## RM ANOVA sphericity assumption

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## RM ANOVA sphericity assumption

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
Attachments
Q5 MPA only.omv
CLeach

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

## Re: RM ANOVA sphericity assumption

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?
CLeach

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

## Re: RM ANOVA sphericity assumption

hey cleach,

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

cheers

jonathon

jonathon

Posts: 1261
Joined: Fri Jan 27, 2017 10:04 am

## Re: RM ANOVA sphericity assumption

Just a quick update that I'm looking into it!

Ravi

Posts: 148
Joined: Sat Jan 28, 2017 11:18 am

## Re: RM ANOVA sphericity assumption

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.

Ravi

Posts: 148
Joined: Sat Jan 28, 2017 11:18 am

## Re: RM ANOVA sphericity assumption

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)

Ravi

Posts: 148
Joined: Sat Jan 28, 2017 11:18 am

## Re: RM ANOVA sphericity assumption

Thanks so much Ravi
CLeach

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