UNIFYING THEORY OF ERRORS FOR THE ANALYTICAL METHODS OF CONCENTRATION-DEPENDENT DISTRIBUTION, IMMUNOASSAY AND SUBSTOICHIOMETRIC AND SUBSUPEREQUIVALENCE ISOTOPE-DILUTION

The statistical uncertainty of results for the concentration-dependent distribution of analyte A, which enters a bimolecular heterogeneous r eaction with reagent B after which individual analytical responses S-A and S-AB are measured, has been expressed as the product of three fac tors, f(1), f(2), and f(3); and these have been tabulated and assessed in numerical form. The first factor f(1) depends on the ratio of vari able amounts of analyte A to a constant added amount (e.g., the tracer ). Ideally, f(1) = 1 at large variable amounts, and at low amounts f(1 ) = infinity; the optimum practical ratio of analyte to additive lies in the interval 1:1 to 4:1. The second factor f(2) depends firstly on the yield of analyte binding; ideally, f(2) = 1 for quantitative yield s of the reaction with substoichiometric (subequivalent) amounts of re agent B; however, even at lower yields, the uncertainty of analysis do es not increase seriously (f(2) < 2). The third factor f(3) depends on the mode of measurement of the analytical responses S-A and S-AB The ideal ratio of signals (e.g., radioactivity or absorbance) used for qu antifying free and bound analyte is I = S-A/S-AB, = 1, for which f(3) = 1. Under optimum performance, the statistical uncertainty for concen tration-dependent distribution, radioimmunoassay, and subsuperequivale nce isotope dilution analysis methods appears to be of the same order as the errors of analytical response measurements. Simplicity of evalu ation of error propagation is demonstrated.