Ratio Scaling of Psychological Magnitude

In Honor of the Memory of S.s. Stevens

Stanley J. Bolanowski, Stanley J. Bolanowski, Jr., George A. Gescheider, Stanley J. Bolanowski, Jr., George A. Gescheider

• Publisher: Psychology Press
• Year: 2013
• eBook ISBN:
  9781134757619
• Topic: Education
• Subtopic: Education General

Presenting the proceedings of a conference held at Syracuse University in honor of S.S. Stevens, a pioneer in the scaling of sensory magnitudes and the originator of the method of magnitude estimation, this volume brings together the work of 20 authorities on the procedures of ratio scaling. These experts--psychophysicists, physiologists, and theoreticians--offer their views on whether or not psychological magnitudes can be measured and whether the judgments of psychological magnitudes constitute the basis for the construction of a ratio scale. Also discussed is the question of whether any single method could stand out as a potential standard technique for measuring psychological magnitudes.

1	Introduction to Conference on Ratio Scaling of Psychological Magnitudes

George A. Gescheider
Hamilton College and Institute for Sensory Research, Syracuse University

Stanley J. Bolanowski, Jr.
Institute for Sensory Research Syracuse University

It is generally agreed that the highest form of measurement is achieved with ratio scales typified by the well-established scales used in the physical sciences such as those used for measuring length and mass. One of the major goals of the conference on the “Ratio Scaling of Psychological Magnitudes” was to evaluate the possibility that ratio scales of psychological magnitudes can be achieved, thereby imparting to psychophysical scaling the quantitative attributes of measurement that have been so important for the development of the physical sciences. There have been arguments that it is impossible to measure psychological magnitudes such as loudness, brightness, and pain intensity because they are private events (Savage, 1966, 1970; Zuriff, 1972). However, we suggest, as did Stevens (1966), that there is no fundamental philosophical difference that distinguishes physical measurement from psychophysical measurement. In both cases, observations are made by operations performed on the subject of interest. These observations form the basis for quantification of theoretical constructs such as force, gravity, electron velocity, and, in our opinion, sensation magnitude. We are hopeful that a careful consideration of progress in psychophysical scaling will eventually lead to the conclusion that true ratio scales for the measurement of psychological magnitudes, validated by the same criteria as those used in the physical sciences (e.g., meeting requirements of additivity and transitivity), can be achieved. The conference was organized to evaluate current knowledge on the topic and to decide whether this position is justified or not.

FIG. 1.1. Hypothetical input–output function of a sensory system. I₀ represents the absolute threshold and ΔI represents a difference threshold for intensity.

Why is it important that we be able to measure psychological magnitude? Perhaps this question can be answered best through an example from sensory science. If we conceptualize a sensory system as having an environmental stimulus as its input and experienced sensation as its output, we can imagine that it has the input–output function illustrated in Fig. 1.1. The absolute threshold (I₀) could be measured with relative ease by measuring the intensity of a stimulus that is detectable 50% of the time. Likewise, difference thresholds (ΔI) could be measured by measuring the difference in intensity that could be discriminated 50% of the time. Although knowing the absolute sensitivity and the differential sensitivity of a sensory system provides valuable information, they cannot in themselves be used to describe the entire input–output function without assuming some fundamental relation between stimulus and response (e.g., Fechnerian integration of the ΔIs.) Indeed, certain procedures (e.g., ratio scaling) produce input–output functions for intensive continua not expected by Fechnerian integration. A formal description of the input–output function is important because it would reveal how the nervous system operates on the barrage of sensory information it receives, thus enhancing our understanding of how the system works. As a natural outgrowth, our ability to diagnose and treat sensory disorders would be greatly improved.

