Psychophysics

Limens.—Psychophysics makes extensive use of the concept of the threshold or limen, of which there are two kinds. (i.) The stimulus limen is that value of stimulus which terminates a sen sory continuum. The visible spectrum is limited by a stimulus limen in the reds (ca. wave-length of light) and another in the violets (ca. 400,44). Tones range between the limen for the lowest audible tone (ca. 16 vibrations per sec.) and the limen for the highest audible tone (ca. 20,000 vs./sec.). The stimulus limens for intensities of weights, sounds, brightnesses, and other sense-qualities have been determined, but depend upon so many factors that no simple statement of their values is possible. Stimulus limens have also been determined for size and for dura tion. In the case of illumination, the size, duration and intensity of the stimulus are interrelated ; a very small stimulus has to be more intense to be perceived. (ii.) The differential limen is that difference between two stimuli which marks the boundary between sensed difference and sensed equality. It is often confused with the just noticeable difference, although in fact it is a statistical quantity for the theoretical point between what is just noticeable and what is just not noticeable. In fact both limens are statistical values, for the variability of the conditions of excitation can not be controlled and what is sensed at one time may not be sensed at another. Hence the limens are averages or mathematically deter mined points where the sensation is as often sensed as it is not.

Methods.—There are three fundamental methods of psycho physics, all of which Fechner invented. (i.) In the method of limits (method of minimal changes, of least perceptible differ ences) the stimulus is varied serially (usually by discrete steps) until a change is noticed. For example, to determine the stimulus limen of intensity, imperceptible intensities are presented in in creasing order until the stimulus is first sensed; then a descending series from perceptible to imperceptible is observed; and finally the results of many such series are averaged. For the differential limen there are always two stimuli, of which one, the standard, is kept constant, and the other, the variable, is altered until a dif ference between the two appears or disappears, according to the direction of change. Here the limen is the distance from the standard to the average point of change, and there are always both an upper differential limen and a lower, since change can be noticed on either side of the standard. (ii.) In the method of average, error (method of production) the experimental sub ject himself changes, by means of appropriate apparatus, the stimulus continuously, usually until subjective equality with a standard has been reached. Since subjective equality is not physi cal equality, the results yield an average or constant error for the subject and also a variable error about this average. (iii.) In the constant method the subject is presented at random with a prede termined set of stimuli for which he judges in every case the pres ence or absence of sensation or of the difference between the sen sations. Because of the variability in the conditions of excitation his judgments are not always the same for the same stimulus, but it is found that, as a difference increases, the frequency with which the difference is perceived increases. When enough judgments have been taken, these relative frequencies can be plotted in a psycho metric function. The figure shows the case of the differential

limen. Reading from left to right, the frequency with which the variable is judged "less" than the standard decreases, the fre quency of the judgments "greater" increases, whereas the remain ing cases, the equality judgments, are maximal at the centre. The liminal values of the stimulus are taken as those values where the probability of the judgment "less" or "greater" is as likely as it is not, i.e., the points on the scale of the stimulus corresponding to the points where the abscissa for 50% crosses the psychometric functions. The limens are the distances of these values from the standard stimulus (the distances L1 to S and to S) and one of them may even be negative when subjective equality deviates widely from the standard. Subjective equality is usually taken as the point where the judgments "less" and "greater" are equally likely, i.e., the intersection of the two psychometric functions. It is customary (as in the figure) to fit to the observed frequencies for the psychometric functions smooth ogives of the normal proba bility integral, sometimes called the phi-function of gamma ; but this curve is only an empirical approximation and has no theoretical significance.

Weber's Law.

The Fechner-Weber Law implies that all dif ferential limens of intensity should bear a constant ratio to the standard stimulus, whatever its value, and for this reason the psychophysical methods have been used most extensively to test the law and to determine these ratios. In general it may be said that the experiments indicate that the law holds approximately, although not exactly, within the middle ranges of intensity, but not for very small or very large intensities. Thus it appears that the liminal ratio for visual brightness is about i/Ioo, that is to say, illumination must be increased by i/Ioo of its amount for a change to be perceived. The liminal ratio for lifting weights with the hand is about 1/4o and for pressure on the skin about 1/2o. For tone the value is about I/1 o; and for smell it ranges as a rule between 1/4 and 1/3. See DISCRIMINATION, SENSIBLE.

Results.

There is a very large body of quantitative results on liminal determinations. For theoretical purposes the constant method with weights, lifted by the hand, has been most used. The psychophysical methods, however, lie at the basis of nearly all quantitative methods of experimental psychology, especially those that deal with sensation. In its mathematical theory psycho physics is identical with the statistical methods that psychology uses in social measurements and with mental tests, and the boundary between the psychophysical and the statistical methods is thus quite properly becoming dim.

BIBLIOGRAPHY.-See

G. Th. Fechner, Elemente der Psychophysik (Leipzig, 186o, 1889) ; J. L. R. Delboeuf, Elements de psycho physique, and Examen critique de la loi psychophysique (both, Paris, 1883) ; G. E. Muller, Zur Grundlegung der Psychophysik (Berlin, 1878), Gesichtspunkte and Tatsachen der psychophysischen Methodik (Wies baden, 1904) ; E. B. Titchener, Experimental Psychology, II., pts. i. and ii. (New York, 1905) ; F. M. Urban, Application of Statistical Methods to the Problems of Psychophysics (Philadelphia, 5908) ; W. Wirth, Psychophysik (Leipzig, 1912) ; W. Brown and G. H. Thomson, Essentials of Mental Measurement (Cambridge, 1921). (E. G. BoR.)