RM ANOVA sphericity assumption

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CLeach
Posts: 3
Joined: Sun May 10, 2020 3:31 pm

RM ANOVA sphericity assumption

Post by CLeach »

I'm testing the sphericity assumption for a Repeated Measures ANOVA with time as the independent variable (baseline; 1 week; 10 weeks):

Baseline, Week 1 and Week 10 are entered as RM Factor 1 and transferred to Repeated Measures Cells. Sphericity tests ticked under Assumption Checks but it returns "The repeated measures has only two levels. The assumption of sphericity is always met when the repeated measures has only two levels."

Can anyone help? I would have thought that Baseline, Week 1 and Week 10 gives three levels? File is attached.

Thanks,
Cait
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CLeach
Posts: 3
Joined: Sun May 10, 2020 3:31 pm

Re: RM ANOVA sphericity assumption

Post by CLeach »

UPDATE:

Sample size is 15, but if it's increased to 16 (i.e. random numbers added across all three time points for the purposes of investigating), testing for sphericity seems to work fine..?

UPDATE #2:

So the SD for two of the three levels is exactly the same, is this why Jamovi is interpreting it as only two levels in total?
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jonathon
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Joined: Fri Jan 27, 2017 10:04 am

Re: RM ANOVA sphericity assumption

Post by jonathon »

hey cleach,

let me attend ravi to this. this is his area.

cheers

jonathon
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Ravi
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Joined: Sat Jan 28, 2017 11:18 am

Re: RM ANOVA sphericity assumption

Post by Ravi »

Just a quick update that I'm looking into it!
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Ravi
Posts: 194
Joined: Sat Jan 28, 2017 11:18 am

Re: RM ANOVA sphericity assumption

Post by Ravi »

So apparently there's some singularity issue, that's not being caught be the jamovi analysis. If you use the following R code (similar to what we use in the background):

Code: Select all

data <- data.frame(
    'id' = 1:15,
    'x1' = c(4, 13, 15, 12, 12, 2, 19, 10, 22, 13, 10, 22, 10, 14, 22),
    'x2' = c(55, 40, 26, 6, 20, 37, 37, 12, 45, 29, 28, 4, 26, 39, 30),
    'x3' = c(51, 36, 22, 2, 16, 33, 33, 8, 41, 25, 24, 0, 22, 35, 26)
)

data_long <- data %>% pivot_longer(cols = c('x1', 'x2', 'x3'), names_to = 'var')

res <- aov_ez("id", "value", data_long, within = c("var"), 
       anova_table=list(correction = "none", es = "none"))

res_sum <- summary(res)
res_sum$sphericity.tests
You get the following warning message:
Warning message:
In summary.Anova.mlm(object$Anova, multivariate = FALSE) :
Singular error SSP matrix:
non-sphericity test and corrections not available
Of course, we should catch this error in a better way and display some sort of warning message to the user.
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Ravi
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Joined: Sat Jan 28, 2017 11:18 am

Re: RM ANOVA sphericity assumption

Post by Ravi »

Oke, I fixed it so that there's a more informative footnote in the table when this happens (https://github.com/jamovi/jmv/pull/256)
CLeach
Posts: 3
Joined: Sun May 10, 2020 3:31 pm

Re: RM ANOVA sphericity assumption

Post by CLeach »

Thanks so much Ravi
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