Tests of three alternatives

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