On the nature of subjective scales

Sccindinaviun Journal of Psychology, 1982,23, 161-171

On the nature of subjective scales

HANNES EISLER University of Stockholm, Sweden

Eisler, H.: On the nature of subjective scales. Scandinavian Journal of Psychology,

A number of problems connected with psychophysical scaling are pointed out and solu- tions suggested. The importance of searching for invariant relations (“laws”) is stressed and the advantage of dealing with intrasubjective relations-thereby avoiding the “physicalistic trap”-is emphasized. Two series of experiments, concerning time perception and similarity, are discussed and it is concluded that they support the validity of subjective scales. Finally the role of the observer in scaling experiments is commented on. H . Eisler, Department of Psychology, University of Stockholm, Box 6706, S-11385 Stockholm, Sweden.

1982,23, 161-171.

When I was a child, it was a game in the family to indicate our well-being on a 20-point scale. The only trouble was, as I recall vividly, that we tended to confuse the two poles: did “20’ imply intense well-being or the opposite? Anyhow, this probably was my first encounter with a subjective scale, and although some time has elapsed, I am still inter- ested in subjective scales and entangled in the problems they pose. Another snapshot, from the comic strip “Dennis the Menace”: on leaving the house one winter morning the five-year-old boy observes, “Today it’s twice as cold as yesterday”. The point of this introduction is simple: associating experi- ences with numbers, i.e. measuring them, is by no means as artificial, as scientifically abstract, as is often claimed.

My aim here is not to give a historical overview of the development of scaling-for a brief and rather exhaustive one I recommend a recent paper by Warren (1981). What I shall do instead is to attempt to convey my feeling of the reality or sub- stance of subjective scales. But the main content of this paper will be a list of caveats, gathered from a sequence of encounters with failures and stumblingblocks. We shall see what can be distilled from them concerning the nature of subjective scales.

Science in general can be regarded as a two- party game: the scientist against Nature (which wants to keep its secrets). Psychology, and espe- cially psychophysics in its broader sense, seems

to me to be a three-party game; the third member being the observer. I shall try to delineate the inter- play between these three parties.

THE SCIENTIST, NATURE, AND PROBLEMS O F INVARIANCE

Let us imagine a category rating experiment with three easily discriminable stimuli and a three-point scale. The experimenter defines the weakest and the strongest stimulus as 1 and 3, respectively, presents the three stimuli a number of times in irregular order to his observer, and will certainly obtain ratings of “ 1” , “2”, and “3” for the stimuli. Thus, he has erected a category scale for the continuum investigated. However, this scale is completely determined by the scientist-as a matter of fact, there was no need to carry out the experiment. This caricature experiment illustrates a risk inher- ent in all scale construction: the information obtained may be about the scientist rather than about Nature. Let me now take two more established examples.

The first is the well-known Fechner scale. By some method, say the method of constant stimuli, just-noticeable-differences (JNDs) are determined and added together one by one, resulting in a subjective scale, characterized by Stevens (1960) as a confusion scale. As opposed to the “sham” three-point category rating experiment mentioned before, such a scale is built on a series

I 1-821942 Scundinoviun Journal of Psychology, 23

162 H . Eisler

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Fig. 1. Magnitude and category scales and their relation for loudness of white noise. A and B differ only in the spacing of the ten stimuli. Upper left panel: Log magnitudes as a function of sound pressure level in db. Note that the psychophysical function approximates a power function for spacing B, but not for spacing A. Upper right

panel: Category scales as a function of sound pressure level in db. Lower panels: Category scales as a function of magnitude scales. The curves in the upper right and the lower panels constitute category scales as predicted by the GPDE from the magnitude scales and the subjective Weber functions. (Data from Eisler & Montgomery, 1974.)

of experiments, viz. the determination of the JNDs, the outcome of which is not as predictable as in the former cases. And there is no ban on adding JNDs. Still, the confusion scale is a pure construct of the scientist-it does not have the characteristics of a law of nature. [Others (e.g. Gregson, 1980) would prefer the term “models of invariances” instead of the word “laws”.]

The other example I want to mention is the Thur- stonian scale. In a way, the arbitrariness of this kind of discrimination scale is still more obvious. Typically, it is based on paired comparisons in which the observer is required to indicate which of the two stimuli in a pair is stronger. This ordinal judgment is then considered to indicate a difference and the scale construction is built on this implicit assumption. As I have shown (Eisler, 1963, taking

the ordinal judgment to indicate a ratio instead, leads to another scale, both scales being data- equivalent.

Before drawing certain conclusions, I wish to touch on the problem of invariance. In the first of the three examples, the invariance is very low. The range within which a middle stimulus is as- signed the category value “2” is wide (cf. Witte, 1960) and thus for each new middle stimulus a different “scale” is obtained. To avoid a similar arbitrariness for the JND-scale, we have to impose the uniqueness requirement that different values of the discrimination index (e.g. the cut-off point when using the method of constant stimuli) yield scales that agree within a linear transformation. This condition is fulfilled only when Weber’s law holds (Falmagne, 1971; Luce & Edwards, 1958).

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Subjective scales 163

For the Thurstonian scale the internal data structure of the frequencies of “stronger” judgments poses restraints on scalability, but the two scale alternatives, being data-equivalent, remain.

The construction of confusion scales is often termed “indirect measurement.” My personal view regarding these scales is that the scientist’s contribution to the scale construction too greatly ex- ceeds the contribution of Nature to make them really interesting.

Let us look at the other endpoint of the scientist- nature continuum, direct scaling. We know, from the work of Stevens and followers, that, say, magnitude estimation results in a power function, showing a straight line when subjective magnitudes are plotted against physical ones, both in logarithmic coordinates. Look at A in the upper left panel of Fig. 1. It shows a log magnitude scale for loudness against decibels for an experiment carried out by Henry Montogomery and myself (Eisler & Mont- gomery, 1974). The relation is definitely not linear, unlike B. The two experiments differ only in the spacing of the stimuli. Accordingly, the power law is not invariant. I would remind those who want to seek refuge in category scales (the “direct pipeline to the psyche”, according to Parducci, 1978) that category scales are even more vulner- able to context effects than magnitude scales. Finally, I want to mention Warren’s (e.g., 1981) “physical correlate theory”, according to which subjective scales are based on estimates of physical dimensions.

So what are we left with? We have confusion scales which, even when showing invariance prop- erties, represent more of the scientist than of Nature, we have magnitude (and category) scales with their apparent lack of invariance, and we have physical scales, which, according to one theory, are the true base of subjective scales. This seems rather chaotic. Can we impose some order?

Ideal and real laws Fig. 1 shows an instance of a strong departure from Stevens’ psychophysical power law. An observation like this seems to be much more disconcerting for a psychologist than a similar one would be for a natural scientist. The latter knows that the simple laws she is working with rarely hold precisely and often not even approximately. The gas laws, for instance, are valid only for permanent gases, or gases with low pressure and high temperature, i.e.

under ideal conditions. For many theoretical considerations it is fruitful to work with ideal conditions; in other contexts a description of the departures is both theoretically interesting and practically necessary; in industrial application, for example, it is often necessary to measure the variables accurately instead of computing them from a natural law. I have previously tried to advocate a similar view in psychology (Eisler & Montgomery, 1974; see also Eisler, Holm & Montgomery, 1979). Arguing along these lines, the power law can be considered the ideal case for the psychophysical function connecting a subjective with a physical scale.

The argument above refers to a scale obtained by magnitude estimation. Such a scale allows checks as to departures from the power law, and studies of invariance over, e.g., stimulus sets, but there is no possibility of checking the internal consistency of data. This is possible, however, in the method of ratio estimation, in which the observer is presented with all possible pairs of the stimulus set and required to judge the ratio between the two stimuli comprising the pair, say the weaker as a percentage of the stronger. Let us denote the estimated ratio between stimuli i a n d j qu=Y#Pj, qi being the subjective scale value for stimulus i . In- ternal consistency, a necessary condition for scale construction, requires for v i < v k < \ v j that qu = q i k ‘ q k j . A similar equation has to hold for each tri- plet of stimuli. Typically, this condition is not fulfilled for the raw data. Transformation of the estimated ratios by multiplying with a constant, however, does usually yield the required internal consistency (Fagot, 1978; Goude, 1962; see also Eisler, 1960) and thus allows the construction of a subjective scale 9. Accordingly, the transformed ratios may be considered as “ideal” ratios in the sense mentioned above. There are two more points to be made regarding ratio matrices. The first is that the problem of internal consistency is completely independent of the existence of physical measures of the stimuli (except on the nominal level). It can be investigated for stimuli like beauty of handwrit- ing or goodness of vegetables, for which no physical scale exists. It is a purely psychological problem. We shall come back to this important point shortly in a more general way. The other point is of an epistemological nature. What are we to regard as the percept: the ratio yij as given by the observer, or the transformed ratio that gives an internally

