How do I average uncertain values?

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• 
  Naceur M'Hamdi · High Agronomic Institute of Chott Mariem

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

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

  Apr 5, 2012
• 
  Wander Silva · Universidade Federal do Amapá

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

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

  Apr 6, 2012
• 
  Juan Gonzalez · South Florida Water Management District

  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.

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  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.

  Apr 10, 2012
• 
  Yury Shimansky · Arizona State University

  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).

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  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).

  Apr 10, 2012