Linear theory, dimensional theory, and the face-inversion effect.

Abstract

We contrast 2 theories within whose context problems are conceptualized and data interpreted. By traditional linear theory, a dependent variable is the sum of main-effect and interaction terms. By dimensional theory, independent variables yield values on internal dimensions that in turn determine performance. We frame our arguments within an investigation of the face-inversion effect-the greater processing disadvantage of inverting faces compared with non-faces. We report data from 3 simulations and 3 experiments wherein faces or non-faces are studied upright or inverted in a recognition procedure. The simulations demonstrate that (a) critical conclusions depend on which theory is used to interpret data and (b) dimensional theory is the more flexible and consistent in identifying underlying psychological structures, because dimensional theory subsumes linear theory as a special case. The experiments demonstrate that by dimensional theory, there is no face-inversion effect for unfamiliar faces but a clear face-inversion effect for celebrity faces.Understanding the implications of any experimental outcome requires a fundamental quantitative theory, within whose context the numbers constituting the data may be transformed into conclusions about the underlying processes that generated the data. This article is about the general consequences for eventual conclusions of deciding to use one such theory or another and about the specific consequences for understanding a well-known phenomenon in the domain of face processing.The article is divided into five sections. In the first section ("The Face-Inversion Effect"), we describe an extant psychological problem that serves as a vehicle for illustrating the points that we make regarding theories. In the second section ("Theories to Analyze Data"), we describe two quantitative theories: The first, traditional linear theory, is used almost universally within many disciplines, including psychology, whereas the second, dimensional theory, is considerably less known and less used. In the third section ("Simulations"), we describe three simulations, whose purpose is to illustrate some costs and benefits of interpreting data using linear and dimensional theory. In the fourth section ("Experiments"), we describe three experiments that, given the foundation we have established, allow us to make some tentative conclusions about the face-inversion effect in particular and about face processing in general. Finally, in the fifth section, our General Discussion, we compare the two theories that we have been considering: We show formal mathematical relations between them, we comment on the advantages and disadvantages of using one versus the other as a tool for inferring the underlying processes that generated a data set, and we articulate the resulting implied conclusions about face processing.These five sections are designed in pursuit of three interrelated goals. The first goal is to demonstrate (yet again) that traditional linear theory has severe limitations as a basis for conceptua...

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