The fundamental problem impeding progress on these matters is that there are no instruments for directly measuring the magnitude of private sensations. The available methods are indirect, at best. To redefine sensation in terms of observable neural activity does little to solve the problem because to do so requires that we know the neural code for stimulus intensity, and presently there is no widespread agreement on this matter. Furthermore, the two-stage model of psychophysical scaling (e.g.. Attneave, 1962; Curtis, Attneave, & Harrington, 1968; Shepard, 1981) merely redefines the problem as illustrated in Fig. 1.2. Sensation magnitude (ψ) and its relation to stimulus intensity (ϕ), otherwise known as the psychophysical law [ψ= f₁(ϕ)], must be inferred from the relationship between the known stimulus and the subject’s observable response [R = f₃(ϕ)]. To do this, however, we must know the relationship between the response and sensation [R = f₂(ψ)]. Unfortunately, the relationship between response and sensation is as inaccessible to direct observation as is the relationship between stimulus and sensation. In spite of these difficulties, psychophysical scales have been constructed and claims for their ratio properties have been made. These claims, as well as the claims of the critics, led us to discussions during the conference about another issue—whether or not results obtained with psychophysical methods can be used to indirectly construct scales of psychological magnitudes that meet the stringent requirements of ratio scales of measurement.

FIG. 1.2. Relations among the psychophysical law (stimulus transformation function), ψ = f₁(ϕ), the response function (response transformation function), R = f₂(ψ), and the empirically determined relation between stimulus intensity and response, R = f₃(ϕ).

The conference was held in honor of the memory of S.S. Stevens. It was he who pioneered many of the topics discussed at the meeting. In particular, he made an important contribution toward helping us to define ratio scales, as well as other scales of measurement, when he (Stevens, 1951) proposed that a scale could be defined in terms of permissible mathematical transformations that leave a scale invariant (i.e., transformations that do not change its essential mathematical properties). Listed in Table 1.1 are the basic operations, mathematical group structure (transformation that leaves the scale invariant), the permissible statistics, and examples. In the nominal scale that determines the equality of the measured property, the permissible transformation is any one-to-one substitution of numbers, thus, preserving the identity of the measurements. The permissible transformation of an ordinal scale, designed to determine greater or less-than relations among magnitudes, is somewhat more restricted than that of a nominal scale and consists of any increasing monotonic function. Under these conditions the order of the measurements will be preserved after such transformations. An interval scale, designed to determine the equality of intervals (i.e., differences) between magnitudes, is invariant to any linear transformation in which the slope and intercept are free to vary. Thus, the interval scale has a variable unit size and an arbitrary zero. A ratio scale, designed to determine the equality of ratios among magnitudes, is invariant to linear transformations in which only the slope is free to vary and the intercept is zero. Thus, the ratio scale has a variable unit size and an absolute zero. Finally, because of current debates about the potential of absolute psychophysical scaling, we have applied Stevens’ concept of in-variance to this type of scale. In this scale the measurements cannot be mathematically transformed without violating the properties of the scale, and thus this scale consists of a special instance of a ratio scale in which the unit is fixed (e.g., numerosity). Note that if absolute scales for sensation magnitude do exist (Zwislocki, 1983), than pitch scales, loudness scales, etc. have the mathematical structure of identity as does numerosity.

TABLE. 1.1.
Scales of measurement. Adapted from Stevens (1951).

In psychophysics, various scaling methods have been devised to obtain quantitative data on psychological magnitudes from the subject’s responses. Indeed, applications of the various psychophysical scaling methods have consisted of attempts to construct interval, ratio, or more recently absolute scales of psychological magnitude. The procedures used to construct scales of psychological magnitude must be critically evaluated in relation to the type of measurement scale claimed by the investigator; that is, the type of scale found is probably a function of the method used.

FIG. 1.3. Illustration of ratio estimation and ratio production. In ratio estimation, the subject estimates the ratio of the sensation magnitude of stimulus A to stimulus B. In ratio production, the subject may be asked to adjust stimulus B so that its sensation magnitude stands in some relation to stimulus A.

At this conference we focused on ratio scaling and the methods that produce such scales. In general, the construction of ratio scales of psychological magnitude has been approached in two different ways. In the earliest experiments, subjects were asked to make judgments of the ratios of their sensation magnitudes. These techniques are illustrated in Fig. 1.3. In ratio estimation, stimulus A and stimulus B are presented and the subject is asked to estimate the ratio of the resulting sensation magnitudes. In ratio production, the subject adjusts the two stimuli so that the resulting sensation magnitudes stand in some prescribed ratio. S.S. Stevens (1936) produced the original loudness scale, the sone scale, based on data obtained from this approach. The assumption underlying these methods is that subjects are capable of accurately estimating sensation ratios.

