The measurement scale of primary interest in psychophiysics is the S-cale which may be called the psychological continuum in contrast with the physical or stimulus-continuum, the R-scale. In the original formulation of Fechner's law the S'scale was described as sensation intensity but this interpretation of the psychological continuum is now pretty much out of date. We now speak of the S-scale as through it measured so-called sense-distances in relation to the corresponding differences or distances on the scale of stimulus magnitude. It is my present purpose to offer a revision of the sense-distance interpretation of the S'scale so that it will be independent of the j.n.d. and the difference limen and to propose a mental unit for mintal measurement instead of the ambiguous physical unit, the j.n.d. I shall also try to show that this revised interpretation of the S-value makes it a continuous function of the stimulus magnitude because Fechner's paradox does not exist.
This continuum which is designated S in Feechner's law, S = k log R, reprezents, first of all, a gradation of qualitative processes. These processes may be described as subjective or physiological to suit individual and temperamental preferences. The continuum implies qualitative variation and it may be unidimensional or multidimensional.
A point on this continuum may be designated only by a corresponding stimulus. The stimulus may in turn be designated (1) by a quantitative stimulus attribute such as intensity or magnitude, or (2) by a qualitatively varying stimus attribute such as exellence of handwriting or the beauty of rug patterns or the degree of pacifism expressed in statements about peace and war. Any perceptual quality which may be allocated to a point on the psychological continuum is not itself a magnitude. It is not twice, three times, or four times as strong, high, beautiful, or good as some other process on the same continuum. It is not a number. It is not a quantity. These are statements about the psychological continuum on which at list fair agreement among psychologists is to be expected.
But furthermore, the j.n.d. is not a reliable unit of measurement along the S-scale. Any point on the scale reprezents a unified indivisible experience. Any two such points represent two such experiences which may be qualitatively entirely different and in every way incommensurate, so that they may represent by their own immediate attributes perhaps no similarity by which any 'distance' between them could be measured.
With these negations granted, just how do these qualitative entities or processes become a measurable continuum?
They acquire conceptual linearity and measurability in the probability with which each of them may be expected to associate with any prescribed stimulus.
This is the crucial characteristic of the psyhological continuum in terms of which psychological measurement is posible. The S-continuum in terms of which psychological measurement is possible. The S-continuum is constructed or defined in such a manner that the frecquency distribution of the S-experience for any given stimulus R is normal. Each modal Sk experience is that particular S-experience which is most frecvently associated with the stimulus Rk. Hence if measurement begin with the stimulus Ra for wich Sa is the most common or modal S-experience, then some other S- experience, Sb, will be spaced far away, along the imaginary continuum, if the probability is low that Sb will be experienced with the stimulus Ra. It will be spaced close Sa if the probability is relatively high that Sb will be experienced with Ra. Fortunately it is possible to verify experimentally the validity of this definition or construction of the S-scale because the continuum may be constructed separately for each stimulus and the attainment of internal consistency of the scale will indicate whether the correct form of frecvency distribution has been used. Therefore the normal frecvency distribution is not blindly assumed. It is tested for. If found incorrect, other forms of distribution may be tried in a similar manner. There is one assumption underlying thisconstruction of the psychological continuum, namely, that all the stimuli in a series project the same form of frecvency distribution on the S-scale, but it is not assumed that their dispersions are equal.
Since the dispersions wich the several stimuli project on the S- continuum are not assumed to be equal, the natural unit for psychological measurement becomes the dispersion of one of these stimuli measured on the psychological scale. This is what I have called the discriminal dispersion or, more specifically,the discriminal error of each stimulus and it should not be confuzed with the customary error of observation. There are two fundamental differences, namely, (1) the discriminal dispersion or error is measured on the S-scale whereas errors of observation are naturally measured on the R-scale, and (2) the discriminal dispersion is the dispersion project on the S-scale by a single stimulus whereas an obsevational error is naturally the pooled effect of two stimuli. The two stimuli are the two terms in the psychophysical judgment by the method of constant stimuli or they are the presented and the reproduced stimuli in the method of reprodution.
It should be noted that an observational error can itself be objectively produced and it can be directly measured on the R-scale. The discriminal dispersion, though more elemental in character than the observational error, cannot by itself be objectively produced. It can be measured only indirectly since it concerns the S-scale. Every judgment when objectively produced constitutes a single observational error wich is loaded with at least two discriminal dispersions or errors. A single discriminal dispersion or discriminal devia tion cannot by itself ever become an objective record and consequently its measurement must necessarily be indirect.
