Monday, 6 February 2017
Sarah's Pearson's r mini-meta analysis (Goh, Hall, & Rosenthal, 2016): Play along and modify for your data in R
There's this really great paper by Jin Goh and colleagues about mini meta-analyses. The idea is that in multiple study papers (and I'm thinking also multiple sample papers) it is a good idea to combine research results at some point. It's a good idea for a number of reasons, including: to subvert the p-hack culture, to help power analyses in future research, to find effects that are only observable across multiple studies (presumably due to moderator effects), and to provide stronger evidence of null findings. Get the pdf here.
I'm a social and/or personality psychology phd student with a penchant for the psychometric side of things, so I'm most interested in mini meta-analyses of Pearson's rs. You can't move for rs in my line of work. So I was naturally particularly interested in the weighted mean correlation mini meta method described on page 542 and demonstrated in an example on page 539.
This is Sarah's data:
Jin has an excel file that accompanies the paper that you can download. I have created an R script which allows you to arrive at the weighted mean correlations (fisher's z and converted back to r). You can download it here from my dropbox. It will allow you to play along with the example given by Goh and colleagues. It can be extremely easily modified to use on your own data - whenever you have comparable Pearson's r across studies or samples! Which is really probably 70% of the time.
This is what it looks like, it's really a simple thing. Just plug your own coefficients in to the cors <- c(.05, .40), taking out the original coefficients and extending the vector as long as you need it to be. Just separate coefficients by commas. And also plug your own study or sample N in to the n <- c(80, 200) part. It is contingent on the psych package being installed and loaded, so make sure that is the case!
So, go forth and mini meta-analyse!
Here's the reference for the paper:
Goh, J. X., Hall, J. A., & Rosenthal, R. (2016). Mini Meta‐Analysis of Your Own Studies: Some Arguments on Why and a Primer on How. Social and Personality Psychology Compass, 10(10), 535-549.
And here's the code from Gist: