The statistical properties of the Survivor Interaction Contrast

Abstract The Survivor Interaction Contrast (SIC) is a powerful tool for assessing the architecture and stopping rule of a model of mental processes ( Townsend & Nozawa, 1995 ). Despite its demonstrated utility, the methodology has lacked a method for statistical testing until now. In this paper we briefly describe the SIC then develop some basic statistical properties of the measure. These developments lead to a statistical test for rejecting certain classes of models based on the SIC. We verify these tests using simulated data, then demonstrate their use on data from a simple cognitive task.

[1]  M. S. Mayzner,et al.  Human information processing : tutorials in performance and cognition , 1975 .

[2]  R. F.,et al.  Mathematical Statistics , 1944, Nature.

[3]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[4]  James T. Townsend,et al.  Issues and Models Concerning the Processing of a Finite Number of Inputs 1 , 2021, Human Information Processing.

[5]  Joseph W. Houpt,et al.  Systems Factorial Technology provides new insights on global-local information processing in autism spectrum disorders. , 2010, Journal of mathematical psychology.

[6]  J. Kujala,et al.  Testing for selectivity in the dependence of random variables on external factors , 2008 .

[7]  E. Dzhafarov.  Selective influence through conditional independence , 2003 .

[8]  James T. Townsend,et al.  The Stochastic Modeling of Elementary Psychological Processes , 1983 .

[9]  G. Marsaglia,et al.  Evaluating Kolmogorov's distribution , 2003 .

[10]  Jason Wittenberg,et al.  Clarify: Software for Interpreting and Presenting Statistical Results , 2003 .

[11]  J. Townsend.  Serial vs. Parallel Processing: Sometimes They Look like Tweedledum and Tweedledee but they can (and Should) be Distinguished , 1990 .

[12]  S. Sawilowsky.  Nonparametric Tests of Interaction in Experimental Design , 1990 .

[13]  A. Diederich,et al.  The relationship of variance to interaction contrast in parallel systems factorial technology , 1996 .

[14]  Eric Maris,et al.  Testing the race model inequality : a nonparametric approach , 2003 .

[15]  Richard Schweickert,et al.  A critical path generalization of the additive factor method: Analysis of a stroop task , 1978 .

[16]  J. Townsend,et al.  Spatio-temporal properties of elementary perception: an investigation of parallel, serial, and coactive theories , 1995 .

[17]  J. Townsend,et al.  Decomposing the reaction time distribution: Pure insertion and selective influence revisited☆ , 1980 .

[18]  H. Lindman.  Analysis of variance in complex experimental designs , 1974 .

[19]  Z. Birnbaum.  Numerical Tabulation of the Distribution of Kolmogorov's Statistic for Finite Sample Size , 1952 .

[20]  J. Townsend.  SOME RESULTS CONCERNING THE IDENTIFIABILITY OF PARALLEL AND SERIAL PROCESSES , 1972 .

[21]  AN Kolmogorov-Smirnov,et al.  Sulla determinazione empírica di uma legge di distribuzione , 1933 .

[22]  R. Bass,et al.  Review: P. Billingsley, Convergence of probability measures , 1971 .

[23]  M. Manosevitz.  High-Speed Scanning in Human Memory , .

[24]  J. Townsend.  Serial and within-stage independent parallel model equivalence on the minimum completion time ☆ , 1976 .

[25]  Douglas Vickers,et al.  Human Information Processing: Measures, Mechanisms, and Models , 1990 .

[26]  J. Doob.  Heuristic Approach to the Kolmogorov-Smirnov Theorems , 1949 .

[27]  J. Townsend,et al.  A theory of interactive parallel processing: new capacity measures and predictions for a response time inequality series. , 2004, Psychological review.