# Meta analysis of test scores in range [0,100]

We have multiple studies of certain test scores which range from 0-100 which we would like to meta-analyze. For each subject within a study a score may vary within this range, however we only have the average test score per study and the number of subjects that took this test.

How can we meta-analyze this using the metafor package in R? I am inclined to use meta-analysis for proportions for this, since you can divide the score by 100 and obtained a proportion which is clearly bounded by 0 and 1 (which is necessary for this data) with escalc(measure="PLO",xi=events,ni=n,data = df);. However this method requires an event count which we don't have since individual test scores are not dichotomous. I can, however, estimate xi by multiplying the mean score per study by the sample size.

Is this ok? Or should we use a different method?

Treating these data as if they are proportions isn't correct. You have means and should treat them as such, that is, by using escalc(measure="MN", mi=mean, sdi=sd, ni=n, data=df). This requires that you know the SD of the scores of the subjects within each study. If this isn't reported, then you should try to get this info from the study authors.
• You can just constrain the CI bounds to the 0-100 range. If you really don't like this, then you can transform the means using $\log(\frac{\bar{x}}{100-\bar{x}})$ (like a logit transformation) which has variance $\frac{100^2 s^2}{(\bar{x}-100)^2 \bar{x}^2}$, where $s^2$ is the variance of the scores of the subjects within a study. – Wolfgang Apr 2 '18 at 12:45