Least-squares analysis of phosphorus soil sorption data with weighting from variance function estimation: a statistical case for the Freundlich isotherm.

Phosphorus soil sorption data are typically fitted to simple isotherms for the purpose of compactly summarizing experimental results and extrapolating beyond the range of measurements. Here, the question of which of the commonly preferred models-Langmuir and Freundlich-is better, is addressed using weighted least-squares, with weights obtained by variance function analysis of replicate data. Proper weighting in this case requires attention to a special problem-that the dependent variable S is not measured, rather is calculated from the measured equilibrium concentration C. The latter is commonly taken as the independent variable but is subject to experimental error, violating a fundamental least-squares assumption. This problem is handled through an effective variance treatment. When the data are fitted to the Langmuir, Freundlich, and Temkin isotherms, only the Freundlich model yields a statistically adequate chi(2) value, and then only when S is taken to include labile residual P (S(0)) estimated from isotope-exchange experiments. The Freundlich model also yields good estimates of S(0) when this is treated as an adjustable parameter rather than a known quantity-of relevance to studies in which S(0) is not measured. By contrast, neglect of weights and labile P can lead to a mistaken preference for the Langmuir model.