Introduction

At last we can focus on g itself. It cannot be directly observed because g is a latent variable, and so we also need to find some empirical substitute for it. This is the so-called g-score.

If it is really true that there is very little we can know about the form of the distribution of g, it is imperative that we consider the implications of this before we go any further. This is all the more important because the fact is not widely understood in the psychometric community, where it is not unusual to find talk of ‘estimating’ the distribution of the latent variable. Doing this invariably involves importing, inadvertently perhaps, some assumption to make it possible. There are a number of topics in intelligence testing, and latent variable modelling more generally, which depend on a distributional assumption for g. If such assumptions are not well-founded, we need to make an immediate assessment of the damage.

One aim of this chapter is, therefore, to look carefully at some of the properties of g and to see how far they depend upon the assumption made about its distribution. This will place our ultimate recommendation to use the g-score in preference to IQ on a more secure footing. A second aim is to discuss the validity, reliability and identity of g as a measure of general cognitive ability.