Sphericity tests on 2 within factors

[Robert Day]

Hi Mike,

I am enjoying being able to run repeated measures easily, thanks to you.

I am using the updated version on devtools.

But could you explain this aspect of the output?  Maybe I am missing something about the nature of repeated measures analysis.

When I put in two within factors, I get sphericity tests only on one of these, plus the interactions.

The data frame is like this below - there are night and day periods in a series of days

d> str(df.HeatRythme)

'data.frame': 80 obs. of  15 variables:

 $ traitement : Factor w/ 2 levels "CONT","HEAT": 1 1 1 1 1 1 1 1 1 1 ...

 $ tank       : Factor w/ 8 levels "1a","1b","2a",..: 1 1 1 1 1 1 1 1 1 1 ...

 $ repet      : Factor w/ 4 levels "1","2","3","4": 1 1 1 1 1 1 1 1 1 1 ...

 $ day        : Factor w/ 5 levels "1","2","3","5",..: 1 1 2 2 3 3 4 4 5 5 ...

 $ period     : Factor w/ 2 levels "J","N": 2 1 2 1 2 1 2 1 2 1 ...

 $ totpourc   : num  30.7 30 29.4 25.5 26.3 ...

 $...

The ez command: 

d> anovaHeat = ezANOVA(df.HeatRythme, totvar_adj, tank, within = .(day,period), within_full = NULL, within_covariates = NULL, between = traitement, between_covariates = NULL, observed = NULL, diff = NULL, reverse_diff = FALSE, type = 2, white.adjust = FALSE, detailed = TRUE, return_aov = TRUE)

gives me the output for the sphericity tests as follows:  - Why is there no test for 'period'?

$`Mauchly's Test for Sphericity`

                 Effect          W         p p<.05

3                   day 0.13665359 0.4908445      

4        traitement:day 0.13665359 0.4908445      

7            day:period 0.07568441 0.2829046      

8 traitement:day:period 0.07568441 0.2829046

 

Thanks for your help. Rob.

[Mike Lawrence]

Sphericity is an assumption that applies to variables with more than 2 levels, so you get out put for day since it has 5 levels, but not period, which only has 2 levels.

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[Robert Day]

Thanks Mike.

I did wonder what a variance covariance matrix would look like for this situation.

Rob

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