For problems concerning enthalpy-entropy compensations, an appropriate regression procedure is presented for the estimation of functional dependencies between thermodynamic parameters. Unbiased parameter estimates and their confidence intervals are derived for the case of a linear dependence between thermodynamic parameters. It is demonstrated that nonlinear as well as linear functional dependencies are readily detectable when enthalpy estimates are plotted vs. free energy estimates. Some linear and nonlinear examples of functional dependencies between thermodynamic parameters are analyzed and discussed.

A statistical analysis of the enthalpy-entropy compensation effect is presented. The correlation coefficient and functionality of the statistical compensation line are derived. A hypothesis test is proposed for application to enthalpy-entropy data to determine if any extrathermodynamic factors are distinguishable from the statistical compensation effect. A review of reported compensations in the literature reveals that detectable extrathermodynamic enthalpy-entropy effects are rare.

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