# Prevalence conversion to effect size in meta-analysis

I'm used to thinking about meta-analyses in terms of evaluating the impact of an IV on an outcome of interest (ex: relationship between a teacher's level of self-confidence and student outcomes), and I'm used to calculating r (or using t-test, F or p-values, etc to calculate g or d and then converting that to r).

However, for my current study I'm interested in first describing the prevalence of a particular attitude; specifically, to what extent do professionals (physicians, police, clergy, etc) hold stigmatizing views of the eldery? However, I'm not initially trying to compare across groups, and many studies only have one type of participant (e.g., all physicians). I've found a bunch of studies that essentially gave a measure of stigma to a set of participants and reported either: a) The number or percent who responded with stigmatizing views or b) The average and standard deviation stigma score (on a continuous scale) for the sample.

Is it possible to convert this data into an effect size? I've found many effect size calculators, but none that seem to deal with converting the prevalence of a trait from a single group into an effect size. I've seen several references to "proportion, prevalence, or central tendency effect sizes" but no formulas.

Any advice on extracting information from these papers and converting it to d, g, or r (or even an odds ratio) would be greatly appreciated!

Following Sutton et al. (2000: 18f), I would suggest converting proportions $p$ to logits:

$logit = log(odds) = log(\frac{p}{1-p}).$

Using the number of cases with an event ($N_{event}$) and without an event ($N_{\neg event}$), the variance of $logit$ is given by

$Var(logit) = \frac{1}{N_{event}} + \frac{1}{N_{\neg event}}$.

Reference

Sutton, A. J., K. R. Abrams, M. Jonas, T. A. Sheldon und F. Song, 2000a: Methods for meta-analysis in medical research. Wiley series in probability and mathematical statistics, Chichester; New York: Wiley.

• Thank you! Now I'm struggling with how to work with the different scales in this format. Studies use different scales which aremeasuring the same construct. I could: – user30295 Feb 2 '14 at 22:24
• Thank you @Bernd Weiss ! Follow up question: These formulas are for dichotomized or categorical data. The literature I have measures stigma on various continuous scales. I could: 1) say that anyone who scores 1 st. deviation above the mean qualified as stigmatizing; or 2) create cut points for each scale (though they would be arbitary). Neither seem like great options. If you are aware of other ways to use continuous scales to determine prevalence/severity, I would appreciate the advice. – user30295 Feb 2 '14 at 22:37
• @user30295 No, I am sorry. In that case you probably have to deal with multiple dependent variables and run one meta-analysis per dependent variable. – Bernd Weiss Feb 5 '14 at 6:15