A Four-Dimensional Sphere? a Paradox in AVA's Vector Model and Profile Analysis Method

Abstract

A mathematical analysis is made of the geometric vector model and profile comparison method developed for the Activity Vector Analysis (AVA), a personality measure widely used in industry. The profile comparison formula is shown to be equal to a Pearson r but less parsimonious than the usual formulas. A contradiction is discovered in that the geometric model is presented in three-dimensional space as a sphere or spheroid, whereas the profile comparison formula mathematically requires four-dimensional space to reflect distances between profiles within the sphere. Some recommendations are made regarding resolution of the theoretical incongruency and revision of the measure based on empirical findings.