Eta-squared

[E. Bernardo]

Hi all,

  I have read an article where ANOVA results were presented in the following format (F, df, p, eta-squared).  What is the use of the eta-squared?  Why was it included?

  Thank you.
  Eins


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[Peters Gj (PSYCHOLOGY)]

Dear Eins,

Eta-squared is the proportion of variation in the dependent variable
that is explained by the factor (independent variable). In contrast to
F, it's magnitude is not a function of sample size, making it comparable
across studies with different sample sizes. Because of this property,
it's called an _effect size_.

Eta squared is calculated by simply dividing the variation, explained by
a factor, by the total variation in the dependent variable:

Eta^2 = SS(between) / SS(total), or

Eta^2 = SS(factor) / SS(total)

An alternative to Eta^2 is Partial Eta^2, and this is what SPSS gives
you when you 'order' Eta^2. The Partial Eta^2 is not the proportion
between the variation, explained by the factor, and the total variation
in your dependent variable, but the proportion between the variation,
explained by the factor, and the variation, explained by the factor,
plus the error variation. The formula for Partial Eta^2 is:

Partial Eta^2 = SS(factor) / (SS(factor) + SS(error))

(For oneway Anova's, Partial Eta^2 is equal to Eta^2)

When you have three factors, their Eta^2's sum to 1, but their Partial
Eta^2's will exceed 1, because you count the error three times. Some
people see this as a disadvantage of Partial Eta^2's. I personally don't
see why this matters, because I don't see when you would want to sum the
Eta^2's. I prefer the Partial Eta^2, because it compensates for other
factors in your model. For example, if you do a study where you
manipulate one factor, let's say stress level, you can expect the total
variation to be:

variation due to individual differences + variation due to different
stress levels

Now, if you also manipulate, eh, the volume of the background music
(say, Wagner), then the total variation becomes:

variation due to individual differences + variation due to different
stress levels + variation due to different music volumes

So, the total variation increases. This means that the Eta^2 of the
factor Stress Levels decreases, even if the effect of stress levels
remains the same. You just created more variation in your dependent
variable by introducing another factor.

Partial Eta^2 corrects for other factors, by only comparing each effect
to the variation due to that effect plus random variation. In other
words, Partial Eta^2 artificially 'creates' a oneway Anova, so that the
effect sizes from both designs I outlined above (both without and with
the music volume factor) are comparable.

However, when I have been speaking to colleagues, they were generally in
favour of normal Eta^2, stating that the fact that it doesn't sum to one
makes it hard to interpret. I myself don't understand this yet, so I'm
kind of hoping perhaps somebody will correct me here :-)

I hope this helps you :-) Once I am certain that this is correct -or of
course something else is correct :-) I will put this on my website,
because I've tried finding information on this myself, and apparently
the internet isn't too knowledgeable about Anova effect sizes :-)

Another effect size for Anova's is Omega-squared, which gives the effect
size as estimated in the population, as opposed to in the sample.
However, all other effect sizes 'we' use (Cohen's d, Pearson's r, odds
ratio's) estimate the effect size in the sample I think, so if you want
to be comparable to other studies with other effect size measures,
(Partial) Eta^2 seems a better choice. But also on this, perhaps others
are more knowledgeable.

Kind regards,

(and a happy 2009 to everybody!)

Gjalt-Jorn


---
Gjalt-Jorn Peters
Work & Social Psychology, faculty of Psychology & Neuroscience,
Maastricht University
Phone: [phone] | Room: 3.015, Universiteitssingel 5, Maastricht
| Mail: PO Box 616, 6200 MD, Maastricht

http://  interventionmapping.com | phdthesis.nl | ecstasyresearch.eu |
interventiondesign.eu | gjyp.nl | vhk1a.nl

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Eins Bernardo
Sent: vrijdag 2 januari 2009 9:24
To: [hidden email]
Subject: Eta-squared

Hi all,

  I have read an article where ANOVA results were presented in the
following format (F, df, p, eta-squared).  What is the use of the
eta-squared?  Why was it included?

  Thank you.
  Eins


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 Spread holiday cheers to your friends and loved ones today!

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[Henrik Lolle]

Hi,

I cannot myself understand that the fact that the partial eta squared
measures in a model do not sum to one should make the measure hard to
interpret. But perhaps the fact that partial eta squared not
necessarily tells much about the importance of the independent variable
can explain why it isn't used much. The size of partial eta depends
also on the model all in all, i.e. on the other variables in the model.
Partial eta does not compare to a standardized partial regression
coefficient but to a partial correlation coefficient, and these aren't
used much either. Some, but not many, use betas from a Multiple
Classification Analysis (which can be computed from ANOVA), and others
use the betas from the NOMREG procedure. These two types of betas are
alike when the dependent variable is interval scaled and the
independent variables are nominal scaled, and they are both comparable
to the betas from an ordinary linear regression.