Scundinuuiun Journul of Psychology, 23

164 H . Eider

consistent ratio matrix? Is it all meaningful to speak about the perception of a ratio? Conceivably, the observer perceives the two stimuli of a pair separately and subjects them to mental (or, to be up-to-date, cognitive) operations corresponding to division, the result of which is given as the response. However, the observation that the SD of an estimated ratio depends on the ratio only, inde- pendently of which particular pair of stimuli pro- duces the estimate (see Eider, 1960), speaks strongly against this conception. Perhaps here it is advantageous to make a distinction between object- and metalanguage. The transformed ratios allowing scale construction belong to the (scientist’s) metalanguage, whereas the ratios as given belong to the object language and can suitably be seen as the observer’s (inconsistent) percepts. However, we should not completely exclude the possibility of assuming consistent percepts and attributing the inconsistency of the ratio judgments to response bias instead.

lntrusubjective relations Intrasubjective relations are relations (“laws”) ob- taining between subjective variables. The first example I want to give is the relation between category and magnitude scales (for the same stimulus set). This relation can be derived from the General Psychophysical Differential Equation (GPDE, see, e.g., Eider, Holm & Montgomery, 1979)

wherey denotes the category scale, x the magnitude scale, and W their corresponding subjective Weber functions, i.e. the uncertainties as functions of the scale values. Consider Fig. 1 once more. We see that for two data sets that differ in the spacing of the stimuli, the psychophysical functions are quite different, but the GPDE is valid for both, since the category scales can be determined by means of Equation 1. [It may be of interest to note that the CPDE has been confirmed also for other than sensory stimuli, viz. social concepts (Shinn, 1974).] In order to understand the problems connected with this finding, let me simplify and formalize somewhat. Assume that a relation exists between :wo subjective variables y =f(x), and a relation 7etween the subjective variable x and the corre- iponding physical stimulus measure X: x = g ( X ) .

Ycandinauian Journal of Psychology, 23

With overall invariance we could uniquely predict y from X:

However, this can be done only in exceptional cases. When, e.g., another stimulus set is used, function h (i.e.fand g) will not predict y any more. How should we handle an observation like this? Abandon bothf and g as general descriptions of Nature and sadly state that there is no generality in psychology? Can we get away with abandoning one only, and, if so, which one? In part, the answer depends on the problem to be solved. If we regard x as a percept that may vary with context, then we have to abandon g as an invariant relation and can keepf. This manner of thinking implies giving up what I call psychophysical invariance and retain- ing the intrasubjective relation, i.e. saving perceptual invariance. This is the position I would recommend. We may also attempt to work with “ideal” scales for which g is fixed and f hopefully is un- changed. Then equation 2 would hold, but we would miss the generality, i.e. independence of context of many intrasubjective relations.

Renouncing psychophysical invariance has a number of interesting consequences. For instance, Torgerson (1965) found, when carrying out multidimensional scaling based on judged differences of stimuli varying in shape and size, that the subjective space was practically the same for two sets of stimuli, differing in the range of sizes. He showed that “. . . similarity does not exist as a unique, invariant relation between a pair of stimuli . . .”, and attributed this finding to context effects. I think Torgerson’s way of putting things obfuscates the issue; there does seem to be a unique relation between similarity (or difference) and the percepts of the two stimuli constituting a pair; it is rather the relation between the stimuli (described in physical terms) and the percepts which is hit by the context effects: lack of psychophysical invariance.

Torgerson is not the only victim of this “physicalistic trap”. On the contrary, in many discussions I have found it surprisingly difficult to get my ideas across, viz. the dropping of physical measures in favor of studying relations between subjective variables. I shall therefore give a few more examples. Beals, Krantz & Tversky (1968) axiomatized multidimensional scaling. Their axioms, however, are practically untestable, because they require


subsets of the stimuli that vary in one dimension only, or that vary in all but one dimension. The term “dimension” is not explicated as referring to psychological dimensions, which, of course, is not necessary under the (not stated) assumption of psychophysical invariance. If there were a one-to- one relation between a physical dimension and its subjective counterpart, independent of the values of the other dimensions, it would be easy to keep a subjective dimension constant by not changing the stimulus values on that corresponding physical dimension. The implicit assumption of psychophysical invariance for rectangles led Krantz & Tversky (1975) to conclude that neither of the two dimensional structures subsumed by them is ac- ceptable: again an instance of the physicalistic trap. Wender (1971) used the same type of stimuli as Krantz & Tversky and his findings and conclusions parallel theirs. That there is no reason to abandon the axioms of multidimensional scaling on the basis of Krantz & Tversky’s (1975) data, i.e. that perceptual invariance can be retained, is nicely demonstrated by Schonemann (1977), who succeeded in constructing transformed physical measures which were one-to-one to the subjective ones. In this way he achieved both psychophysical and perceptual invariance for rectangles, though at the cost of having to use rather contrived and ‘‘unnatural” physical measures.

The same confusion between physical and subjective measures can be found in functional measurement (e.g. Anderson, 1970) and conjoint measurement (Luce & Tukey, 1964; cf. also, e.g. Krantz & Tversky, 1971). Let us take a simple example, Brown’s (1931) law, according to which subjective length I, time t , and velocity v combine in the same way as their physical counterparts: 1 = t.v. Think of an experiment in which an observer is presented with a point that moves for a certain duration at a certain speed and is to estimate the path length for all combinations of a number of durations and a number of velocities (cf. Mashhour, 1964). We replace the multiplication in Brown’s law by addition, using the logarithms of the length estimates and insert them into a matrix, each ele- ment of which thereby corresponds to a combina- tion of a duration and a speed. To investigate the validity of our model (Brown’s law) we subject the matrix to an analysis of variance and test for the significance of interaction. If there is no interaction, everything is OK and Brown’s law is

supported (neglecting the risk for a type I1 error). But if there is an interaction, a largely unregarded problem of interpretation arises. Either our model is wrong (the common conclusion) or we do not have psychophysical invariance. If the percept of time also depends on velocity, and vice versa, then Brown’s law may well be correct, despite the interaction. Remember that the elements of the matrix are obtained for combinations ofphysical measures of time and velocity. (Anderson, 1977, calls this type of interaction stimulus interaction.) I did not mention explicitly this building principle of the matrix above to demonstrate how easy it is to fall into the physicalistic trap. Did you notice that rows and columns of the matrix correspond to physical measures? A valid test of Brown’s law presupposes that the rows and columns of our matrix represent constant subjective values of duration and speed, not physical ones. Models like Brown’s law are psychological models, laws describing relations between subjective, not physical, variables.

The risk of getting caught in the “physicalistic trap” is not limited to strictly psychophysical problems. The subjective expected utility (SEU) model might be a case in point. Somewhat simplified, the model says that the subjective expected utility of an uncertain event is the product of the subjective utility u of the event and the subjective probability p of its occurring

SEU=p-u . (3)

Equation (3) was mostly not supported empirically (Slovic, Fischhoff & Lichtenstein, 1977). The reason for this (apparent) failure may well be that the experiments and the ensuing data treatment built on the assumption that subjective probability is independent of utility, and subjective utility independent of probability, i.e. on the probably in- correct assumption of psychophysical invariance. It is conceivable that Equation (3) might hold if scale values for subjective utility and probability are obtained for any one pair of their “objective counterparts”.

THE VALIDITY O F SUBJECTIVE SCALES

The validity of subjective scales, particularly those obtained by direct scaling methods, has often been doubted. I want to give two examples from my own


166 H . Eisler

Fig. 2. One of the stimuli in the similarity study by Eisler and Roskam (1977a, 1977b). For all 15 stimuli in this study, the lower left point is not changed, whereas the other point is positioned at any of the 15 intersections between horizontal and vertical lines.

research which I at least regard as convincing support for the concept of real, valid subjective scales. The first example is a series of experiments concerning similarity, the second concerns time perception.

