CONFIDENCE-LIMITS FOR THE ABSCISSA OF INTERSECTION OF 2 LEAST-SQUARES LINES SUCH AS LINEAR SEGMENTED TITRATION CURVES

The confidence limits for the abscissa of the intersection of two least-squares lines, such as linear segmented titration curves, are calculated by using a simple method, based on the intersection of confidence bands, that always overestimates the width of the confidence interval, and by using a more accurate computationally intensive method based on integration of the transformed bivariate normal distribution (i.e., Creasy's method). Numerical results obtained by applying the foregoing methods to experimental and simulated data are compared with those obtained by Fieller's theorem and first-order propagation of variance as previously applied in the primary chemical literature. A discrepancy is resolved by correcting the pooling of variance in the prior work. Relationships between the various methods are shown. Fieller's method, with proper pooling, gives reliable results unless the data are very noisy, whereas Creasy's method gives finite inclusive confidence intervals even when Fieller's method fails.