An inquiry into the validity of mathematical methods used in evaluating theories of occupational choice

Abstract

An examination of the ontological basis of sociology reveals that sociology is inherently statistical. Various critiques of the use of mathematics and statistics are shown to be based on incorrect views of science and a confusion of different concepts of various ontological bases. As an introduction to some of the later discussion, a case study in inference is made.
The nature of the sampling distribution of a statistic is made clear in detail, arguments against the traditional (frequentist) approach to statistical inference are shown to be compelling. We start therefore from the idea of belief in the value of a parameter being the most important thing» with the cumulation of findings being essential. This is discussed from the point of view of Bayesian, Maximum Likelihood/Support, and Fiducial inference.
A way in which frequentist studies may be cumulated is given.
Finally the importance of the ontological status of variables in an equation is shown with respect to two particular types of mathematical manipulation of variatosi A analogue is drawn with the importance of dimensions in scientific formulae and it is shown that certain eqiations are not even possible, never mind correct.
The Appendices contain material (some previously published) which amplify the approach contained in the main thesis, and are of varying statusses.