The Measurement of Psychological Value
L.L. Thurstone
THE very title of this paper may strike the reader as a paradox, for how can one measure a value which is admitted to be psychological`? Psychological value has to do with the strength of the desire for an object or aversion against it, and since it is psychological value that we are studying, our analysis must not be limited to physical objects. Our analysis must cover also the value of psychological objects which are not always limited physical entities that may be perceived and possessed.
The object which has psychological value may be a physical object. Its value is measured by the strength of the desire to possess it. This is not the same as the rational evaluation of its utility, because the free air has, by any rational criterion, infinite utility, always being immediately necessary for life. But this object is so common that rarely do we experience any strong desire for it and consequently it does not normally have much psychological value. A basic principle for the evaluation of an object is that a desire for it must be experienced before it can be said to have psychological value. If situations arise in which air to breathe is at a premium, then certainly air takes on psychological value. The concept of value, psychologically considered, is then independent of the rational estimate of the utility of the object, and it is
( 158) also independent of the labor or trouble required to produce it.
The object which has high value may be an idea, a perceptual form, or a certain mode of conduct with which the individual strongly desires to identify himself or which he strongly desires to establish, maintain, or defend. If you very much prefer to associate with Russians rather than Italians, or vice versa, then one of these associations is a higher value than the other. How high is this value in comparison with your preference for Germans as against Spaniards, or vice versa? If you strongly desire to see prohibition continued or established, how much of a value is this for you as compared with somebody else's degree of preference for or aversion against the same object? Or, how much more beautiful is this rug pattern than that one? Is the increment in excellence between these two handwriting specimens twice as great as that between those two handwriting specimens? These are psychological values. It is our purpose to describe the logic by which some of these values may truly be measured with criteria that satisfy our fundamental concepts of measurement.
Some of the postulates underlying physical measurement are so obvious and so common that ordinarily they need not be stated. But when these same postulates are used for psychological measurement they need explicit formulation. One of these postulates is that a measurement describes only one attribute of the object. It would be ludicrous to say formally, when measuring the height of a table, that only one of the attributes of the table has been described; to call attention to the fact that the height measurement really does not state whether the legs are carved and whether the table has any drawers. But it is apparently expedient to make this reservation when we claim to be able to measure attitudes or psychological values. The reservation is that in measuring the degree
( 159) of appetition-aversion in a person's attitude toward an object or the psychological value of that object, we say nothing about the source of the value nor about the history of the attitude. Your attitude toward prohibition and the psychological value which this object has for you cannot be completely described in a single measurement any more than a table can be completely described by merely counting the number of its legs. No matter what the object of measurement may be, the measurement describes only one attribute of the object. An object may be more completely described by measuring several of its attributes.
Another postulate that underlies all measurement is that the measured attribute is always uni-dimensional. Since not all attributes are clearly uni-dimensional, not all attributes can be measured. If you measure the volumes of a series of objects, you are postulating that volume is a uni-dimensional attribute, which is correct in the sense here implied. In certain types of problem, the term dimensionality is used differently; but here it refers very simply to the fact that each object whose volume you measure is allocated to a point in a single linear abstract continuum, namely volume. This universal characteristic of measurement applies also to psychological measurement. If a series of landscape pictures is arranged by a group of judges in order of estimated excellence or artistic merit, it is tacitly assumed that it is possible to allocate all of the pictures to as many points in a single continuum of excellence, no matter how much the judges might object to so direct a statement of what they are doing.
Our first postulate was that measurement describes only one attribute of the object, and this is, of course, also true of the measurement of psychological value. Just as the measurement of the height of a table describes only one attribute of that object, so also the measurement of
( 160) the psychological value of an idea describes only the degree of appetition-aversion of the percipient for that idea, regardless of what, in other detail, the idea may really turn out to be. And just as it is possible to compare a table and a child as to which stands higher from the floor, just so is it also frequently possible to compare in psychological value two disparate objects or ideas as to the degree of appetition-aversion that they arouse in the percipient.
All measurement consists in allocating the object measured to a point in an abstract continuum, as when a sack of flour and a child are assigned to their respective points in the abstract continuum of weight. Similarly, to measure the psychological values of two disparate objects or ideas, consists also in allocating the symbols of the two ideas to their respective points in the psychological continuum of appetition-aversion. Our second postulate regarding the nature of measurement is here also satisfied, namely, that the measured attribute is uni-dimensional.
