Mauchly's Test of Sphericity - how to handle data when data fails test?

Hello,

I would like to do a repeated measures anova but my data does not pass the test of sphericity. I have very low p-values, one example shown below.

1×4 table

       W        ChiStat    DF      pValue  
    ________    _______    __    __________

    0.012023    88.971     35    1.3687e-06

Now, I read that I can correct this with Epsilon, also conducted that. I know that it is not recommended to use the Lower Bound estimate, but Greenhouse Geisser or Huynh Feldt.

But how exactly am I going to use the result from the epsilon correction on my repeated measures data? Do I choose either GG or HF and report the corrected p-value from the rm anova table? Or do I have to write some code to change the rm anova table?

1×4 table

Uncorrected GreenhouseGeisser HuynhFeldt LowerBound

___________ _________________ __________ __________

1 0.45526 0.55152 0.125

I am already thankful for your help!

regards

[Scott MacKenzie]

It would help if you posted your data and any script you've used so far.

[deejt]

Hey Scott,

I dont have an own dataset yet, as I am just preparing and practicing right now. I have used this example dataset (fishiris) of matlab doc itself. https://www.mathworks.com/help/stats/repeatedmeasuresmodel.mauchly.html

I get how to perform the Mauchlys Test and I know how to perform the Epsilon test for correction, but once I have this 1x4 outcome table of epsilon, what do I do with it and my data? Thats what I have been wondering.

The doc of Matlab of this specific example says: "The small p-value (in the pValue field) indicates that the sphericity, hence the compound symmetry assumption, does not hold. You should use epsilon corrections to compute the p-values for a repeated measures anova. You can compute the epsilon corrections using the epsilon method and perform the repeated measures anova with the corrected p-values using the ranova method."

But after I calculated Epsilon, I get a 1x4 table, what do I do with it next and how do I report my p-values then?

Answer 1

[deejt]

I just found this explanation:

"To correct for this inflation, multiply the Greenhouse–Geisser estimate of epsilon to the degrees of freedom used to calculate the F critical value."

Does this mean, I have to take the GG epsilon value and multiply it with the DF in my original repeated measures anova table and correct the F value?