Hi Sebastian,

The uncertainty of sums and differences goes as the sqrt of the sums of the individual uncertainties.

The @Risk software (Palisade) for this application easy to use Excel can help you without complications.

A general formula for computing the SD based on k estimates of SDi's each with ni samples, is:

SQRT[Sum[(ni-1)*SDi^2]/(Sum(ni)-k)] where i goes from 1 to k.

This expression applies to popuations that the same variance but differnt means.

I do not know what you mean by technical, and suppose that your experimental replicates are based on samples form the same process. If the instrument with which you are measuring has a bias that dependes up the mean of the sample, you may wnat to include systematic uncertainties (which are not removed by repeated measurments and defined by specifiactions of the instrument). For this, I reocmend you to look into ways of combining uncertaitnites as it is done in metrology.

For each replicate j you must have number of samples Nj, mean Mj, and variance Vj=SDj^2. The mean across the three replicates is M=(N1*M1+N2*M2*N3*M3)/(N1+N2+N3). For each replicate, calculate the mean square Qj=Mj^2+Vj*(Nj-1)/Nj. Note that the adjustment coefficient (Nj-1)/Nj is needed only if you computed Vj using (Nj-1) as the number of statistical freedom degrees (to obtain unbiased estimate). The mean square across the three replicates is Q=(N1*Q1+N2*Q2*N3*Q3)/(N1+N2+N3). Finally, the variance across those replicates is V=Q-M^2, and SD=sqrt(V). If the numbers of samples is small, you may want to adjust the above formula for V to one less statistical freedom degree by multiplying it by (N1+N2+N3)/(N1+N2+N3-1).

Dr. Vencken. The sample size is 3, so you may estimate U. I have worked this case expressing each value of variable in medias, that is, you take X1/U, X2/U and X3/U. This is done to separate real units from structure of distribution. It is possible to make a preliminar model approach using Xmaximum/U, Xminimum/U (the extreme values). Give me those two values and I will send you the equations of model. The explanation may come later. Ok, best wishes, emilio

You need to combine all your data into one big table and use that to calculate the overall SD. You can't just average the 3 SD's, although the result will probably be similar :)