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[R-meta] Inverting negative correlations

4 messages · david detullio, Gerta Ruecker, Danka Puric +1 more

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.
Gerta Ruecker
# 
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:
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 R?cker <ruecker at imbi.uni-freiburg.de>
wrote:

  
  


  


      

    

    

      
      

        


  

        

      Michael Dewey
    

    

      
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Note that this question has already been asked and answered on 
CrossValidated

https://stats.stackexchange.com/questions/503654/inverting-a-negative-correlation

Michael

        
On 06/01/2021 19:06, Dr. Gerta R?cker wrote: