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INTERVAL MEASUREMENT of Sljbjective MAGNITUDES with Sljbliminal D:Tf'ferences

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INTERVAL MEASUREMENT of Sljbjective MAGNITUDES with Sljbliminal D:Tf'ferences INTERVAL MEASUREMENT OF SlJBJECTIVE MAGNITUDES WITH SlJBLIMINAL D:tF'FERENCES BY MURIEL WOOD GERLACH TECHNICAL REPORT NO. 7 APRIL 17, 1957 PREPARED UNDER CONTRACT Nonr 225(17) (NR 171-034) FOR OFFICE OF NAVAL RESEARCH REPRODUCTION IN WHOLE OR IN PART IS PERMITTED FOR ANY PURPOSE OF THE UNITED STATES GOVERNMENT BEHAVIORAL SCIENCES DIVISION APPLIED MATHEMATICS AND STATISTICS LABORATORY STANFORD UNIVERSITY STANFORD, CAL:tF'ORNIA I l f INTERVAL MEASUREMENT OF SUBJECTIVE MAGNITUDES WITH SUBLIMINAL DIFFERENCES by Muriel Wood Gerlach I. INTRODUCTION: THE PROBLEM OF PSYCHOLOGICAL MEASUREMENT There are many aspects of things and events which are best discrimi­ nated, if at all, by the direct responses of living beings, human or animal. For example, while the objective weight of an object may be determined by placing it on an equal arm balance, the determination of its felt weight to an individual requires his own response to hefting the object. The problem of subjective (psychological, sensory) measure­ ment arises when we are concerned with discriminating such aspects of things as their felt weight, seen color, perceived tone, or psychological value, (in contrast to their objective weight, luminosity, physical acoustics, or monetary worth). The discrimination in question is obvi­ ously a matter of the sensory responses of living observers, it is not based on the mechanical or electrical variations of physical instruments (scales, dials, meters). Is such discrimination capable of yielding quantitative orders? Can the subjectively discriminated aspects of things be systematically arranged to form consistent arrays? In brief, is psychological measurement possible? The purpose of our introduction is to discuss some of the answers which have been given to this question and to indicate the relevance of our theory to the iiproblemii of subjec- tive measurement as we see it. -2- We shall consider three types of answers to the question. The first two are categorical in character, the third is hypothetical or conditional. Onthe first view, presented in uncompromising fashion by several members of the British "committee appointed to consider and report upon the possibility of quantitative estimates of sensory events, il the answer is a categorical negative 0 The members of this committee suggest as one reason for their skepticism that HfundamentalH measurement is impossible in psychology, asserting that the measurement of psychological magnitudes depends on the prior measurement of physical magnitudes. Since, according to these scientists, Hfundamental" measure­ ment is the only type of measurement worthy of the name, they argue that psycho­ logical measurement, in any true sense of the word, is impossible. Their point seems to be that when, for example, Stevens and Volkmann construct a pitch func­ tion (Stevens and Volkmann [23]), pitch, a psychological attribute, scaled in subjective units (mels), is plotted against frequency, a physical attribute measured in physical units. Hence, they say, the measurement of pitch depends on the prior measurement of frequency. Similarly, the measurement of any other psychological magnitude depends on prior physical measurement of the correlated stimulus, and is therefore not fundamental. This argument has been convincingly answered by Reese (Reese, [18], pp. 44­ 46) who reminds us that subjective measurement has been effected where the stimulus correlate is unknown (as in the measurement of I.Q.); or where no independent physical measurement exists (as in the scaling of attitudes); or where the stimulus correlate is exceedingly complex, i.e., the psychological attribute in question is not a perfectly monotonic or linear or single-valued function of a single physical dimension (as in the case of the pleasingness of -3- o handwriting which is no doubt correlated with the size, shape, etc., of the physical inscriptions but in an obscure and complicated manner). Reese goes on to point out that where the stimulus correlate can be identified and measured, the use of 'physical measures in constructing psychological scales may be regarded as incidental. Despite classical psychophysical procedures, there is nothing about subjective measure­ ment which essentially requires the direct quantitative use of an underlying physical continuum. Some method for identifying the subjec­ tive phenomena under investigation is required; (for example, the different identifiable pitches must somehow be indicated); where a physical correlate is known, it is convenient to identify a psychological element by reference to the physical stimulus with which it is associated; where the correlated physical magnitude is