# [R-meta] effect size similarities

Michael Dewey ||@t@ @end|ng |rom dewey@myzen@co@uk
Wed Jun 23 15:23:31 CEST 2021

```Dear Patrizio

I have not contributed to this so far but I think the root problem here
is the so-called XY problem https://en.wikipedia.org/wiki/XY_problem as
we do not know what you really want to do, rather we know what you think
the solution might be. Wolfgang has already outlined how that is not
going to work but if you explained your scientific question and data we
might be able to be more helpful although obviously we can give no
cast-iron assurances.

Michael

On 23/06/2021 08:57, Viechtbauer, Wolfgang (SP) wrote:
> This is for the case of two dependent samples, that is, we want to compute
>
> d = (mean1 - mean2) / SD_change
>
> where mean1 and mean2 are the means at the two measurement occasions and SD_change is the standard deviation of the change scores. Then indeed
>
> d = t / sqrt(n)
>
> where t is the t-statistic from the two-dependent samples t-test.
>
> But this whole discussion started out with the case of a z-test of a binomial proportion. This is neither the case of two independent samples, nor the case of two dependent samples, and so none of this is relevant.
>
> Best,
> Wolfgang
>
>> -----Original Message-----
>> From: Patrizio E Tressoldi [mailto:patrizio.tressoldi using unipd.it]
>> Sent: Wednesday, 23 June, 2021 9:42
>> To: Viechtbauer, Wolfgang (SP); r-sig-meta-analysis using r-project.org
>> Subject: Re: [R-meta] effect size similarities
>>
>> Il 23/06/2021 09:28, Viechtbauer, Wolfgang (SP) ha scritto:
>>> I understand. What I tried to say is that this equation does not apply for a
>> one-sample t-test. Cohen's d is
>>>
>>> d = (mean1 - mean2) / SD,
>>>
>>> where mean1 and mean2 are the means of two groups and SD the (pooled) SD and
>> hence it reflects the difference between two groups. If there is only one group,
>> then Cohen's d cannot be computed.
>>>
>> In Lakens (2013) it is stated: "The effect size estimate Cohen’s dz can
>> also be calculated
>> directly from the t-value and the number of participants using the
>> formula provided by Rosenthal (1991): Cohen′s dz = t√n
>>
>> Lakens, D. (2013). Calculating and reporting effect sizes to facilitate
>> cumulative science: a practical primer for t-tests and ANOVAs. Frontiers
>> in psychology, 4, 863.
>>
>> Patrizio
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>
>

--
Michael
http://www.dewey.myzen.co.uk/home.html

```