In all of these examples the essence of a psychological value is the degree or intensity with which we desire to realize, maintain, or protect the object or idea, quite aside from the cognitive complexities of our thought and conduct in respect of the psychological object in question. We shall refer to value as a continuum of appetition-aversion. An object has high psychological value for the man whose positive affect or appetition is strong for it, whether it be a strong desire to own a car, enthusiasm for a presidential candidate, or the idea of spending six months in Europe.
The appetition-aversion continuum implies uni-dimensional variation in the affect that the object calls forth. This affect may be positive, as being friendly toward the idea, admiring it, defending or endorsing it; or it may be negative as being hostile toward it, despising or destroying it. Between these two extremes of appetition and
( 161) aversion lies a neutral zone to which the object is allocated if it calls forth no noticeable affect, either positive or negative. Neutrality in our present sense may express itself as informed neutrality, informed indifference, or as the indifference of ignorance. Other description is necessary to ascertain which of these or other cognitive aspects of the percipient will explain his zero- or neutral affective tone to any object in question. These examples suffice to show the manner in which the psychological values of objects, symbols, and ideas presuppose a linear continuum. It rests on the tacit assumption that the objects, institutions, or ideas that are psychologically evaluated, can be allocated to an abstract continuum of positive and negative affect.
In situations where a sharp contrast exists between the money value of a physical object and its psychological value, we sometimes say that the object has no "real" value but that it has sentimental value. A keepsake, or a souvenir, is often an example of this contrast between economic value and psychological value. There is no doubt some correlation between these two forms of value, but the correlation need not be very close. A student, who is deprived of the privilege of attending a certain football game and who is also deprived of the privilege of buying a new suit of clothes, may actually feel more keenly about the football ticket than about the suit of clothes although the latter has much the higher money value. At the moment considered and for the particular person, the football ticket has, by our definition, the higher psychological value. If he were actually put to the test of choosing between the two objects we should expect him to make what we might designate as the rational choice. His overt action would not necessarily agree with the relative psychological values of the two objects at the moment of choice. However, he might be willing to admit that, other things being equal, he would really get more enjoyment in being
( 162) presented with the football ticket than with the new suit. The choice is rational in so far as it is determined by future as well as present psychological values, so that fundamentally there is no sharp distinction between these two forms of value.
In any attempt to determine these values experimentally, one would guard against complicating the conditions by factors that influence rational choice as against immediate preference, and also one would guard against factors of social pressure. For these reasons it is not always possible to determine experimentally the psychological values of different objects, but it is feasible whenever we can rule out of the experiment these complicating circumstances. For example, the subject may be asked to rank a series of pictures in the order in which they please him, and the result might be a series of psychological values if the subject can be left quite free to make his own preferences without trying to please others, and if there is no ulterior gain for him in making one choice rather than any other. There is a very wide range of stimuli whose psychological values may be experimentally determined without these complicating and invalidating circumstances.[1] We sometimes speak of values to mean the objectives that we live and strive for, such as friends, prestige, money, power, peace, freedom, or Heaven. If we can obtain a man's spontaneous preferences among various objectives or career motives, the result might be a series of psychological values; but to the extent that the decisions are made after rational deliberation, to that extent the results may deviate from the spontaneous preferences which we have called psychological.
( 163)
We have spoken of the psychological value of an object as though it were an attribute of the object but that is not quite correct. Psychological value is an attribute of the percipient or actor, and consequently it varies from one individual to the next and from one occasion to another. It is expedient to assign that value to an object which shall be most representative of the affective states of those who may be concerned about it. When an object or idea has been assigned a psychological value, either descriptive or quantitative, such evaluation constitutes in effect more of a description of a group of people than of the object itself. Since any psychological value may change markedly as it constitutes a description of one group or another, it is clear that the psychological value of an object or idea is entirely indeterminate, except with reference to a stated or implied group of individuals. While we recognize that fundamentally the value of an object is primarily a function of the individual percipient or actor, still it is of some service to use a sort of median attitude of a group of people toward an object as an attribute of the object so long as the fundamental nature of the description is recognized. The degree of universality of the psychological value of an object or idea depends on the relative stability and generality of people's attitudes toward the object. If we should measure attitudes toward the French, for example, the measurements would constitute a description of our group of subjects, and it is pretty certain that the measurements would change markedly from one group to another.
This leads to another fundamental consideration. it is possible to describe the attitude of an individual toward an object by allocating him to a point on the affective continuum. But it is also possible to describe the object by allocating it to the same point on the same continuum. Here we see that the measurement of the attitude of people toward an object or idea, and the measurement of the
( 164) psychological value of the object are identical operations. If the measurement. is used as a description of a person or of a group of people, then it is a measurement of attitude. But if the same measurement is used as a description of the object or idea, then it is a measurement of the psychological value of the object. These two concepts, attitude and psychological value:, as here defined, are quantitatively identical. They differ only in the purposes to which they are put. They are the two faces of the same thing.
It is now clear how the same methods that have been used for the measurement of attitude can be used also for the measurement of psychological value. In one case, we pivot on the group of subjects in order to describe the object, while in the other case we pivot on the object in order to describe a group of people. In the statistical processes there is no difference between the two procedures.
We may refer briefly to several of these procedures with psychological evaluation especially in mind. If a series of objects or symbols of ideas is sealed on a psychological continuum by the psychophysical method of equal appearing intervals, then the resulting scale values will constitute the psychological values of the respective objects.[2] These values have generality corresponding only to that of the group. Change the group of subjects and it is possible that the psychological values of the objects would change entirely, and this is as it should be.
Theoretically, the same procedure may be followed for measuring the psychological values of objects even when only one person is involved ; but in order to make this experimentally feasible, it is necessary that the increments in affective response to the several objects in the series be very small, small enough to be of the same order of magnitude as the variable errors of the affective responses
( 165) of the individual to the same object on repeated occasions. This is entirely possible experimentally, but it is rarely of sufficient interest to make it worth doing. For this reason, the experiments are more readily carried out on groups of subjects rather than repeatedly on the same individual subject.
The method of paired comparison has been used for measuring attitude, and it can also be used in exactly the same manner for determining the psychological values of objects. In the classical form of the method, it has been used for determining the psychological values of tones, chords, and cadences, and of different colors and color combinations. It has been used more recently for measuring the attitudes of a group of individuals toward different nationalities, and the same results may also be spoken of as measurements of the psychological values of these nationalities in the specified group. These values vary of course from one group to another, and the same is true of the values of musical chords which vary with the musical training of the subjects, the consonances being preferred by naive subjects while the dissonances were more often preferred by the professional musicians.
The method of equal appearing intervals is perhaps the only direct method of measuring psychological value, but it does not lend itself readily to tests of internal consistency, and for that reason other methods are preferable. The method of paired comparison is more suitable from this standpoint. We shall now consider this method of measuring psychological value more in detail with special regard to the unit of measurement, and the procedure whereby an essentially subjective unit may be rendered objectively recordable. We shall consider first the simpler case of a single individual repeatedly judging a series of objects as to his relative preference or liking for them. The same reasoning may then be extended with another assumption to the situation where a group of individuals
(166) express their preferences for a series of objects in which each individual member of the group expresses his preferences only once.[3]
Postulate a continuum of appetition-aversion which may also be referred to here as the psychological continuum. The degree of affect of an individual percipient toward a particular object may be described as a point on this continuum. Now, if the percipient repeats his expression of preferences a good many times, it is reasonable to suppose that the degree of affect for a particular object will not always be the same. It will be subject to fluctuations that may be regarded as variable errors. In the practical application of this method, we rarely ask the subject to repeat his judgments a great many times, so that the possibility of recall of previous judgments need not bother us here. With some types of stimuli it is possible to rule out effectively the memory factor, but for many types of stimuli this cannot easily be done. We shall also assume that the repeated judgments are carried out within a period of time (tiring which the subject does not markedly change his attitude toward the several objects. He might give a great many judgments of the stimulus series during one or two afternoons, and he may feel quite differently about these stimuli next week; but during the experimental run, we assume that no constant errors or systematic shift takes place.
Assume that the mean degree of affect for a particular object has been determined for a series of occasions, and that it has been allocated to the continuum as a point. The fundamental assumption of our measurement method is that if a certain value higher than the mean, and a certain value lower than the mean, occur equally often for the one subject who repeatedly perceives the same object,
( 167) then these two points are equally distant from the mean.[4] This seems reasonable enough.
In actual scale construction it is assumed that the distribution of variable errors in the affective value of an object is Gaussian, but this analysis is not necessarily dependent on that assumption. The fact that a stimulus has more or less fluctuating affective values for the same subject on repeated occasions may be described by saying that the stimulus projects a frequency distribution of values on the affective continuum.
