Comparison of the different approximation equations and procedures to estimate the volume of a brain region with an irregular shape contained in parallel sections indicates that the 'basic volume estimator' using systematic section is very efficient and sufficiently accurate. Important in estimating the volume is the correction for shrinkage and the accuracy of the section thickness determination. Methods to estimate thickness of section are outlined, and the method of differential focusing is discussed. In the Appendix, the corrections are described for overestimation of the volume by overprojection of the cross-sectional area and underestimation by underprojection when the size of cross-sectional area changes non-negligibly within sections. Statistical techniques to compare bivariate linear relations of different groups are reviewed. Emphasis is laid on Model II regression techniques that are used when the two variables considered are both subject to biological variation and measurement error. A new Model II procedure is proposed to compare the coincidence of the slopes of bivariate distributions and to test whether or not an experimental bivariate sample deviates significantly from a control sample when only the control group shows a significant bivariate linear relationship.