The Theory of Chemical Sampling

Thus consider the variances derived for the problem in Chapter XI (f). Between Vats = = 1.09 

Suppose we have one analysis on one sample from one bag from one vat. This will have a variance of (1.09 -J- 0.00 -f- 1.85 0.83) = 3.77 or a standard 

If this is too inaccurate an estimate of the quality of the batch, we might reduce the error in our estimate by doing duplicate analyses. It would then have a variance of (1.09 fi- 0.00 4- 1.85 -1- 0.83 /2) = 3.35 or a standard deviation of 1.83. It is clear that this is very little improvement upon our original estimate of 1.94 based on a single analysis. 

We might take a pair of samples from a bag, and perform single analyses upon them. Our estimate would thus have a variance of (1.09 + (1.85 - - 0.83)/2) = 2.43, or a standard deviation of 1.56. This is a definite improvement upon our earlier estimates. 

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