Dear researchers,
I am conducting a meta analysis which analyses the correlations between personal values and different well-being scales across different studies and by that across different samples.
What is the state of the art procedure of calculating the average correlation between 2 variables across several samples?
My current procedure is:
1. Transorming the correlations of each sample into fisher's z
2. Calculating the sample-weighted average fisher's z
3. Transform the sample-weighted averge fisher's z back into a sample weighted correlation
I am sure that there are many different ways to solve the problem, but I would be very thankful to hear some of your thoughts about it.
Best regards and thank you,
Benedict
I recently conducted a meta-analysis and found the attached papers to be useful resources, particularly in terms of helping me identify the most appropriate analytic strategy. If interested, there are also free macros in SPSS for meta-analystic tests. For example, see: http://mason.gmu.edu/~dwilsonb/ma.html
Yes, this approach sounds about right. If you only focus on correlations, you can also use the Excel spreadsheets of Borenstein et al (2009) who made them openly available as part of their book "Introduction to meta-analysis".
The idea of your meta-analysis sounds very interesting. I assume you are going to include the data of the European Social Survey, especially the 6th wave where they measured many well-being related variables?
I would avoid the r-to-z transformation, it is known to inflate rho, introducing bias into the estimate (for a good discussion of this problem see: Schmidt and Hunter 2015. Methods of Meta-Analysis, 3rd Edition). I suggest sticking with good old fashioned sample size weighting.
Thank you all for your advices.
Shannon thank you for the papers, they already helped me a lot in getting more knowledge about how to conduct a meta analysis.
Paul thank you for the recommendation of the free excel tool. I will check that out.
Michael thank you for letting me know about the transofrmation problem and the bias that can occur. I am also going to check that in my future research.
Gilad thank you for letting me know about the other research. I am already in contact with Shalom Schwartz and Florenca Sortheix, who have made research in this field 2017. So I realized last week, that a meta analysis does only make sense, if I not only include Schwartz research about values but also Kasser's research on aspirations/values. However, I am not sure if it will create any new essential knowledge and does not 100 percent fit to my personal motivation.
I will probably build on the existing knowledge that was created by the 2017 study by Schwartz and Sortheix and build up on this with my own data constisting of more than 400 German students who filled out the most recent Portraits Values Questionnaire by Schwartz (56 items) and 5 scales of well-being (Three Fundamental Psychological need by Deci and Ryan, subj. vitality by Ryan and Frederik, Presence of meaning in life scale by Steger & Frazier, Satisfaction with Life Sclae and Positive Affect by Diener). By that, I can create new knowledge of the relation of well being scales with the newer, refined model of values by Schwartz.
Cordially,
Benedict
My understanding is that the Fisher z transformation is sensible here. It is biased but less biased than average correlations and its distribution has superior properties for meta-analysis (in terms of skew etc.).
See https://link.springer.com/content/pdf/10.3758/BF03334037.pdf
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