How to calculate effect sizes from mean and CI

Question

I use escalc() function from metafor package to calculate various effect sizes or outcome measures (and the corresponding sampling variances) that are commonly used in meta-analyses.

In most of articles are tables of mean and standard deviation which can be easily used by escalc().

# for example:
# group A == mean=7; sd=1.8; n=13
# group B == mean=3.5; sd=3; n=179
escalc(m1i=7, sd1i=1.8, n1i=13, m2i=3.5, sd2i=3, n2i=179, measure="MD")
      yi     vi
1 3.5000 0.2995

...unfortunately, in some articles are tables consisting of mean and confidence intervals.

Is there any way how to compute effect size by using confidence intervals instead of standard deviation?

# for example
# group A == mean=19.25; CI=17.1-20.1; n=28
# group B == mean=8;     CI=6.8-9.2;   n=72

P.S. or if not from CI than maybe from range (probably impossible).

Answer 1

It would not be too hard for simple analyses like a $t$-test, as long as you know the sample size. The range of a confidence interval is $2\cdot t\cdot \mathrm{SD}/\sqrt{N}$, which is also the margin of error times 2. If the $t$-value is not reported, it can be found with the appropriate df (from sample size) and alpha value.

I'm sure similar things can be done in more complicating tests, but but I'm not quite sure how off the top of my head. It might get messy dealing with df.