Let the probability that the stimulus R1 will be perceived on any particular occasion at any point x on the continuum be designated
y = f(x) ..................1
Then it is clear that
..................2
because the sum of these probabilities for all points along the continuum must equal unity.
A second stimulus R2 projects a similar distribution of values on the same continuum, and we shall assume for simplicity that these two stimuli have the same degree of ambiguity so that the dispersions are the same or at least of the same order of magnitude. The two distributions will then be identical except for displacement along the continuum as a base line. The projection of the second stimulus will then have the equation
y = f(x-a) .................3
(168) in which a is the displacement between the two means, and
..................4
Now, the probability that R1 will be perceived at any value x on the continuum is
y = f(x)
and the probability that R2 will be perceived at a value higher than x on the same continuum is
Therefore the probability that R1 will be perceived at any value x and that the simultaneously perceived stimulus R2 will, on the same occasion, be perceived higher than x is the product of these two probabilities, or
But what we want to know is the probability that R1 will be perceived higher than R2, irrespective of where R1 is perceived. Therefore
If, for experimental purposes, the function f(x) is assumed to be Gaussian, then the scale separation a between the two stimuli may be expressed as a function of the ex-
( 169) -perimental observable proportion F2>1.[5] The statistical detail for calculating these scale separations have been previously described as Case V in the application of the law of comparative judgment.[6]
A very important consideration in rendering objective a value-increment that is essentially subjective is that as long as each of these psychological values is considered separately, it can never register objectively. Every scientific observation is, in fact, a comparative situation and neither of the terms of a percept can be objectively recorded in isolation. This is true of cognitive as well as of affective comparison. If we are willing to make the underlying assumption that the distribution of variable errors of affective values is symmetrical, as for example that it is Gaussian, then the scale separation between two stimuli on the subjective continuum can be measured as a function of the relative frequency with which one of the stimuli is actually experienced as higher, larger, heavier, better, or preferable, to the other. It is in this manner that an experienced value-increment, either cognitive or affective, which is essentially subjective may be quantitatively described. The psychological continuum which in the older psychophysics was a cognitive one, as well as the affective continuum of the present discussion, is of course an abstract continuum that serves purposes of description just as the more common but equally abstract continua of weight, volume, temperature, length, or area. Neither type has more physical reality than the other.
In developing a system of subjective measurement for affective as well as for cognitive values, the central prob-
( 170) -lem is the unit of measurement. Our unit for psychophysical measurement is the discriminal error, the standard deviation of the projection of a standard stimulus on the continuum.[7] This is an operational unit which has the same meaning when it is carried out in different parts of the continuum.
Measurement with this unit does not presuppose that a sensation or subjective experience has as such any magnitude or intensity. The old question, whether Fechner's law assumes that sensations have magnitude is entirely irrelevant with this unit of measurement. We are reinterpreting Fechner's law and the other psychophysical concepts in a manner which entirely avoids this dilemma. We are postulating that the sensation, the subjective moment, the cognitive or affective value as actually experienced, may be entirely devoid of magnitude or other quantitative attributes. That which we are measuring is not necessarily a part of the subjective experience itself. It is merely the frequency with which its external symbol is experienced as subjectively equivalent to some other symbol. If the two symbols or stimuli are declared by the percipient to be equivalent with regard to the cognitive or affective value under consideration, then the two symbols are said to be of the same value, or the two experiences are then assigned to the same point on the psychological continuum. Psychological measurement is then a measurement of frequency of discrimination, or frequency of confusion, with the assumption that if two symbols are frequently confused with regard to any specified form of value, then the corresponding subjective experiences are to that extent very similar and they are therefore assigned a small separation on the psychological continuum. To the extent that the two symbols are frequently discriminated, to that extent the subjective counterparts
( 171) must be very different so that they are assigned a larger separation on the psychological continuum. We are interpreting the s-variable in Fechner's law, and the corresponding s-variable in psychological measurement generally in this manner so that the measured psychological increment between two symbols or stimuli is a function of frequency of subjective similarity, i. e. frequency of confusion. Our measurements of subjective increments, therefore, do not impute any quantitative attributes to the momentary subjective experience as such. This reformulation of the psychophysical concepts clears away many of the disputed issues and paradoxes which filled the older literature on this subject.
