Composite Sampling with Random Weights

Abstract

Composite samples are formed by physically mixing aliquots of individual samples. If aliquots of equal volumes are used, then the composite sample values are simply the arithmetic averages of individual sample values. If aliquots are not equal in volume, then statistical techniques need to be adjusted to account for unequal volumes. In this case, the composite sample values are weighted averages of individual sample values. The weights associated with individual sample values are proportional to the volumes of aliquots of the respective individual samples. If volumes of the aliquots are known, so that the weights also are known, then they can be treated as constants. The statistical properties of the composite sample values follow rather easily from those of the individual sample values. However, it can be the case that the volumes of the aliquots are unknown because they have resulted from a random process. In such a case, the statistical properties of the composite sample values depend not only on those of the individual sample values but also on those of the volumes (or, equivalently, of the weights) and are affected by the interrelationships between the individual sample values and the volumes of the aliquots.