The similarity study: Converging operations A detailed description of the experiments, the data treatment, and the results of this investigation can be found in Eisler & Roskam (1977~7, 19776). Here I shall dwell on a few points, pertinent to our dis- cussion.

The set of stimuli presented to the observers was the same in all part-experiments. Each stimulus consisted of two luminous points, one of which can be considered to be positioned in the origin of a two-dimensional coordinate system, the other at any of 15 positions in the first quadrant. Fig. 2 shows one of these stimuli, though with a grid added for clarity and the points in black instead of luminous. The observers were presented with pairs of these stimuli and required to make estimates according to the following five different instructions.

1. Similarity rating. (“Estimate the similarity between the two point patterns on a scale between 0 and 10.”)

2. Commonality ratio rating. (“The two point patterns have something in common. Estimate the

fraction the common part constitutes of the left/ right pattern.”)

3. Multidimensional ratio rating. (“How much of or how many times can the sensation produced by the leftlright pattern be found in the right/left pattern.”)

4. Length estimation. (“Estimate the length /distance between points/ of the variable as a percentage of the standard.” The standard was the stimulus with the greatest distance.)

5 . Angle estimation. (“Estimate the angle of the variable with the horizontal as a percentage of the standard.” The standard was at right angles to the horizontal.)

These are not the verbatim instructions but they should suffice to convey the observers’ tasks. What I want to demonstrate is that the observers share an invariant subjective space corresponding to the stimulus set, and that (most of them) are able to carry out the instructions, taking the necessary variable values from this space. The correctness of this statement is shown by the possibility of predicting the ratings from each other, based on the same theoretical network. Let us describe each percept (evoked by a stimulus, that consist of two luminous points) as a vector in space with length h . Let the angle between the two vectors representing percept i and perceptj be cpu. The theory states that

2.min ( h i , h j ) 1. Similarity sii = COScpij,

hi +hj (4)

min (hi, h j ) 2.Commonality ratio cii= COSRjOii, ( 5 )

hj and

3. Multidimensional ratio 9ii =- coscpii. (6)

There are many possible ways of treating the three data sets according to the proposed theory. Let me here mention the following outcome. Taking similarity as reference, commonality ratio rating data yielded coscp in agreement with similarities, and multidimensional ratio ratings gave vector length h in agreement with similarity. Vector lengths computed from commonality ratio estimates, and coy0 values computed from multidimensional ratio estimates, showed discrepancies and required one- and two-parameter transformations, respectively. Fig. 3 shows how well the similarities are predicted from vector lengths, computed from multidimensional

hi h j



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Fig. 3. Similarity as a function of vector lengths (from multidimensional ratios) and cosp (from commonality ratios). (From Eisler & Roskam 1 9 7 7 ~ . Copyright 1977 by North-Holland Publishing Company. Reprinted by permission.)

ratio rating data, and c o v values, taken from commonality ratio rating data. Also, with these vector lengths and coscp values, the scalar products h$h, coscpii were computed and the matrix was sub- jected to component analysis. After rotating to best fit with the length and angle estimates, estimated length and angle were plotted against the first two dimensions. Fig. 4 shows the fit. I think these last

two figures demonstrate convincingly the validity of subjective scales.

Time perception One of the objections levelled against the validity of subjective scales is that, say, magnitude estimation reflects an observer's number behavior rather than her perception. As I was able to show (Eisler, 1975) in an experiment requiring the observer to repro- duce a time interval (the standard duration @, sec), the response given (the variable duration @" sec) is subjectively half of the subjective duration corresponding to the physical sum of standard and variable. Using Stevens' power law with exponent p and subjective zero a0 we thus obtain:

(7)

If the experiment comprises a few standards, Equa- tion 7 allows us to compute p and @,, and we can thus construct the subjective scale for duration. Note that the task is number-free (from the point of view of the observer), and thus cannot reflect number behavior. In a series of experiments I had observers not only carry out duration reproduction, but also duration halving, duration doubling, and magnitude estimation of duration. The exponents obtained agree wuite well with each other (with one exception, to be mentioned below), supporting the validity of the subjective duration scale by converging operations. In order to test the generality of the

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COMPUTED L E N G T H

Fig. 4. Ratings of length and angle plotted against length & Roskam 19776. Copyright 1977 by North-Holland and angle as predicted from the coordinates of the first two dimensions of the component analysis. (From Eisler

Publishing Company. Reprinted by permission.)

