Hello Minnitt,

A representative sample is a part (a mass or a volume) of a whole (a sampling unit) selected in such a manner that a test result for the part is an unbiased estimate for the whole. A single test result does not give information about precision whereas duplicates give the lowest degree of precision for the mean due to the fact that a pair of test results gives only a single degree of freedom.

It makes sense to apply a stratified systematic sampling protocol by selecting primary increments at intervals of constant volume, mass or time. For a homogeneous liquid, a set of eight (8) primary increments per hour may be enough to obtain an acceptable degree of precision.

Optimize the sampling protocol by dividing a set of primary increments into a pair of subsets such that the A-primary sample consists of increments 1, 3, 5 and 7, and the B-primary sample of 2, 4, 6 and 8, and by selecting and testing duplicate test portions of each primary sample. This is ISO jargon!

Examine the ratio between var(t), the sum of the variance of the primary sample selection stage and the variance of the analytical stage, and var(a), the variance of the analytical stage. If the liquid is indeed homogeneous, var(t) and var(a) will be of the same order of magnitude. The variance of selecting a test portion of a primary sample is deemed to be an integral part of the analytical variance.

In case of doubt, repeat the sampling experiment until sufficient degrees of freedom are obtained to apply Fisher's F-test and compare the calculated F-value with tabulated F-values at 5% and 1% probability and with proper degrees of freedom.

More info about Fisher's F-test can be found in several papers posted on 'geostatscam.com' under 'Reviewed papers'.

Kind regards,

Jan W Merks ■