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I need to combine two measurements (morning and evening Peak Flow Rate)
in a single daily score. I don't have individual values, just the means
and standard deviations.
How should I compute the estimated SD of their average?

My guess was that the SD of the sum of two means should be the same as
that of their difference, the pooled SD, for which the formula is easily
found in  textbooks. (Since SD(a-b)= SD(a-(-1*b), where a and b are two
samples).
But then, when I divide the sum by two to obtain the average, I must
divide also the SD (since SD(a/2)=SD(a)/2), and the resulting SD appears
to be unrealistically low.

Where is the catch?
Thanks,

Piersante Sestini
Institute of Respiratory Diseases
University of Siena
Italy


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