# computing mean and sd of $d^\prime$ from mean and sd of hits and false alarms

I'm working on a meta-analysis. Some studies report $d^\prime$, others report accuracy (hits and false alarms). I would like to transform all the data into the same measure, $d^\prime$ (also $c$). However, for many studies, I only have the mean and sd of the accuracy measures. If I compute $d^\prime$ from the mean hit and false alarms, the outcome is not the same as the mean $d^\prime$, but it is at least closely correlated with mean $d^\prime$. However, I cannot figure out how to figure out the variance of the $d^\prime$ based on the mean and sd of the accuracy data. Is this possible, or am I going to have to request individual subject data?

• I take it these are all within subjects or repeated measures studies. And if so, are you more interested in individual condition variances or effect variances? And finally, what kind of measure is the preponderance of scores, proportions or d'?
– John
Aug 20, 2014 at 20:13
• They are generally within-subject studies, yes. I want the individual condition variances because most studies yield more than one comparison, and I also want to plot the d' data before showing the forest plots. Aug 20, 2014 at 21:52
• I would say it's about half and half between the two measures. But my primary hypotheses are in terms of detect ability vs criterion, which is why I prefer the SDT measures to straight accuracy. Aug 20, 2014 at 21:53
• Could you compute hit and false alarms as odd ratios? Then, you could convert OR in d... Aug 22, 2014 at 19:13