The Measurement of Value
Part II Subjective Measurement: Introduction
Louis L. Thurstone
"Psychophysical Analysis" was my first paper in the field of psychophysics, or psychological measurement proper. In my judgment, this is my best contribution to psychology. It probably has more implications for psychological science than any other paper that I have written. The next four papers develop the theme of psychological measurement further without introducing any applications. Perhaps the principal characteristic of the law of comparative judgment is that it is entirely independent of any physical measurement. Its unit of measurement is frankly subjective, and yet it provides formal checks of internal consistency.
For many years it has puzzled me that the methods of subjective measurement have not been popular in psychology in comparison with factor analysis, for example, which has attracted so much interest that no one man even attempts to read the many hundreds of papers that are being written every year in that field. This circumstance seems all the more strange, since the methods of subjective measurement are mathematically simple at the high school level, whereas multiple factor analysis requires some degree of mathematical sophistication at the senior college level for physical science students.
Some friends have suggested that we should call this subject "Psychological Measurement" instead of psychophysics. I should be willing and, in fact, I would prefer this title for what we have been doing in this field, but I have been afraid that such a title would be interpreted to mean mental tests, mental ages, intelligence quotients, test norms, and the prediction of school grades. We ordinarily refer to this subject as test theory. The title "psycho-physics" has been unfortunate because it denotes the dead subject of lifted weights and limen determinations and arguments about the best way to compute somebody's limen for lifted weights to many decimals. Graduate students are right when they agree with William James that the psycho-physics of his day was, and still is, the dullest part of psychology.
In recent years I have referred to this field as "modern psychophysics" because in teaching it we always start with the classical psychophysical methods, which are then altered to fit the subjective measurement of stimuli which do not have any physically measurable attributes of interest. To make the transformation from the classical limen determination methods to the measurement of social, moral, aesthetic, and other psychological values has required the rewriting of psychophysical logic. More recently I have referred to this subject frankly as "subjective measurement" because we deal with a subjective unit of measurement and with stimuli that are generally acknowledged to have no ordinary physical dimensions.
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My own introduction to the interesting problems of the subjective metric came in teaching the classical psychophysical methods when I went to the University of Chicago. Instead of asking students to decide which of two weights seemed to be the heavier, it was more interesting to ask, for example, which of two nationalities they would generally prefer to associate with, or which they would prefer to have their sister marry, or which of two offenses seemed to them to be the more serious. After obtaining the data for such a problem, we tabulated the proportion of subjects who preferred stimulus j to stimulus k. With a complete table of this kind I asked myself if we could write some rational theory that would fit all of the observed proportions. If such a rational theory could be found, and if some of the experimentally observed proportions were erased from the table, we ought to be able to re-construct the missing proportions by means of the theory.
In dealing with a problem of this kind, the first impulse is to obtain the correlation between a pair of columns and to use a regression equation to fill in the most likely missing entries, but this is an unimaginative thing to do. It leaves us no wiser as to the underlying phenomena because the regressionis only an empirical equation. I worked for many months on this problem, longer than I should admit, and finally found the equation of comparative judgment. It is a rational equation that represents a theoretical formulation of the problem. It worked. This solution introduced the concept of the discriminal dispersion which has since been found useful in describing the subjective ambiguity or stability of each stimulus.
The sixth paper deals with the application of the law of comparative judgment to the measurement of social values, namely, the relative seriousness of offenses. There is wide range of application of the new psycho-physical theory in the social sciences. The complete freedom from physical measurement in a subjective metric should enable us to deal quantitatively with a wide range of social phenomena that can be studied as science. I did not then anticipate that the subject could be extended even further to the obverse psychophysical problem in the prediction of choice which did not occur to me until about twenty years later.
In teaching the classical psychophysical methods, there was trouble with several current methods. For example, the phi-gamma hypothesis was found to be entirely inconsistent with Weber's law or with any other law in which the limen increases with the stimulus magnitude. Analysis of this inconsistency led to the paper on the phi-gamma hypothesis which was modified so as to be consistent with Weber's law. The discrepancy of phi-gamma was conspicuous with coarse discrimination, and this characteristic has been experimentally verified.
The paper on the indifference function was the outgrowth partly of my sincere belief that economics could and should be an experimental science. I have found that my colleagues in this field are divided on this question. Some of them deny emphatically that economics could be an experimental
( 17) science, while others welcome the idea. Around 1930 I had many discussions with my friend Henry Schultz, who was a mathematical economist. I was curious as to why he read my psychophysical papers. In our discussions it became apparent that we were interested in different aspects of the same problem. Our discussions were clarified when we considered a three-dimensional model. The two co-ordinates for the base of this model were the amounts of two commodities that were owned by the imaginary subject. The ordinates for the model were measures of utility. If horizontal sections are taken in this model, we have a family of indifference curves, and when vertical sections are taken parallel to the base co-ordinates, we should have Fechner's law. I set up an experiment with one subject to determine whether these relations could be experimentally verified, and the results were quite encouraging. In a current experiment in our laboratory in Chapel Hill we have made an experimental determination of the zero point in a scale of utility with a demonstration that subjective values are additive. I am pretty sure that much economic theory could be experimentally studied in captive populations.
In the next two papers I tried to develop an obverse psychophysical problem. Most of the methods concerned with the subjective metric have for their purpose the allocation of each psychological object to a point in a subjective space which may be unidimensional or multidimensional. When this has been accomplished, we might ask whether it is possible to predict what the subjects will do. This is in a sense an obverse psychophysical problem. I have called it the prediction of choice. As far as the theory is concerned, it matters little whether the objects are people who are candidates for elective office or different brands of canned goods. Even a superficial examination of this problem leads to some curious theorems. It may be assumed that practical politicians have intuitive awareness of some of these results, but it seems equally certain that they would never think of their problems in terms of psychophysical theorems. I doubt whether the pollsters have used these methods so far. It would be an interesting problem for someone to investigate the different systems of preferential balloting as a psychophysical problem.
In the fifteenth paper of this section we have a short summary of new problems in the subjective metric that was presented at a Chicago conference in October, 1953. The main ideas of that report are in improved methods of scaling which are now being investigated in our new psychometric laboratory. In the equation of comparative judgment for a group of subjects, it is assumed that the subjective distribution is normal for each stimulus. For many types of stimuli this assumption is defensible, but for others the assumption is almost certainly not valid. For example, if food preferences are being studied, one can hardly assume that the distribution of subjective values will be normal for artichokes, oysters, or corn bread. The distribution will depend on the selection of the experimental group. The new scaling
( 17) method assumes merely that when a person repeats his judgments, they will show a normal error distribution on the subjective continuum. When the scaling has been accomplished by this assumption, it becomes a question of fact whether the distribution of subjective values for the experimental population and for each stimulus is normal or skewed or even bimodal. This scaling principle is less restrictive than the usual form of the equation of comparative judgments except in Case 1, which is not ordinarily feasible for practical situations. The equation of comparative judgment will still be used, but it will be applied to individual consistency records.
The sixteenth paper of this section is a general summary of the measurement of values in which I tried to show the diverse implications for research of this fascinating field.
