I want to calculate the standard deviation for the mean reduction in a paired sample T test. I only have the mean measurements as well as the standard deviation for pre and post measurements, so no raw data. So for example:
Mean monocytes count pre treatment: 8.5, SD = 5.3
Mean monocytes count post treatment: 8.1, SD = 4.4
Mean difference would be = 8.1 - 8.5 = -0.4
Yet I still want the standard deviation for the mean difference, is it possible to calculate from this data?
Let m0 and sd0 = mean and SD of the pre-treatment scores.
Let m1 and sd1 = mean and SD of the post-treatment scores.
Let r = the Pearson correlation between pre & post
Let n = the number of pairs of scores
SD of the paired differences = sddiff = sqrt(sd0^2+sd1^2-2*r*sd0*sd1)
SE of the mean difference = sddiff/sqrt(n)
Do you have n and r?
You need to find the difference for each observation and then find the Standard deviation for the differences.
Bruce Weaver explained the problem. If the t statistic and df for the paired t test are reported you can work out n and r.
Thank you all for your input, truly appreciate it!
Thom Baguley Abdulmuhsin S. Shihab Bruce Weaver
As for Bruce Weaver answer, I believe this solves the problem yet I have the n but not r, and I don't recall having the t statistic. The only values I have are the mean + SD for pre and post measurements, would it be possible to reach the SD for the paired difference with these numbers only?
Hello Hassan Abushukair. I think the best you can do under the circumstances is to come up with a plausible range of possible r-values (e.g., based on what you can find in the relevant literature) and show the results for r-values at the low end, middle and high end of that plausible range. HTH.
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