Clinical Chemistry, Vol 16, 124-128, Copyright © 1970 by the American Association for Clinical Chemistry

Calculation of Normal Ranges by Methods Used for Resolution of Overlapping Gaussian Distributions

¹ Department of Pathology, Rockford Memorial Hospital, Rockford, Ill. 61103.

Distribution of a quantity, e.g., concentration of a serum constituent, in a typical general hospital population is considered. It is assumed that the distribution within any subpopulation is Gaussian and that adjacent subpopulations overlap somewhat, presenting overlapping Gaussian distributions. Bhattacharya’s procedure for resolving such overlapping distributions, based upon differentiation of the Gaussian distribution equation, is applied to the determination of the apparent normal range as well as, in some cases, an abnormal range. Gaussian probability paper is used for estimating the normal range and the conditions discussed under which this method may be expected to give a valid estimate. Use of the chi-square test to evaluate the long-term constancy of clinical laboratory data distribution, normal and abnormal, is also considered.