for each replicate), and subsequent columns are phosphorus concentrations for each time point (total of 11 time points, unevenly spaced). I've also included my data file with this post.

So, my questions:

1.) I performed a mixed model test as a repeated measures ANOVA on my data, but a JMP article says I have to test for sphericity to see if I need to adjust my F value in case I violate the sphericity test. To test for sphericity, I have to perform the multivariate test. However, I have missing data for certain time points, and JMP throws out the entire subject if any data are missing with the multivariate approach, which is why I went with the mixed model approach (I only have 12 subjects). How can I perform a sphericity test then, which seems to require the multivariate approach?

2.) I'm also trying to perform a repeated measures ANOVA using the multivariate approach on a subset of my data just to at least that subset for sphericity. I tried to run a MANOVA model with my data, but the sphericity test did not show up in my results. If I cut down on the number of time points that I have (I have 11 time points), which are my "y" values, the sphericity test does show up, but, depending on how many time points I include, the Mauchly criterion is either significant or not significant. I'm not very familiar with statistics in general, so I was wondering if anyone knows what's going on?

Does anyone have any idea why the sphericity test is behaving as I described? Are there other options for testing for sphericity that don't require a multivariate approach?

Thanks so much for any input! I'm not strong in stats at all, so any help would be appreciated!

Stephanie

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Stephanie,

I saw zeros in your data, but no missing values. The error I received was "insufficient error degrees of freedom." With 2 df for each treatment group that gives you 8 df for each time period (repeat). So I expected only 4 time periods would be allowed for the test. To be fair or to show what is seen in the data, use 4, 12, 72 and 120 it will show the sphericity issue.

Actually, your dataset is quite interesting. I don't think you need a statistical test to note an important difference in the materials' results. The data exhibits a growth pattern.

Using the wide data set you had attached, create the covariance matrix using the Multivariate analysis, and select Covariance. You will see that the covariance structure (and correlation) are quite different for early periods vs. later periods where the measured values are not changing very much. Again you should look at the data and covariance you can see that sphericity rule is violated without a test. In my opinion, a p-value has no value here.

So the next step is to chose a different test. You should at least model a time series component for your repeated measures. (See suggestion below.)

If you want to quantify the difference, I suggest you model the growth for each treatment group. The pictures above display the measured values, the results of Fit Curves using a Weibull Growth curve and the perforfmance. Note the Weibull Growth model is not in JMP13, but is available in JMP14. The predicted values were saved to the data table and plotted vs. actual with the line y=x. The scripts for both are saved to the stacked version of your table (attached). The Fit Curves script might not work, depending upon your version of JMP.

You should investigate the instability of the BF treatment. Is there something in the material, the environment like the location of the box or temperature that might be affecting the precision of your readings for the phosphorous concentrations.

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Stephanie,

I saw zeros in your data, but no missing values. The error I received was "insufficient error degrees of freedom." With 2 df for each treatment group that gives you 8 df for each time period (repeat). So I expected only 4 time periods would be allowed for the test. To be fair or to show what is seen in the data, use 4, 12, 72 and 120 it will show the sphericity issue.

Actually, your dataset is quite interesting. I don't think you need a statistical test to note an important difference in the materials' results. The data exhibits a growth pattern.

Using the wide data set you had attached, create the covariance matrix using the Multivariate analysis, and select Covariance. You will see that the covariance structure (and correlation) are quite different for early periods vs. later periods where the measured values are not changing very much. Again you should look at the data and covariance you can see that sphericity rule is violated without a test. In my opinion, a p-value has no value here.

So the next step is to chose a different test. You should at least model a time series component for your repeated measures. (See suggestion below.)

If you want to quantify the difference, I suggest you model the growth for each treatment group. The pictures above display the measured values, the results of Fit Curves using a Weibull Growth curve and the perforfmance. Note the Weibull Growth model is not in JMP13, but is available in JMP14. The predicted values were saved to the data table and plotted vs. actual with the line y=x. The scripts for both are saved to the stacked version of your table (attached). The Fit Curves script might not work, depending upon your version of JMP.

You should investigate the instability of the BF treatment. Is there something in the material, the environment like the location of the box or temperature that might be affecting the precision of your readings for the phosphorous concentrations.

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Re: Sphericity test not showing in model results

Thanks so much for your detailed reply! I really appreciate your taking the time to explain the concepts and providing actual examples based off of my data!

Stephanie

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I am having a similar problem with the sphericity test not showing in JMP. I have a feeling that it is because my data does not say very much, or because of issues with my sample sizes but I am unfortunately too green to know for sure. Can I check the partial correlation box to see that the assumption of sphericity is violated anyway (without the test)? I've attached my dataset. Will be greatful for any and all help.

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