Scandinavian Journal of Psychology. 23

168

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Fig. 5. Equal settings for Subject 1. A: Response duration Qv as a function of total duration Q. The lines are fitted by least squares. B: Subjective duration as a function of physical duration, showing the two segments of the psychophysical function. Open circles refer to standards, closed circles to variables. The ordinates of the points are computed; their abscissas are empirical values. (From Eisler 1975. Copyright 1975 by American Psychological Association. Reprinted by permission of the publisher.)

model, and the scale, I collected more than 500 exponents for subjective duration from the data of 11 1 studies based on a variety of experimental procedures, and covering the period 1868-1975 (Eisler, 1976). Though both interindividual scatter and scatter due to experimental procedures were far from absent, the general agreement was very good. [The model also worked well when applied to duration discrimination rather than duration scaling (Eisler, 1981). The exponents for duration obtained in this study were only slightly different from the average given in Eisler (1976).]

Finally, an observation that convinced me more

than anything else that subjective scales are not just constructs of the scientist, bur real, even if not directly observable. According to the model for duration reproduction, when the reproduced duration is plotted versus the total duration (both in physical measures, say sec), a straight line is obtained. Many of the observers showed two straight lines, differing in slope and intercept, and a few showed three. Consider the example in the upper panel of Fig. 5. The interesting feature is that the discontinuity between the upper and the middle line lies at an ordinate of 4, and the one between the middle and the lower line at an abscissa of 4. The explanation is found in the lower panel, which shows the psychophysical function. This function has a break at 4 sec (implying different scale units and/or different subjective zeros for the upper and the lower segment). These two segments of the psychophysical function imply three straight lines: one, for which both standard and variable lie on the upper segment, one for which both lie on the lower segment, and the middle one, for which the standard lies on the upper and the variable on the lower segment. This means that, contrary to the common finding that complicated data require a still more complicated theory, there is a simple explanation. One discontinuity in the psychophysical function entails two in the data, as just shown.

THE OBSERVERS PART IN THE GAME

In psychophysical experiments, the instruction should convey to the observer (i) which features in the stimulus or stimulus aggregates she is to attend to, and (ii) how this information is to be processed. It is not uncommon for this communication to fail, and I shall give a few examples together with suggestions how such failures can be discovered and handled.

A necessary condition to obtain valid responses is what I would like to call the naturalness of the task, where by naturalness I mean that the observer is not forced to apply a conscious or semi-conscious strategy to generate the required response. If the responses of a group of observers are heterogeneous (e.g. if they split into a number of sub-groups when a factor analysis is performed with observers as variables), there may be good reason to suppose that the task was not a natural one. In an experiment studying the subjective attributes of visual textures (as in walls, etc.) I had observers estimate



the subjective variable “texture-strength’’ (Eisler & Edberg, 1982). When the stimuli consisted of real textures, like cardboard, wood, burlap, marble, there was pretty good agreement between the observers. However, the use of “stylized textures”, viz. dot patterns, subdivided the observers into groups. The conclusion we drew was that texture- strength is indeed a natural attribute of real textures, but not of dot patterns. However, the division into sub-groups does not necessarily imply un- naturalness. In the same investigation, observers who judged the pleasantness of the same real textures, likewise showed low interindividual agreement. In this case it rather indicates interindividual variation of taste.

Another instance of an unnatural task is one which requires observers to judge similarities of pairs of stimuli that vary in dimensions that cannot be combined or unified in a self-evident way, like Shepard‘s “rim and spoke” stimuli, circle contours varying in size with radii varying in inclination (Shepard, 1964; Eisler & Knoppel, 1970). For these stimuli, the observers clearly used different strategies, and most of them even switched their strategy unsystematically betweeen the stimulus pairs presented.

