Estimators of the Precision of Stereological Estimates: an Example Based on the CA1 Pyramidal Cell Layer of Rats

Because of the complex and dynamic structure of the brain, there is perhaps no other organ system in which the application of stereological methods can contribute so much with regard to understanding normal and pathological processes. In order to design the studies in an optimal manner, with regard to the number of individuals, sections, probes, and to be able to critically evaluate the stereological studies made by others, it is important for neuroscientists to have an understanding of the precision or reproducibility of a stereological estimation procedure. This precision or reproducibility is often referred to as the coefficient of error of the estimate, which is a statistical expression for the size of the standard error of the mean of repeated estimates, relative to the mean of the estimates. Like the 'margin of error' associated with public opinion polls, it indicates how much the estimate would vary if it were repeated numerous times. It is difficult and time consuming to empirically derive the coefficient of error of estimates made of features observed in histological preparations. To overcome this obstacle, it is common practice to try to get a feeling for the precision of an estimate by estimating the coefficient of error itself. In this paper, we will compare and discuss the coefficient of error of estimates of volume and cell number made with different numbers of sections and probes in the CA1 pyramidal cell layer of the rat hippocampus. The conclusions drawn from this analysis indicate that, using practically feasible and anatomically sensible sampling schemes, the Gundersen-Jensen coefficient of error estimator or the 'Split-Sample' coefficient of error estimator can provide useful information about the precision of stereological estimates even in highly irregular brain regions and requires little work.