Best,
Henrik

Quoting "Peters Gj (PSYCHOLOGY)" <[hidden email]>:

> Dear Eins,
>
> Eta-squared is the proportion of variation in the dependent variable
> that is explained by the factor (independent variable). In contrast to
> F, it's magnitude is not a function of sample size, making it comparable
> across studies with different sample sizes. Because of this property,
> it's called an _effect size_.
>
> Eta squared is calculated by simply dividing the variation, explained by
> a factor, by the total variation in the dependent variable:
>
> Eta^2 = SS(between) / SS(total), or
>
> Eta^2 = SS(factor) / SS(total)
>
> An alternative to Eta^2 is Partial Eta^2, and this is what SPSS gives
> you when you 'order' Eta^2. The Partial Eta^2 is not the proportion
> between the variation, explained by the factor, and the total variation
> in your dependent variable, but the proportion between the variation,
> explained by the factor, and the variation, explained by the factor,
> plus the error variation. The formula for Partial Eta^2 is:
>
> Partial Eta^2 = SS(factor) / (SS(factor) + SS(error))
>
> (For oneway Anova's, Partial Eta^2 is equal to Eta^2)
>
> When you have three factors, their Eta^2's sum to 1, but their Partial
> Eta^2's will exceed 1, because you count the error three times. Some
> people see this as a disadvantage of Partial Eta^2's. I personally don't
> see why this matters, because I don't see when you would want to sum the
> Eta^2's. I prefer the Partial Eta^2, because it compensates for other
> factors in your model. For example, if you do a study where you
> manipulate one factor, let's say stress level, you can expect the total
> variation to be:
>
> variation due to individual differences + variation due to different
> stress levels
>
> Now, if you also manipulate, eh, the volume of the background music
> (say, Wagner), then the total variation becomes:
>
> variation due to individual differences + variation due to different
> stress levels + variation due to different music volumes
>
> So, the total variation increases. This means that the Eta^2 of the
> factor Stress Levels decreases, even if the effect of stress levels
> remains the same. You just created more variation in your dependent
> variable by introducing another factor.
>
> Partial Eta^2 corrects for other factors, by only comparing each effect
> to the variation due to that effect plus random variation. In other
> words, Partial Eta^2 artificially 'creates' a oneway Anova, so that the
> effect sizes from both designs I outlined above (both without and with
> the music volume factor) are comparable.
>
> However, when I have been speaking to colleagues, they were generally in
> favour of normal Eta^2, stating that the fact that it doesn't sum to one
> makes it hard to interpret. I myself don't understand this yet, so I'm
> kind of hoping perhaps somebody will correct me here :-)
>
> I hope this helps you :-) Once I am certain that this is correct -or of
> course something else is correct :-) I will put this on my website,
> because I've tried finding information on this myself, and apparently
> the internet isn't too knowledgeable about Anova effect sizes :-)
>
> Another effect size for Anova's is Omega-squared, which gives the effect
> size as estimated in the population, as opposed to in the sample.
> However, all other effect sizes 'we' use (Cohen's d, Pearson's r, odds
> ratio's) estimate the effect size in the sample I think, so if you want
> to be comparable to other studies with other effect size measures,
> (Partial) Eta^2 seems a better choice. But also on this, perhaps others
> are more knowledgeable.
>
> Kind regards,
>
> (and a happy 2009 to everybody!)
>
> Gjalt-Jorn
>
>
> ---
> Gjalt-Jorn Peters
> Work & Social Psychology, faculty of Psychology & Neuroscience,
> Maastricht University
> Phone: [phone] | Room: 3.015, Universiteitssingel 5, Maastricht
> | Mail: PO Box 616, 6200 MD, Maastricht
>
> http://  interventionmapping.com | phdthesis.nl | ecstasyresearch.eu |
> interventiondesign.eu | gjyp.nl | vhk1a.nl
>
> -----Original Message-----
> From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
> Eins Bernardo
> Sent: vrijdag 2 januari 2009 9:24
> To: [hidden email]
> Subject: Eta-squared
>
> Hi all,
>
>  I have read an article where ANOVA results were presented in the
> following format (F, df, p, eta-squared).  What is the use of the
> eta-squared?  Why was it included?
>
>  Thank you.
>  Eins
>
>
> ---------------------------------
>  Happy Holidays from Yahoo! Messenger
> Spread holiday cheers to your friends and loved ones today!
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>

************************************************************
Henrik Lolle
Department of Economics, Politics and Public Administration
Aalborg University
Fibigerstraede 1
9200 Aalborg
Phone: [phone]
************************************************************

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