Stefan,

You can convert between r and Cohen's d and vice versa. See P. 48-49 in Introduction to Meta-Analysis by Borenstein et al. (2009). (See attached file.) It also shows how to interconvert the variances.

Gordon

Hello Gordon, 

Thanks a lot for the conversion equations! 

One more question: Do you know how to calculate the variance of the correlation coefficient (Vr) that is mentioned on p. 48, eq. 7.6. in the chapter you sent me? (eq. 7.9. does not work for that, because I don't have d and Vd, but want to calculate it from r)

Best, 

Stefan 

I guess you cam compute variance and CIs of a correlation coefficient using Fisher's Z transformation. Please find details here http://www2.sas.com/proceedings/sugi31/170-31.pdf

Hi,

For easy conversion, you may look for the following IP:

http://gunston.gmu.edu/cebcp/EffectSizeCalculator/r/r.html

Hi Stefan,

Effect sizes are interchangeable, and for example an effect size d can be converted into correlation coefficient and vice versa. Please see the attached file.

Stefan,

The equation to calculate the variance for a correlation (Vr) is shown in the attached file.

Gordon

Thanks a lot for your help!

While the suggestions about conversion of parameters here are true - there is a problem with your approach.

Let's look at an example:

Say there is a strong correlation between intelligence and creativity. Say we test the correlation of intelligence (IQ) and creativity. IQ is your X. Creativity is your Y. You draw a random sample from the population and test for intelligence. Then you test the same subjects for creativity. After that you draw correlation which is say r= .50.

Say we know that IQ is normal in population and has a mean value of 100. Say we know that Creativity is normal in population and has a mean value of 60 in our creativity test.

Now you split your sample by X. High X is IQ >100, low X is IQ

Der Alexander

You wrote: "We split the low IQ group in two groups again: lowLow IQ and lowHigh IQ ... Now here comes the problem ..."

Maybe there is a misunderstanding here. I didn't mean that subgroups are formed within a particular group in the dataset on group differences. I meant that the "normal" groups that have been compared in the dataset could in principle also described by a dimensional variable. For instance, on study has anxious vs. non-anxious subjects (group difference data) but in another study one has looked at anxiety in a dimensional fashion (correlative data). 

This was just an example why you can't (or shouldn't) combine those values together.

If you are keen to have an effect size that describes the power of the effect in reality then your combined effect size should be generally replicable (or refoundable to be concise). Your combination of those effect sizes would be: [general value of effect (r) and  study-specific value of effect (d)].

This is all because the mean difference found in the creativity comparison is just a difference between two samples. And those samples do not represent a normal distribution of values in a population. Don't forget: we only use means (Mittelwerte) to describe samples because they are the best estimates of the unobservable values that mark those populations. 

Let me say again: if you compare means of two samples and those do not represent a randomly drawn set of values which are normally distributed, then your sample means do not represent the "effects" that create those samples. --> Thus the effect size found won't be representative for any effect but the creation of groups (sample split).

^Puh this sounds tricky...

But why are there conversions for different effect sizes when one should'nt combine correlation coefficients and mean differences to a combined effect? There has to be an appropriate application ... 

The conversions are to make comparison of results simple. An other example:

Two groups: effect group and control group. The effect group get the intervention then you test for significance. If you find significance you argue that those groups are different and the effect group wouldn't be likely drawn from the population from which the control group is drawn. Then you argue that the all other conditions were controlled for and so on.

Now an other person does an other experiment on the same topic but with an other intervention. He gets a significant result too and wants to know which intervention is more effective. Here comes the effect size. He looks at your paper and finds your effect size value, then calculates his own and compares them. This way he can compare the intervention methods to find the better one.

These samples' values are represented by their means. If you split any sample which is drawn randomly and has a normal distributed value (in its population) by any pattern but randomness (split half method in reliability calculation is done before sorting them, so this is random too), then you bring in a pattern which defines the new subsamples.

Get that so far, but that doesn't explain then why correlations can be converted to cohen's d. Correlations describe a pattern in one sample. I guess this conversion is done for direct comparisons, so there should be a case where this is suitable. 

This fetch I found on the web gives a hint to it. (see attachment).

It says that to compare correlation studies you transfer the correlation values to fisher's z and then sum-up the results before transferring them back to correlation coefficients to report in the publication!

Unfortunatelly it does not say why you should transfer them first (or I paid not much attention to the content).

The idea you approach seems interesting to me and there might be a way but the approach you took till now won't work out. 

Yes, correlation coefficients are often combined via transformation to Fisher's Zr (and then converted back for illustration). 

Still, there are also conversion formulas for correlations to cohen's d, etc., which are group difference measures (!). So there should be cases where correlational data and group difference data can be directly compared (which would imply that they also can be aggregated), otherwise these conversions make no sense at all, right? 

Hi Stefan,

These conversion formulas could be used if a a correlation coefficient is reported for a research design with two groups. It is still technically possible to calculate a correlation coefficient then, but much more useful to think of the effect in terms of group differences. This is thus a very strict assumption before the conversion makes sense.

As you already found out, it is not useful for associative effect sizes to be expressed as group differences, or the other way around.