Converting eta squared to Cohen's d

#1
I need to convert eta squared effect sizes to Cohen's d. It's for a meta-analysis paper, so I don't have the original data set.

Is it possible to do this? How is the formula different if you're converting from partial eta squared? I'm a research assistant so I don't know much about stats to begin with. If anyone could explain what exactly the difference is between eta squared and cohen's d (specifically how is effect size different from cohen's d--I don't mean in terms of scale and what's a large effect size. I mean conceptually, why would one pick eta squared over cohen's d and vice versa) that would be very helpful too.

Thanks,

LK
 

CB

Super Moderator
#2
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CB

Super Moderator
#3
I need to convert eta squared effect sizes to Cohen's d. It's for a meta-analysis paper, so I don't have the original data set.

Is it possible to do this? How is the formula different if you're converting from partial eta squared? I'm a research assistant so I don't know much about stats to begin with. If anyone could explain what exactly the difference is between eta squared and cohen's d (specifically how is effect size different from cohen's d--I don't mean in terms of scale and what's a large effect size. I mean conceptually, why would one pick eta squared over cohen's d and vice versa) that would be very helpful too.

Thanks,

LK
Googling the topic of your post brought this up:
http://www.stat-help.com/spreadsheets/Converting effect sizes 2009-06-25.xls

It uses a formula from Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.),Hillsdale, NJ: Erlbaum. pp. 281, 284, 285

Caution: SPSS gives a partial-eta squared value labeled as eta-squared, causing a bit of confusion for some researchers - partial eta-squared is sometimes labeled as eta-squared in articles. I'm presuming the sheet above assumes a classical eta-squared is given.
 
#4
Thanks, but I also need to convert partial eta-squared to Cohen's d too, which is not on the spreadsheet and googling didn't bring up anything obvious.

Also, if anyone out there has an answer as to why one would choose Cohen's d over eta-squared or partial eta-squared and vice versa, that would also be very helpful.

Thanks!

LK
 

CB

Super Moderator
#5
Thanks, but I also need to convert partial eta-squared to Cohen's d too, which is not on the spreadsheet and googling didn't bring up anything obvious.
I'm not sure if this conversion is possible (though I might be wrong). Partial eta squared represents "the proportion of total variation attributable to the factor, partialling out (excluding) other factors from the total nonerror variation" - whereas Cohen's d is a purely bivariate effect size measure (i.e. control factors are not considered; the two effect size measures are measuring different things).

Also, if anyone out there has an answer as to why one would choose Cohen's d over eta-squared or partial eta-squared and vice versa, that would also be very helpful.
I don't know of any guideline articles offhand, but Statistical power analysis for the behavioral sciences (Jacob Cohen) might well have some suggestions. To me, it'd make sense to use Cohen's d when you have just two IV groups, and classical eta-squared with multiple groups. The article linked to above might also be useful re distinction between usefulness of classical and partial eta-squared.
 
#6
Which metric you use will be a matter of context and convenience rather than correctness. Cohen's d is best suited to group differences while eta squared deals with the % of variance in a Y that can be predicted by an X. One thing that may be helpful is that eta squared is conceptually akin to r squared, and there are easy formulas for converting r to d and vice versa, so you might substitute eta for r and do that conversion. Just google "effect size" conversion for the formula.