An Evaluation of Fitting Methods for the Sum of Two Hyperbolas: Application to Uptake Studies

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Abstract
Analysis of data in terms of the sum of two rectangular hyperbolas is frequently required in solute uptake studies. Four methods for such analysis have been compared. Three are based on least‐squares fitting whereas the fourth (partition method I) is an extension of a single hyperbola fitting procedure based on non‐parametric statistics. The four methods were tested using data sets which had been generated with two primary types of random, normal error in the dependent variable: one of constant error variance and the other of constant coefficient of variation. The methods were tested on further data sets which were obtained by incorporating single 10% bias errors at different positions in the original two sets. Partition method I consistently gave good estimates for the four parameters defining the double hyperbola and was highly insensitive to the bias errors. The least‐squares procedures performed well under conditions satisfying the least‐squares assumptions regarding error distribution, but frequently gave poor estimates when these assumptions did not hold. Our conclusion is that in view of the errors inherent in many solute uptake experiments it would usually be preferable to analyse data by a method such as partition method I rather than to rely on a least‐squares procedure.