For random errors, the overall variance is the sum of the variance of the analytical procedure and the variance of the sampling operation.
If either the variance of the analytical procedure or the variance of the sampling operation is sufficiently smaller than the other, there is little point in trying to reduce the smaller one. For example, if the variance of the analytical procedure is 5% and the variance of the sampling operation is 10%, the overall standard deviation is 11%.
A more expensive and time consuming analytical procedure that reduces the variance of the analytical procedure to 1% only improves the overall variance from 11% to 10%.
Sampling uncertainty arises from the random nature of drawing
particles from a mixture. If the mixture is a liquid and the particles
are molecules, there are about 1022 particles/mL. It
will not require much volume of homogeneous liquid solution to
reduce the sampling error to a negligible value. Solids, however,
must be ground to very fine dimensions, and large quantities must
be used to ensure a small sampling variance. Grinding invariably
contaminates the sample with material from the grinding apparatus.
