Seth Roberts & Saul Sternberg
Introduction
Alternative Explanations of Additive Effects
Implications for the Additive-Factor Method
General and Stochastically-Independent Stage Models
Definition of the Models
Additivity of Factor Effects on Mean and Variance
The Summation Test
The Alternate-Pathways (AP) Model
Definition of the Model
- - Generality: Embedded AP Structure
- - Generality: Multiple Pathways
- - Plausibility
The Central Property and the Mixture Test
Additivity of Factor Effects on the Mean and other Raw Moments
The AP Model as a Special Stage Mechanism
Tails of the RT Distribution and Mixture-Test Failures
The McClelland-Ashby Cascade Model
Definition of the Model
The Processing-Time Distribution
Additivity of Factor Effects on Mean and Variance
Four Experiments
Experiment 1.: Detection
Experiment 2.: Identification
Experiment 3.: Classification
Experiment 4.: Overlapping Tasks
Additivity of Factor Effects on the Mean.
Relations Among the Variances
Additivity of Factor Effects
Evidence against the Alternate-Pathways Model
The Summation Test: Further Support for the Stage Model
Violation of the Translation Condition
The Test Procedure
- - Partitioning of Data
- - The Cartesian-Product Sums
- - Adjustment of Distributions
Results of the Test
- - Comparison of Proportions
- - Comparison of Quantiles
- - Comparison of Moments
The Mixture Test: Further Evidence Against the Alternate-Pathways Model
The Test Procedure
- - Adjustment of Distributions
Results of the Test
Evidence Against the Cascade Model
Allowed and Forbidden Regions in a Statistic Space
Dimensions of the Statistic Space
The Test Procedure
Test Results: Data versus Allowed Region
Excess Model Variance in the Best-Fitting Case
Application of the Summation Test to a Cascade Mechanism
Future Tests
Discussion
Appendix: Proofs and Comments on Equations
Notes
References