Elements of Psychophysical Theory 1st Edition by Jean Claude Falmagne 0195148320 9780195148329

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ISBN 10: 0195148320

ISBN 13: 9780195148329

Author: Jean-Claude Falmagne

This book presents the basic concepts of classical psychophysics, derived from Gustav Fechner, as seen from the perspective of modern measurement theory. The theoretical discussion is elucidated with examples and numerous problems, and solutions to one-quarter of the problems are provided in the text.

Elements of Psychophysical Theory 1st Table of contents:

Part I. BACKGROUND

1. Ordinal Measurement

Binary Relations

Equivalence Relations, Partitions, Functions

Algebraic Theory—Weak Orders

Biorders

*Complements

Exercises

2. Extensive Measurement

Construction of a Physical Scale for Length

Axioms for Extensive Measurement

Representation Theorem

Other Empirical Examples

*Complements and Proofs

Reference Notes—Further Developments

Exercises

3. Functional Equations

Cauchy and Related Equations

Plateau’s Experiment

*Normal Distribution of Sensory Variables

A Functional Inequality

Sincov Equations

Additive Systems

*Two Proofs

Exercises

Part II. THEORY

4. Fechner’s Psychophysics

Gustav Theodor Fechner, the Psychophysicist

Construction of a Fechnerian Scale

Fechner’s Problem

Psychophysical Discrimination Systems

Some Necessary Conditions

Representations and Uniqueness Theorem

*Proofs

Reference Notes

Exercises

5. Models of Discrimination

Random Variable Models

Thurstone’s Law of Comparative Judgments

*Extreme Value Distributions and the Logistic Model

Bradley-Terry-Luce Representations

A Model Inconsistent with a Fechnerian Representation

Statistical Issues

Selected References

Exercises

6. Psychometric Functions

Psychometric Families

Parallel Psychometric Families

Subtractive Families

Necessary Conditions for the Existence of a Subtractive Representation

Symmetric Families

Reference Notes

Exercises

*7. Further Topics on Psychometric Functions

Redefining Psychometric Families

Ordering the Backgrounds

Homomorphic Families

Representation and Uniqueness Theorems for Subtractive Families

Random Variables Representations

Exercises

8. Sensitivity Functions—Weber’s Law

Sensitivity Functions, Weber Functions

Linear Psychometric Families—Weber’s Law

Alternatives to Weber’s Law

Inequalities

Fechner’s Problem Revisited

Exercises

9. Psychophysical Methods

Traditional Psychophysical Methods

Adaptive Methods

Reference Notes

Exercises

10. Signal Detection Theory

ROC Graphs and Curves

A Random Variable Model for ROC Curves

ROC Analysis and Likelihood Ratios

ROC Analysis and the Forced Choice Paradigm

ROC Analysis of Rating Scale Data

The Gaussian Assumption

The Threshold Theory

Rating Data and the Threshold Theory

A General Signal Detection Model

Reference Notes

Exercises

11. Psychophysics with Several Variables or Channels

A General Model for Two-Channel Detection

Probability Summation

Two Addditive Pooling Rules

Additive Conjoint Measurement—The Algebraic Model

Random Additive Conjoint Measurement

Probabilistic Conjoint Measurement

Bisection

*Proofs

Exercises

12. Homogeneity Laws

The Conjoint Weber’s Laws—Outline

The Conjoint Weber’s Law—Results

*The Strong Conjoint Weber’s Laws

*The Conjoint Weber’s Inequality

Shift Invariance in Loudness Recruitment

Exercises

13. Scaling and the Measurement of Sensation

Types of Scales

Unidimensional Scaling Methods

The Krantz-Shepard Theory

Functional Measurement

The Measurement of Sensation—Sources of the Controversy

Two Positions Concerning the Scaling of Sensory Magnitudes

Why a Psychophysical Scale?

Exercises

14. Meaningful Psychophysical Laws

Examples

Scale Families

Meaningful Families of Numerical Codes

*Isotone and Dimensionally Invariant Families of Numerical Codes

An Application in Psychoacoustics

Why Meaningful Laws?

*Complements

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