FIG. 1.4. Illustration of magnitude estimation and magnitude production. In proportion to the sensory magnitude of stimuli. In magnitude production, the subject must adjust the intensity of the stimuli so that their sensation magnitudes are proportional to numbers given by the experimenter.

Later, Stevens (1953, 1955) proposed the use of magnitude estimation and magnitude production to obtain more direct estimations of sensation magnitude. In the techniques of magnitude estimation and magnitude production, the subject makes a numerical estimation of subjective magnitude. As illustrated in Fig. 1.4, in magnitude estimation, numbers are assigned to the sensation magnitudes of stimuli, and in magnitude production, stimulus intensity is adjusted by the subject to produce a prescribed numerical value of sensation magnitude. The assumption in these methods is that numerical judgments are directly proportional to sensory magnitude. This assumption has been challenged (e.g., Anderson, 1982), but work on the additivity of measurements seems to indicate that, at least for data averaged over several subjects, the assumption is correct (Cain. 1976; Dawson, 1971; Hellman & Zwislocki, 1964; Marks, 1978, 1979, 1987; Marks & Bartoshuk, 1979; Murphy, Cain, & Bartoshuk, 1977; Zwislocki, 1983).

In conclusion, psychophysical measurements of psychological magnitude are indirect. Indeed, they are based on various assumptions and models that we have about what subjects’ observable responses tell us about the magnitude of their psychological experiences. These assumptions and models determine whether ratio or some other scale will be found. One of the main purposes of our conference was to evaluate these assumptions and models as they apply to the various ratio scaling methods. The other major function of the conference was to examine empirical results obtained by these methods, with the hope of coming to some conclusion about their general utility. This conference offered a special opportunity for a direct exchange of ideas on this important problem.

REFERENCES

Anderson, N. H. (1982). Cognitive algebra and social psychophysics. In B. Wegener (Ed.), Social attitudes and psychophysical measurements (pp. 123–148). Hillsdale, NJ: Lawrence Erlbaum Associates.

Attneave, F. (1962). Perception and related areas. In S. Koch (Ed.), Psychology: A study of a science (pp. 619–659). New York: McGraw–Hill.

Cain, W. S. (1976). Olfaction and the common chemical sense: Some psychophysical contrasts. Sensory Processes, 1, 57–67.

Curtis, D. W., Attneave. F., & Harrington, T. L. (1968). A test of a two-stage model of magnitude judgment. Perception and Psychophysics, 3, 25–31.

Dawson. W. E. (1971). Magnitude estimation of apparent sums and differences. Perception and Psychophysics, 9, 368–374.

Hellman, R. P., & Zwislocki, J. J. (1964). Loudness function of a 1,000 cps tone in the presence of a masking noise. Journal of the Acoustical Society of America, 35, 856–865.

Marks, L. E. (1978). Binaural summation of the loudness of pure tones. Journal o...

Table of contents

• Cover
• Title
• Copyright
• Contents
• Preface
• A Small Oral History
• 1. Introduction to Conference on Ratio Scaling of Psychological Magnitudes
• 2. What Is a Ratio in Ratio Scaling
• 3. Natural Measurement
• 4. The Dynamics of Ratio Scaling
• 5. Magnitude Matching: Application to Special Populations
• 6. A Single Scale Based on Ratio and Partition Estimates
• 7. Associative Measurement of Psychological Magnitude
• 8. Toward a Unified Psychophysical Law and Beyond
• 9. Derivation of an Index of Discrimination From Magnitude Estimation Ratings
• 10. Multiple Moduli and Payoff Functions in Psychophysical Scaling
• 11. Quality Assurance in Environmental Psychophysics
• 12. Brightness Sensation and the Neural Coding of Light Intensity
• 13. Chemosensory Representation in Perception and Memory
• 14. Loudness Adaptation Measured by the Method of Successive Magnitude Estimation
• 15. Loudness Measurement by Magnitude Scaling: Implications for Intensity Coding
• 16. The Loudness of Non-steady State Sounds: Is a Ratio Scale Applicable?
• 17. Ratio Scaling, Taste Genetics, and Taste Pathologies
• 18. Measurement of Vibrotactile Sensation Magnitude
• 19. Intersensory Generality of Psychological Units
• 20. Final Comments on Ratio Scaling of Psychological Magnitudes
• Author Index
• Subject Index