I have attempted to state briefly a definition of the psychological continuum and to show that a truly psychological scale. The psychological S-scale then in effect a frcquency scale as far as its experimental identification is concerned. It is an imaginary scale we allocate and space aut the psychological counterparts of the several stimuli in the stimulus series. Since the stimulus series is regarded as strictly continuous, we define the corresponding psychological scale similarly so that any stimulus magnitude or quality may be allocated to a point on the continuous S-scale. Similarly, since the psychological continuum is not directly or physically accessible or controllable, we identify any point on the S-scale by a stimulus magnitude.
The customary definition of the S-scale as the measurement of so-called sense distance is not here entirely rejected but it is made more definite. As long as we define the S-scale as the measurement of sense distance and still deny that it measures sensation intensiv or any other quantitative characteristic of sensation, there remains an unsatisfactory vagueness about the nature of the psychological continuum. If we insist that the sense quality is not itself an intensity or magnitude of any sort,how does it happen that we get quantitative measurement in the form of measured distances between these sense gialities which are themselves denied measurable and quantitative attributes? What constitutes the sense distance that is mesured between two qualitative
entities? That is a question concerning the very natureof the psychological continuum which, as far as I am aware, has not hitherto been answered. It is the answer to just this question that I have attempted in formulating a revised definition of the S-scale so that it may also fit the experimental facts.
Let the S-scale consist in a gradation of qualities by means of wich we perceive any specified stimulus continuum. Allow that a given stimulus is not always perceived by the same processon the S-continuum. Let the quality most commonly perceived in the given stimulus be designated the modal quality or process for that stimulus. Than we can assign numerical values to other qualities in the S-scale in accordance with the frequency with which they are perceived in the given stimulus. It does not matter whether the S-qualities or processes are in any real sense actually spaced aut in a continuum so long as thei behave as though they were so spaced aut. Mental measurement depends according to the present interpretation on the frecquency with each of the processes constitutes the response to a given stimulus. It is reasonable to assume that two perceptual sense qualities or processes which are close together on the psychological continuum are qualitatively similar and that therefore either one of the them may more or less readily be perceived in the same stimulus. To the extent that two perceptual processes are qualitatively similar, to that extent will their probabilities of association with the same stimulus be nearly the same, and to that extent will they thend to be adjacently spaced on the imaginary psychological continuum. It is sufficient for the purposes of mintal measurement that the qualitative perceptual processes behave as though their respective probabilities of association with a given stimulus were a normal frequency distribution.
The natural psychological unit of measurement becomes, then, the standard deviation of the frecquency distribution for a specified stimulus. This unit of mental measurement I have called the standard discriminal error for the specified stimulus and it is of course measured directly on the psychological continuum. It is entirely independent of stimulus measurement. It is independent of the validity of Fechner's law. It is also independent of the validity of Weber's law. It is a valid unit of measurement even when the obiective stimulus cannot itself be quantitatively measured. It should be noted that the unit of mintal measurement that I have proposed is not in any sense a j.n.d. The just noticeable difference is in every case a stimulus measurement. It is measured on the R-scale. Hence it is in reality a physical unit which in some situation can serve indirectly the purposes of mintal measurement. The discriminal error is a mental unit of measurement since it is defined on the psychological continuum. Its physical equivalent will vary from one situation to another depending primarly on the validity of Fechner's law or same other S-R, relation for the particular perceptual function under consideration. This proposed mental unit for mintal measured may be defied as the standard deviation of the frequency distribution projected by a standard stimulus on the psychological continuum. I propose to call this mental unit of measurement the standard discriminal error. The assumption, the correctness of which will determine the validity of this unit of measurement, is that an S-scale with internal consistency will be obtained by spacing the perceptual qualities on it so that their probabilities of association with any given stimulus will be Gaussian. With the psychological continuum so defined the standard discriminal error, as a mintal unit of measurement, will be the standard deviation of the perceptual qualities perceived in a standard stimulus.
The Continuity of the S-scale
We have so far taken for granted the continuity of the S-scale but the descriptions of the psychological S-R relation so frequently give the idea of a discrete series of steps or jerks that the error of such a notion needs clearly to be corrected. The typical description of the psychophysical S-R relation starts with stimuli R1, R2, R3, so nearly similar that they differ succesively by one ,j.n.d.' Corresponding to these stimulus magnitudes are postulated S-values S1,S2,S3. Then the implication is that any stimulus difference less than (R1 - R2) cannot be discriminated at all and that as soon the stimulus difference becomes as large as (R1 - R2), then suddenly the difference jumps into perceptibility and it is designated ,a least peceptible difference', a sence minimum, the unit of mintal measurement, the j.n.d. Even so clear a writer