eta squared in ANCOVA versus Gamlj

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Arnaud Mortier
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Joined: Tue Apr 27, 2021 11:39 am

eta squared in ANCOVA versus Gamlj

Post by Arnaud Mortier »

[Update : this should probably be a question filed in the jamovi modules section, since this is a question about the reason for the choices made in developing jamovi (which invariably arise when you teach) rather than a statistics question]

Hi,
I am curious about a difference that can be found between the ANCOVA module and Gamlj: the former reports eta squared values computed via the formula SS effect / (SS effects + SS error) while the latter uses SS effect / SS total.
I am more familiar with the latter formula. What would be the implications of using the former one? Is there a particular reason/context where it would be more natural? Why make a different choice for the two modules?

Here are two screenshots to illustrate my point - same data, basically the same analysis (first with ANCOVA, second with Gamlj):
ANCOVA1.png
ANCOVA1.png (9.72 KiB) Viewed 1407 times
where 0.388 = 48.5/(48.5+10.3+66.2)
and on the other hand
glm1.png
glm1.png (15.52 KiB) Viewed 1407 times
where 0.257 = 48.5/(122.7+66.2)

Thanks!
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MAgojam
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Location: Parma (Italy)

Re: eta squared in ANCOVA versus Gamlj

Post by MAgojam »

Hey Arnaud,

I see you've been waiting for a while.
Considering you always start from using the R effectsize package, maybe you haven't seen this:
https://gamlj.github.io/details_glm_effectsize.html#(eta^2):_(semi-partial)_eta-squared
where Marcello explains the reason for this corrective choice in GAMlj.

Cheers,
Maurizio
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Arnaud Mortier
Posts: 32
Joined: Tue Apr 27, 2021 11:39 am

Re: eta squared in ANCOVA versus Gamlj

Post by Arnaud Mortier »

Hi Maurizio,

Thank you for your answer and for this reference! However, unless I've missed something, it only makes a case for the choice made in GAMLj, which is already the version I prefer. What I don't understand is why or when people would use the other version, present in the ANCOVA module.

All the best,
Arnaud
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Arnaud Mortier
Posts: 32
Joined: Tue Apr 27, 2021 11:39 am

Re: eta squared in ANCOVA versus Gamlj

Post by Arnaud Mortier »

Hi again,
Digging in old conversations I was able to find this explanation once given by Marcello on another topic:
mcfanda@gmail.com wrote: Sat Oct 30, 2021 5:14 pm Eta-squared has been defined by Pearson as

Code: Select all

eta_squared=SS_model/(SS_model+SS_error)
(see Cohen, 1973). Other authors have simplified the formula as

Code: Select all

eta_squared=SS_effects/(SS_effects+SS_error)
mainly because in balanced anova the two formulas yield exactly the same results. In general, the two results are not identical, even if the results are usually very, very close.
(...)
When it comes to individual effects, many software and R packages use

Code: Select all

SS_x/(SS_effects+SS_error)
This is because it's easier to compute the eta-squared only knowing the SS of each individual effect.
Still not convinced though, it can actually be not so close to the original formula, and it can be misleading to report this version when everyone's standard goes by the other one. Especially when in a lot of situations this actually makes the eta squared artificially bigger than it should be. Not saying that this is a potential reason it was used in the first place :rolling_eyes: O:-)

Arnaud
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