The use of statistical theory in fitting equations to dielectric dispersion data

Abstract

This paper shows how a choice may be made on the basis of statistical theory between alternative dielectric dispersion equations hypothesised to fit sets of experimental data. It also shows how to find the best values and probable ranges of the parameters in the equations.

It is intended for non-specialists in statistics, and to this end the application of statistical inference to the problem is outlined descriptively, with detailed references to some recent textbooks, so as to enable the necessary background to be rapidly pieced together.

A computational approach appropriate to dielectric dispersion equations, and some features of programs devised to implement it for the Debye and the Cole—Cole equations are described.

The best fit parameters and confidence intervals obtained for these two equations when the procedures are applied to an extensive literature collection of data on water are tabulated and discussed.

It is found that the improvement in fit of the Cole—Cole equation over the Debye throughout the complete temperature range from 0 to 75 °C makes it a near statistical certainty that there is some spread of relaxation times in water over all this temperature range. At 20 °C, for example, the probability of the improvement in fit not being due to chance is greater than 99.5 %, while the 90 % confidence interval for h, the Cole—Cole spread parameter, is 0.008 < h < 0.018.