# How do I average uncertain values?

Hi all,

I would like to combine all my experimental and technical replicates into one value with a standard deviation. The easy part was calculating mean and standard deviation for each experimental replicate from the three technical replicates used. The part I find difficult is how to calculate the SD of the three experimental replicates, each with their own SD. The sample size is always 3 and the values are quite similar, so I don't believe I need any fancy weighted calculations. Could anybody help me out?

Thanks

I would like to combine all my experimental and technical replicates into one value with a standard deviation. The easy part was calculating mean and standard deviation for each experimental replicate from the three technical replicates used. The part I find difficult is how to calculate the SD of the three experimental replicates, each with their own SD. The sample size is always 3 and the values are quite similar, so I don't believe I need any fancy weighted calculations. Could anybody help me out?

Thanks

## All Answers (5)

Naceur M'Hamdi· National Institute of Agronomy, TunisThe uncertainty of sums and differences goes as the sqrt of the sums of the individual uncertainties.

Wander Silva· Universidade Federal do AmapáJuan Gonzalez· South Florida Water Management DistrictSQRT[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.

Yury P Shimansky· Arizona State UniversityEmilio José Chaves· University of NariñoDr. 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

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