Precision of the fractionator from Cavalieri designs

A popular procedure to predict the variance of the fractionator consists in splitting the initial collection of fragments into two subsets, in order to use the corresponding particle counts (or any other pertinent measure), in the calculation. The current formula does not account for local or 'nugget' errors inherent in the estimation of fragment contents, however. Moreover, it does not account for the fact that the contribution of the variability between fragments or slices should rapidly decrease as the sampling fraction increases. For these reasons, an update to the formula is overdue. It should be stressed, however, that the formula applies to Cavalieri slices designs - its application for arbitrary partition designs is therefore not warranted.