# [R-meta] Cohen's d in 2-way ANOVAs

David Cicchetti d@v|d@c|cchett| @end|ng |rom @tudent@un|-tueb|ngen@de
Tue Jun 22 18:15:38 CEST 2021

```Hi Tobias,

thank you, however I cannot use that because I often do not have
access to means or MSE, also I was looking for a formula if possible.

I have already seen this mail where Wolfgang Viechtbauer exaplained
how to compute Cohen's d of an interaction effect here:
https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2018-February/000658.html

d = ((mean_A1 - mean_A2) - (mean_B1 - mean_B2)) / sqrt(MSE) = t *
sqrt(1/n_A1 + 1/n_A2 + 1/n_B1 + 1/n_B2).

Would the calculation for main effects look like this?
d = ((mean_A1 + mean_A2) - (mean_B1 + mean_B2)) / sqrt(MSE) = t *
sqrt(1/n_A12 + 1/n_B12)
And is it the same for within and between subject?

However, for these calculations I would need means and the MSE or
t-values, which are often not avalable.
If I have a repeated measures two-way ANOVA with F value, degrees of
freedom and partial eta squared given, it is possible to calculate
cohen's d?

On this site I found a conversion from partial eta to cohen's d via cohen's f.
https://www.ibm.com/support/pages/effect-size-relationship-between-partial-eta-squared-cohens-f-and-cohens-d
Would this hold for a repeated measures two-way ANOVAs?

If there is no way to compute cohen's d with the aforementioned
values, what is then the minimum requirement needed in addition to
those values?

Thank you very much in advance.

Best regards,
David

Quoting Tobias Saueressig <t.saueressig using gmx.de>:

> Hi David,
>
> You might want to take a look at this:
> https://www.campbellcollaboration.org/escalc/html/EffectSizeCalculator-SMD30.php
>
> Regards
>
> Tobias Saueressig
>
> --
> Diese Nachricht wurde von meinem Android Mobiltelefon mit GMX Mail
> gesendet.
> Am 21.06.21, 15:07 schrieb David Cicchetti
> <david.cicchetti using student.uni-tuebingen.de>:
>
>> Hello everyone,
>>
>> I am conducting a meta analysis for the first time and for some papers
>> I need to calculate the wanted effect sizes (Cohen's d) of main
>> effects and interactions of 2x2 repeated measures ANOVAs.
>> Unfortunately, I have found barely information about how to do this so
>> far (actually only for one-way ANOVA).
>>
>> Is it possible to do this only with F-values, degrees of freedom or
>> directly from (partial) eta squared (as often reported)? Thus,
>> assuming we have no information of means, MSE, etc.
>>
>> Thank you very much in advance!
>>
>> Best regards,
>> David
>>
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```