A new nonparametric test for the race model inequality

Abstract

The race model inequality (RMI), as first introduced by Miller (Cognitive Psychology, 14, 247-279, 1982), entails an upper bound on the amount of statistical facilitation for reaction times (RTs) attainable by a race model within the redundant-signals paradigm. A violation of RMI may be considered as empirical evidence for a coactivation model rather than a race model. Here, we introduce a novel nonparametric procedure for evaluating the RMI for single participant analysis. The statistical procedure is based on a new probabilistic representation that highlights some neglected, but important distributional features of the RMI. In particular, we show how the reconstructed distribution function under maximal statistical facilitation for a race model is characterized by a specific truncated-type property. The results of two Monte Carlo simulation studies suggest that our procedure efficiently controls for type I error with reasonable power. Finally, unlike previous proposals for single participant analysis (e.g., Maris and Maris (Journal of Mathematical Psychology 47, 507-514, 2003)), our approach is also more consistent with the typical way to collect RT data in experimental works. R script functions for running the statistical analysis on single participant data are made freely available to the readers on a dedicated web server.

Interactive Parallel Models: No Virginia, Violation of Miller's Race Inequality does not Imply Coactivation and Yes Virginia, Context Invariance is Testable

“…A critical assumption in the field of race models, reviewed and analyzed in detail below, that has played a dominant role in multi-sensory perception, is that of context invariance. For approximately 40 years this assumption has been thought to be empirically untestable (see e.g., Lombardi, D'Alessandro, & Colonius, 2019;Luce, 1986;Ashby & Townsend, 1986). A contribution of the present investigation is that we demonstrate that if the experimenter utilizes both an OR (i.e., disjunctive stopping rule) as well as an AND (i.e., conjunctive stopping rule), then certain types of outcomes concerning workload capacity predictions, can falsify context invariance.…”

“…Considerable experimental and methodological effort (i. e., Colonius, 2016;Lombardi et al, 2019) has followed papers by J. Miller and colleagues (1978Miller and colleagues ( , 1982Miller and colleagues ( , 2016…”

Using relative-speed-of-processing to explain the shielding function of task rules

“…From a broad perspective, the attention bias account is more compatible with the classical information processing co-activation model (Diederich, 1995;Lombardi et al, 2019;Miller, 1982Miller, , 1986. Instead of assuming a target and a distractor have two parallel processing channels and competing for a single response selection process and essentially the "winner takes all" (i.e., the relative-speedof-processing model), the co-activation model assumed that both channels combine in satisfying a single criterion of the response selection.…”

Combining reaction-time distributions to conserve shape

“…) And inferential methods have been developed that depend on the properties of observed distributions, differences between them, and combinations of them, with no commitment to a particular theoretical distribution. Examples include skewness and kurtosis (Vickers, 1979), the survivor interaction contrast (Nozawa, 1992;To wnsend & Nozawa, 1995;Schweickert, Fisher, & Sung, 2012;Little, Altieri, Fific, & Yang, 2017), the summation test (Roberts & Sternberg, 1993;Schweickert et al, 2012), the race model inequality (Miller, 1982;Colonius & Vorberg, 1994;Lombardi, D'Alessandro, & Colonius, 2019;Gondan & Vorberg, 2021 ), the delta plot (de Jong, Liang, & Lauber, 1994;Schwarz & Miller, 2012;Miller & Schwarz, 2021;Ellinghaus & Miller, 2018;Mackenzie, I. G., Mittelstadt, V., Ulrich, R., & Leuthold, H., 2022), tests of RT mixtures (Reynolds & Miller, 2009;Yantis, Meyer, & Smith, 1991), and the "short RT" and "long RT" properties (Sternberg, 1973;Vorberg, 1981;Townsend & Ashby, 1983, Ch. 8).…”