Another problem arises when the observers con- sistently interpret their task in a different way from the researcher. An example of this is the duration reproduction experiment mentioned above. What I expected in carrying out this experiment was that the observer would store the standard duration, probably in her longterm memory, and compare this memory content with the variable duration. I also expected that the response would not be veridical, possibly due to some memory distortion. But the data simply did not make sense when looked upon from this preconception; I had to attempt to find out what the observers really were doing, and arrived at the description given in Equation 7.

There are also instances in which observers dis- obey instructions by trying “an easy way out”, i.e. by replacing a more demanding task by an easier one. (According to Norman’s, 1981, categorization of slips this is referred to as a “mode error”.) In the similarity study mentioned in a previous section, observers were required to carry out commonality ratio ratings. A commonality ratio for the same pair of stimuli should differ according to which of the stimuli is designated the standard. In my first attempt at the commonality ratio instruction, the ob-

servers estimated ratios that showed no such difference. A comparison with the (necessarily symmet- ric) similarity ratings showed that they had rated similarity instead, an easy and natural task for these stimuli. I had to replace this group of observers by a new one, who were taught set theory, as it were, with Venn diagrams, before their real task. Then, the majority of the observers followed the instruction as intended, as was demonstrated by their judgments depending on the standard, yielding the relations to the other kinds of ratings as described before.

A final example, derived from the time perception studies. Reproducing duration is an easier task than halving or doubling duration. Two of my 12 observers (Eisler, 1975) reproduced durations instead of halving them as instructed, which entailed poor agreement between the exponents calculated from reproduction and halving data (assuming in- correctly that all observers followed the instruction), as mentioned in the section on time perception. The same thing happened in a corresponding experiment carried out by Allan (1978). As the data clearly show, one of her four observers reproduced the standards rather than doubling them, as required.

SUMMING UP

The case I have tried to make is that for the reality, validity and-to a certain extent-generality of subjective scales. I want to summarize what I have said in a number of rules. These rules express my personal opinion regarding problems arising in the field of scaling. I am sure that not everybody would endorse them. (1) For any one scale, be careful to distinguish between the contributions of Nature and the scientist. (2) If the interest focuses on the scale itself, try to use ideal (or standard) conditions for its construction. The sone scale is a good example. (3) When the interest focuses on psychological laws of nature-intrasubjective relations-it is often a re- commendable strategy to abandon psychophysical invariance and regard an estimate, etc. as the (often inconsistent) percept. Keep perceptual invariance. (4) Avoid the physicalistic trap. Be careful in your conclusions when working with a factorial design- are you investigating relations between physical or psychological variables? (5) Don’t rely blindly on your observers. Try to find out what they are really doing.


170 H . Eisler

OUTLOOK

I am often asked about the usefulness of working with subjective scales. Perhaps somewhat provoca- tively, I usually answer: There is, 1 hope, none. The intention of this answer is to underline my view that the gaining of knowledge is an en- deavour worth pursuing for its own sake. But, of course, subjective scales have applications in, e.g., human engineering or the study of environmental immissions (noxious stimulation).

However, I want to point out two other uses which I envisage-not entirely facetiously-for the future. One is the settlement of interpersonal con- flicts. Assume that a married couple disagrees on whether to buy a new car or take a vacation trip. They could indicate their preferences quantitatively and the issue could be decided according to the relation between the preference values. Numbers might prove more efficacious (and less disruptive) than statements like “I feel more strongly about that than you.” Of course, there might be some difficul- ty with the interindividual comparability of the subjective scales, though this does not seem to be in- tractable. And there is no reason to suppose that they would try to cheat more in this connection than in others.

Finally, the stability of the party political system in Western democracies is under pressure, since many issues which produced the present party structure have diminished in importance and new issues have arisen which seem to split the parties. Take, for instance, the problem of environmental pollution, where very different opinions are found within parties. I imagine that, rather than electing parties, the voter could quantitatively indicate her set of values. These ratings, after adequate process- ing, should determine subsequent policy.

If as a child I was able to use a 20-point scale, why should the voting behavior of adults be con- fined to simple qualitative choices?

This work was supported by the Swedish Council for Research in the Humanities and Social Sciences.

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Anderson, N. H. Functional measurement and psychophysical judgment. Psychological Review, 1970, 77, 153-170.

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Documents

On the nature of subjective scales