[R-meta] Inverting negative correlations

[Danka Puric]

Dear David,

If I understood your question correctly, you are interested in the
relationship between (for example) social anxiety and extroversion and the
majority of primary studies report this correlation, but some report the
correlation between social anxiety and introversion.

In this case, I'd say you have to reverse the correlations for
introversion, because all effect sizes need to reflect the relationship you
are interested in. Otherwise, the overall estimate will be wrong.
You really don't need a specific reference for this (except maybe that
introversion is the opposite pole of extraversion), it's a situation
equivalent to recoding inversely worded items in a personality
questionnaire before calculating the summary score.

Also, I'm not sure it's best to think about this as taking the absolute
value of a correlation. Only if all correlations with extraversion in your
dataset are positive, and all correlations with introversion are negative
taking the absolute value of the correlation would give you the correct
estimate. In any other case, you would be treating a negative correlation
(of social anxiety and extroversion) as positive. If the true effect size
is positive but low, you would expect to find a few negative correlations
in primary studies.

To sum up, I think you should take the correlations for studies measuring
extraversion as they are, but reverse them for measures of introversion.

All the best,
Danka


On Wed, Jan 6, 2021, 20:06 Dr. Gerta Rücker <ruecker using imbi.uni-freiburg.de>
wrote:

> Dear David,
>
> Yes, this is correct because
>
> Cov(X,-Y) = - Cov(X,Y)
>
> and the same holds for the correlations.
>
> It is important that the wording is correct. For your example, the
> interpretation would be that if there is a negative correlation between
> social anxiety and extraversion, there is a positive correlation between
> social anxiety and intraversion.
>
> Best,
>
> Gerta
>
> Am 06.01.2021 um 19:50 schrieb david detullio:
> > Hello all, I want to include correlation coefficients in a random-effects
> > model for meta-analysis. If the majority of the correlations are
> positive,
> > could I use the absolute values of any negative correlations if such
> > correlations would have been positive had one of the measures been
> reverse
> > scored? As an example, say there is a negative correlation between a
> > measure for social anxiety and a measure for extraversion. Would it be
> > possible to take the absolute value of the correlation under the
> assumption
> > that the correlation would be positive if the measure for extraversion
> was
> > reverse scored? Any answers would be appreciated, and if anyone knows of
> > source material that talks about this process, the reference would be
> > appreciated as well.
> >
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