Stereological ratio estimation based on counts from integral test systems

SUMMARY The stereological practice of using integral test systems in the estimation of the fundamental stereological ratios is studied in the light of recent theoretical developments in sampling. The estimation of a ratio is based on counts only, obtained from two, in general different, test sets constituting the integral test system. The ordinary ratio‐of‐sums estimator based on counts from uniformly positioned integral test systems is compared with two estimators based on non‐uniform, weighted sampling. It is shown that the estimators based on weighted sampling are not, in general, unbiased. Furthermore, it is pointed out that the mean‐of‐ratios estimator based on replicated weighted sampling needs not have smaller MSE than the ordinary ratio‐of‐sums estimator based on replicated uniform sampling. The fact that the estimation is based on counts as opposed to complete 2‐d observations does not necessarily mean a reduction in information. For certain types of stereological ratios, the ordinary ratio‐of‐sums estimator based on complete observation is shown, counter to intuition, to be less accurate than that based on simple and fast counting.