measurable, it is helpful for the investigation of functional relationships to plot the subjective magnitudes against the physical magnitudes arranged in their order as measured, rather than plotting the subjective magnitudes against the physical magnitudes considered merely as identification tags for the former, and therefore random in their position along the abscissa. But the fact remains that any method of identifying the subjective phenomena in question will do. Reese remarks that arbitrary marks on the dial of the reproducing instrument will serve the purpose; Goodman suggests identifications with no physical connotations whatsoever: A particular color may be singled out as lithe color of the left-hand one of the two round patches now near the center of my visualfield~i (Goodman [9], p. 226.) -4- To Reese's cogent refutations of the argument that psychological measure- ment cannot be regarded as "fundamental" measurement and therefore does not really constitute measurement, we should like to add a further consideration, It is not clear to us that the traditional distinction between "fundamentall' and "derived" measurement can be upheld. The orthodox view is that "derived" measurement is dependent on prior measurement of some sort where "fundamentallV measurement is independent in this respect, (Hempel [10], pp. 62-74,) But, just as defined notions are theoretically eliminable in favor of the primitive notions by which they are defined, so too the prior measurement supposedly assumed in "derivedH measurement is eliminable in favor of the non-quantitative concepts from which it was originally constructed, The distinction between :fundamental and derived measurement thus appears to be dubious; and in so far as the case against psychological measurement rests on this dichotomy, it is lacking in force. More compelling arguments have been advanced against the possibility of quantifying subjective phenomena. These arguments often take the general form f• of asserting that it is impossible to find empirical operations in the sub- jective realm which will correspond to the numerical operations of measurement (addition, subtraction, division, multiplication). It has been said, for example, that to assign numbers to sensations requires that one sensation be half or twice another sensation which is absurd since sensations are simple, unanalyzable, unitary; they are not the sort of things that can be divided and fragmented, This sort of objection is clearly naive; for to characterize a sensation x as twice as intense as another sensation y is not to say that sensation y is half of sensation x in the same way that half an apple is half of a whole apple, (Stevens' choice of such names as lifractionation" -5- or "bisection" for his methods of sensory scaling seems, therefore, excep­ tionally unfortunate.) Actually no operation of sensory fragmentation or division is required. The numerical statement might mean that sensation y if added to itself in an appropriate way would produce sensation x. If this interpretation were chosen, clearly an operation for sensory iladditions" would be required. Such phenomena as the monaural-binaural phenomenon in auditory sensation provide evidence that such a requirement can be met in some sensory domains. For there is some evidence that a sound y intro­ duced into one ear may be "added" to itself by being introduced into both ears to produce a sound x which is subjectively twice as loud as y. In fact, Campbell himself has admitted that the monaural-binaural method of scaling satisfies the requirement for a subjective operation of lIaddition.t! An even more natural interpretation of the characterization of a sensation as "half" of another sensation than the 'iadditive," one just discussed is suggested by Wiener. He writes that lisuch a proposition as IX is twice as intense as y' is simply a paraphrase for some such statement as "the interval of intensity between x and y equals that between y and some sensation of zero intensity i • Ii (Wiener [29), p. 1830) According to this view, the half judgment requires neither the fragmentation nor the liaddi­ tiont! of sensation, but only the equation of sense-distances and a natural zero. It is usually granted that sense-distances are introspectively com­ parable; and, recently, members of the Stanford group have shown that behavioristic interpretations can be provided for the notion of equal sense distances 0 (Davidson and Suppes [6] ,pp 0 12-16, Suppes and Winet [24], pp. 259.f6lo) It seems probable that the mathematical notions essentially required for measurement are, after all, amenable to psychological interpretation. But the critics of sensory measurement may raise a more serious objection. -6- They may protest that the subjective operations specified as empirical inter­ pretationsfor the formal notions are incapable of satisfying the logical criteria
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