# Ratio Scaling of Psychological Magnitude: In Honor of the Memory of S.S. Stevens

By Stanley J. Bolanowski Jr; George A. Gescheider | Go to book overview

2
What Is a Ratio in Ratio Scaling?

R. Duncan Luce Irvine Research Unit in Mathematical Behavioral Science University of California, Irvine

THE PROBLEM

Ratio Scales and Ratio Scaling

The terms ratio scale, apparently first introduced by Stevens ( 1946, 1951), and ratio scaling, apparently first introduced by Krantz ( 1972) but closely related to previous phrasing, denote different but interrelated things. Although Krantz was very clear on the matter,1 the similarity of the terms seems to invite confusion and confounding. My goal here is to explicate some aspects of the differences and relations.

A ratio scale concerns one aspect of numerical measurement representations2 for a certain class of one-dimensional, empirical structures. In particular, it refers to those cases where the numerical representation of a qualitative structure of stimuli is uniquely specified up to multiplication by a positive constant. The most familiar physical examples of ratio scales are length, mass, and time intervals. They are all examples of what are called extensive structures, and they have in common two primitives. The first is a binary ordering relation ≳ that reflects the ordering induced on

____________________
1
On p. 169, he wrote: "I use the term 'ratio scaling' to refer to a family of interrelated psychophysical methods, discussed and classified by Stevens [ 1975]. The quotation marks are used to emphasize the distinction between the term 'ratio scaling' and the term ratio scale, the latter having its usual technical meaning in measurement theory . . . . 'Ratio scaling' need not lead to ratio scales."
2
That is, isomophisms between the empirical structure and a numerically based structure.

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Ratio Scaling of Psychological Magnitude: In Honor of the Memory of S.S. Stevens

• Title Page i
• Contents v
• Preface vii
• A Small Oral History ix
• List of Participants xiv
• 1: Introduction to Conference on Ratio Scaling of Psychological Magnitudes 1
• References 7
• 2: What Is A Ratio in Ratio Scaling? 8
• Acknowledgments 16
• References 17
• 3: Natural Measurement 18
• Introduction 18
• Summary 25
• References 25
• 4: The Dynamics of Ratio Scaling 27
• Introduction 27
• Acknowledgments 41
• References 41
• 5: Magnitude Matching: Application to Special Populations 43
• Introduction 43
• Acknowledgments 57
• References 57
• 6: A Single Scale Based on Is Ratio and Partition Estimates 59
• Introduction 59
• References 77
• 7: Associative Measurement of Psychological Magnitude 79
• References 98
• 8: Toward A Unified Psychophysical Law and Beyond 101
• Introduction 101
• References 111
• 9: Derivation of An Index of Discrimination from Magnitude Estimation Ratings 115
• 9: Derivation of An Index of Discrimination from Magnitude Estimation Ratings 115
• Acknowledgments 127
• References 127
• 10: Multiple Moduli and Payoff Functions in Psychophysical Scaling 129
• Introduction 129
• Acknowledgments 138
• References 138
• 11: Quality Assurance in Environmental Psychophysics 140
• References 160
• 12: Brightness Sensation and the Neural Coding of LIght Intensity 163
• Introduction 163
• Acknowledgments 181
• References 181
• 13c: Hemosensory Representation in Perception and Memory 183
• Acknowledgments 197
• References 197
• 14: Loudness Adaptation Measured by the Method of Successive Magnitude Estimation 199
• Introduction 199
• Acknowledgments 212
• References 212
• 15: Loudness Measurement by Magnitude Scaling: Implications for Intensity Coding 215
• Introduction 215
• Acknowledgment 226
• References 226
• 16: The Loudness of Non-Steady State Sounds: Is A Ratio Scale Applicable? 229
• Introduction 229
• Conclusions 243
• Acknowledgment 244
• References 244
• 17: Ratio Scaling, Taste Genetics, and Taste Pathologies 246
• References 257
• 18: Measurement of VIbrotactile Sensation Magnitude 260
• Introduction 260
• Summary 272
• Acknowledgments 273
• 19: Lntersensory Generality of Psychological Units 277
• Introduction 277
• Acknowledgments 293
• References 293
• 20: Final Comments on Ratio Scaling of Psychological Magnitudes 295
• Introduction 295
• References 309
• Author Index 313
• Subject Index 321
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