The method of paired comparison can be extended for application to a group of individuals each of whom expresses himself only once, as contrasted with the older psychophysical experimentation on a single subject who repeated each comparison several hundred times. The extension can be effected, if we are willing to assume that the distribution of value-increments between any two stimuli is a Gaussian distribution for the group in question. In most situations this is a fair assumption, but it would be easy to constitute a statistical group for some stimuli so that this assumption would almost certainly be violated. If a list of ten American presidents and presidential candidates were submitted to a group of Protestants and to a group of Catholics, combined into one group for statistical purposes, and if comparative preferences were called for, it is possible that each of the names would project a Gaussian distribution on the affective continuum, but it is quite certain that the distribution projected by Al. Smith would be bimodal. One mode would probably be very high. However, a statistical device is available for discovering such situations, namely the criterion of internal consistency.
The criterion of internal consistency is one which is
( 172) tacitly assumed in all physical measurement, but it needs explicit statement for psychological measurement. If several points, a, b, c, d, are designated on a straight line, the linear distance between any two points such as a and c can be ascertained by adding the separations in any order. For example,
(c-a) = (b-a) + (c-b)= (d-b)+(b-a) - (d-c) = etc.
This additive criterion is part of common sense in dealing with linear space. If the same four points represent as many objects that have been assigned to a psychological continuum, the additive criterion applies in the following manner. Each subject in the group is presented with every one of the (n(n-1))/2 possible pairs from the series of n objects. For each presented pair of stimuli he expresses a preference. For the whole group this gives the experimentally observed proportion of judgments F2>1 for each presented pair of stimuli. Each of these experimental proportions gives a measured scale separation between the two stimuli. If any one of these stimuli be taken as au origin of measurement, all the others may then be allocated to their respective points on the continuum. The criterion of internal consistency, the additive criterion, now demands that the distance between any two points on this line should agree with the experimental determination of the separation between these two points. This condition must be satisfied within the errors of measurement for all the possible pairs of stimuli in the series. No quantitative description of anything can be called a measurement except in so far as this additive criterion is satisfied. It is so obvious in physical measurement that it need rarely be stated. If, for a particular set of data, the criterion is not satisfied, one of several inferences may be drawn. It is possible that the distribution of affect toward each of the stimuli in the experimental group is
( 173) not Gaussian. It is possible that the criterion will exclude only one or two stimuli and that the rest of the stimuli do satisfy the criterion. If the whole series of experimental stimuli fails to satisfy the additive criterion, it may be possible that the assumed functional relation between the experimental proportion F2>1 and the corresponding scale separation between the two stimuli is incorrect. In a recent experimental study of national and racial preferences it was found, for example, that the additive criterion was satisfied within the errors of measurement for all of the twenty stimuli except that of "Jew." Our inference was then that the distribution of affective values for this stimulus in the experimental group was not Gaussian as our theoretical formulation had assumed. The discrepancy was not so gross but that it was still possible to allocate even this stimulus to the affective continuum, although its scale value has a larger probable error than those of the other stimuli in the list.
Our analysis of the possibility of measuring psychological value may be summarized in terms of several of the principal concepts involved. A measurement of anything is limited to the quantitative description of one attribute of the object, and it is further limited by the fact that the attribute must be uni-dimensional in character. Just as all measurement implies a uni-dimensional continuum, so also the measurement of psychological value implies a linear psychological continuum. In the older psychophysics this continuum was a cognitive one such as apparent weight, brightness, or loudness as distinguished from the continuum of physically measured weight, brightness, or loudness. Fechner's law is a statement of the functional relation between the psychological and the physical continua. In the present discussion we are postulating in a similar manner an affective continuum of appetition-aversion. These two types of psychological continua differ in that the cognitive one can
( 174) be matched or compared with the corresponding physically measured stimulus magnitude; whereas, the affective continuum has no such physically measured counterpart.
The attitude of a person toward a psychological object may be described by a point on this affective continuum. If this point or measurement is used to describe the person, we call it a measurement of the person's attitude toward the object. If this same point is used to describe the object, then it is a measurement of the psychological value of that object. In this sense, the measurements of attitude and of value are identical processes. The same psychophysicaI methods that have been used for measurement of cognitive values of stimuli can also be used for measuring the attitudes of people toward the object and for measuring the affective value of the object in terms of the percipient. The unit of measurement along the psychological continuum is the discriminal error. Finally, the validity of any measurement must satisfy the criterion of internal consistency. The uni-dimensionality of the scale values of the stimuli is demonstrated when this additive criterion is satisfied.
