Statistical treatment of a sigmoid curve from potentiometric data

A common experimental procedure used to establish a cause-effect relationship between related phenomena is the assessment of a dose-response curve, that is the function relating the variations of each of two variables (usually X is the causal phenomenon or dose and Y is the effect or the response). The basic assumption is that if there is a true cause-effect relationship between the two phenomena the function describing related couples of values manifested by the two phenomena is a linear or first order function. Unfortunately the dose-response curves are usually higher order functions: it is commonly accepted that a function of higher order defines a relation between more than two variables, one or both of whose is “composed “ by a number of interacting factors; interacting factors are statistically impossible to interpret. In many instances the deviation from linearity is evidently due to errors: in fact, when the two phenomena to be related are unitary any deviation from linearity should be attributed to extraneous, non-additive factors, not truly belonging to the cause-effect relationship. In the related paper a method is presented which seems to allow the statistical treatment of a dose-response curves obtained from raw data of a potentiometric titration of humic acids from different origin. The data are analyzed with different procedures: results of these analyses are compared and discussed in the light of a sound evaluation of the information really available, within the scientific method constraints.