In R Metafor package, there is a way to use the escalc function to calculate the effect sizes for a single group design using measure = MN. My question is how can I find studies that derived the y and v like in this case? I need the citation.

On page 102 of the documentation for R metafor package, it says "The goal of a meta-analysis may also be to characterize individual groups, where the response, characteristic, or dependent variable assessed in the individual studies is measured on some quantitative scale. In the simplest case, the raw mean for the quantitative variable is reported for each group, which then becomes the observed outcome for the meta-analysis. Here, one needs to specify mi, sdi, and ni for the observed means, the observed standard deviations, and the sample sizes, respectively.".

I know how to program the syntax to produce the output but I need to explain the formula it is using to estimate the effect size and its variance in this case (yi, vi). It does not give a citation for the raw mean but it gives a citation for if ratio scale or if variation is the focus. I have checked out Nagakawa et al, 2015; Raudenbush & Bryk, 1987) and none of them dealt with the formula for the effect size and the variance of raw means for quantitative variables. Studies that used the formula and calculated effect sizes like this is what I need. Thank you.

  • $\begingroup$ The documentation for the escalc function is about 10 pages long, and includes about 3 pages of citations. Since I don't think it would help you to copy and paste text that you've already reviewed, can you edit your post to explain what you understand from the documentation, and what specific parts of it you find unclear? $\endgroup$
    – Sycorax
    Commented Mar 31, 2021 at 5:01

1 Answer 1


When measure="MN", the "effect size" [1] is simply the mean, that is, whatever variable you specify for argument mi is the yi variable. And the sampling variance of a mean is just sdi^2 / ni, which is just the square of the standard error of a mean (see: https://en.wikipedia.org/wiki/Standard_error_of_the_mean#Standard_error_of_the_mean).

[1] The term "effect size" is a bit strange in this context. This is why I personally prefer the term "outcome measure".

  • $\begingroup$ Thanks @Wolfgang. I understand the formula now as the usual regular variance (I thought it should be more complicated than that) but was I was wondering if there are actual published papers that have reported using this measure (just the raw mean for a single group) as their effect size and the sample variance as effect size variance. Something I could use to lend credibility beyond stat101 class but would allow explaining the rationale for using it and its limitations. Thank you. $\endgroup$
    – cyflo
    Commented Mar 31, 2021 at 17:41
  • $\begingroup$ Not sure if there are any published applications. But it's a measure that could be used for a meta-analysis as long the the same variable is being measured across multiple studies and the goal is to synthesize them or to look for predictors thereof. Or if, instead of a contrast-based model for mean differences, I fit an arm-based model, then the outcome measure would be just the mean within each study arm. Raw mean differences are meta-analyzed in medicine for example when looking at effects on blood pressure or other well-defined outcomes. $\endgroup$
    – Wolfgang
    Commented Apr 1, 2021 at 19:12

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