I'm trying to determine sample sizes for some straight-forward studies looking at quality of life measurements pre/post intervention using multiple survey tools. I'm using effect size from previous studies in my sample size estimation via power analysis, but most don't provide the standard deviation of pair-wised changes needed to calculate a Cohen D for dependent samples. What most of these do have, however, is the mean change from baseline with a 95% confidence interval.
I can see in the Cochrane Handbook 6.5.2.3 (https://training.cochrane.org/handbook/current/chapter-06#section-6-5-2) a method of obtaining the SD for differences in means using CI to calculate SE, then SE and group n's to calculate SD. My question is whether this method is only valid for getting the SD for the difference between two independent groups (as the example in the handbook shows) or could it also be valid for getting the SD of difference between baseline and post-intervention within the SAME group?
P.S. I know the topic of imputing SD with dependent samples when you only have summary statistics is a previously discussed topic here. After hours of reading I'm still having trouble determining clearly if this is even possible.
If I follow, you know the mean difference and its 95% CI, and you wish to work out the SD of the paired differences. Is that right? Do you also have the sample size (i.e., the number of paired differences)? I hope so! If you do, then try the following.
df = n-1
t025 = the critical value of t for two-tailed alpha = .05
se = (upper limit of CI - mean diff)/t025
sd = sediff*sqrt(n)
If you say what software you use, someone can probably help you convert that pseudocode into code. E.g., pasted below is Stata code demonstrating that these computations correctly recover the SD of the paired differences using only the mean difference and CI. HTH.
// Carry out a paired t-test
clear
webuse fuel
ttest mpg2==mpg1
// Read the summary statistics into a new dataset
clear
input n meandiff sterr stdev lower upper
12 1.75 .7797144 2.70101 .0338602 3.46614
end
// Compute the SD of the paired differences using only
// the mean difference, its 95% CI, and the sample size.
generate df = n-1
generate t025 = invt(df,1-.025)
generate se = (upper-meandiff)/t025
generate sd = se*sqrt(n)
list stdev sd, clean noobs
Here is the output from that list command:
stdev sd
2.70101 2.70101
stdev = the SD of the paired differences copied from the t-test output. sd = the SD of the paired differences computed using only the mean difference, the 95% CI, and the sample size. As you can see, they match.
If I have misunderstood your question, please clarify what it is you are trying to do.
https://www.calculator.net/standard-deviation-calculator.html
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