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?

Answer 2

[Divyam]

Hi @deejt,

To perform the right epsilon adjustment first check the corresponding p-values for the epsilon correction adjustments with respect to each term of your ANOVA analysis. You will find the respective p-values for the Greenhouse-Geisser, Huynh-Feldt and Lower-Bound adjustments in the columns "pValueGG", "pValueHF", and "pValueLB" respectively.

To correct the results, find the adjustment for which the null hypothesis is rejected and then perform the epsilon correction of the term by multiplying its degree of freedom by the corrected value of epsilon. Then, find the correct p-value for the F-distribution.

Here is an example,

Suppose for the term "Variable1"

To perform epsilon correction on "Variable1", you have to perform the following correction in the DOF, .

To find the new p-values, you can use an F-distribution calculator and find the correct p-values by providing & DOF as inputs.