Elements of Psychophysical Theory

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Oxford University Press, 2002 - Psychology - 387 pages
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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.
 

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Contents

Ordinal Measurement
13
Binary Relations
14
Equivalence Relations Partitions Functions
18
Algebraic Theory Weak Orders
23
Biorders
30
Complements
38
Exercises
46
Extensive Measurement
50
Alternatives to Webers Law
210
Inequalities
215
Fechners Problem Revisited
217
Exercises
219
Psychophysical Methods
221
Adaptive Methods
223
Reference Notes
231
Exercises
232

Construction of a Physical Scale for Length
51
Axioms for Extensive Measurement
58
Representation Theorem
60
Other Empirical Examples
62
Complements and Proofs
65
Reference Notes Further Developments
71
Exercises
72
Functional Equations
76
Cauchy and Related Equations
81
Plateaus Experiment
90
Normal Distribution of Sensory Variables
92
A Functional Inequality
95
Sincov Equations
97
Additive Systems
101
Two Proofs
103
Exercises
108
THEORY
111
Fechners Psychophysics
113
Construction of a Fechnerian Scale
114
Fechners Problem
118
Psychophysical Discrimination Systems
119
Some Necessary Conditions
122
Proofs
123
Reference Notes
130
Models of Discrimination
133
Random Variable Models
134
Thurstones Law of Comparative Judgments
136
Extreme Value Distributions and the Logistic Model
139
BradleyTerryLuce Representation
143
A Model Inconsistent with a Fechnerian Representation
146
Statistical Issues
147
Selected Families
148
Exercises
149
Psychometric Functions
151
Psychometric Families
156
Parallel Psychometric Families
158
Subtractive Families
161
Necessary Conditions for the Existence of a Subtractive Representation
166
Symmetric Families
167
Reference Notes
170
Further Topics on Psychometric Functions
172
Redefining Psychometric Families
174
Ordering the Backgrounds
180
Homomorphic Families
185
Representation and Uniqueness Theorems for Subtractive Families
191
Random Variables Representation
196
Exercises
197
Sensitivity FunctionsWebers Law
199
Sensitivity Functions Weber Functions
201
Linear Psychometric Families Webers Law
203
Signal Detection Theory
233
ROC Graphs and Curves
234
A Random Variable Model for ROC Curves
236
ROC Analysis and Likelihood Ratios
239
ROC Analysis and the Forced Choice Paradigm
244
ROC Analysis of Rating Scale Data
247
The Gaussian Assumption
249
The Threshold Theory
251
Rating Data and the Threshold Theory
254
A General Signal Detection Model
256
Reference Notes
258
Exercises
259
Psychophysics with Several Variables or Channels
260
Probability Summation
263
Two Additive Pooling Rules
268
Additive Conjoint MeasurementThe Algebraic Model
270
Random Additive Conjoint Measurement
272
Probabilistic Conjoint Measurement
277
Bisection
279
Proofs
281
Exercises
282
Homogeneity Laws
284
The Conjoint Webers LawsOutline
285
The Conjoint Webers LawResults
287
The Strong Conjoint Webers Laws
293
The Conjoint Webers Inequality
298
Shift Invariance in Loudness Recruitment
299
Exercises
303
Scaling and the Measurement of Sensation
305
Unidimensional Scaling Methods
306
The KrantzShepard Theory
311
Functional Measurement
315
The Measurement of SensationSources of the Controversy
317
Two Positions Concerning the Scaling of Sensory Magnitudes
322
Why a Psychophysical Scale?
323
Exercises
324
Meaningful Psychophysical Laws
325
Examples
327
Scale Families
330
Meaningful Families of Numerical Codes
331
Isotone and Dimensionally Invariant Families of Numerical Codes
336
An Application in Psychoacoustics
341
Why Meaningful Laws?
345
Exercises
351
References
353
Answers or Hints to Selected Exercises
366
Author Index
377
Subject Index
381
Copyright

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Page 7 - The aim of natural science," says Mach, "is to obtain connections among phenomena. Theories, however, are like withered leaves, which drop off after having enabled the organism of science to breathe for a time."3 This phenomenalistic conception, as it is called, was already familiar to Goethe. In his posthumous 'Maxims and Reflections...
Page 356 - Falmagne, J.-C. (1978). A representation theorem for finite random scale systems. Journal of Mathematical Psychology, 18, 52-72. Falmagne, J.-C.

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About the author (2002)

Jean-Claude Falmagne is at Columbia University.

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