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Methods for the quantitative study of the relations between physical stimulus magnitudes and the corresponding magnitudes of sensation, for example, between the physical intensity of a light and its perceived brightness or the concentration of a sugar solution and its observed sweetness. To establish these relations, measurement scales are needed, not only for physical magnitudes but also for subjective magnitudes. Subjective scales are not obtained directly from observation but are theoretical models which summarize observed relations between stimuli and responses. See Sensation
The term psychophysical methods is sometimes extended to include certain scaling techniques which are most often used with subjective dimensions to which there correspond no simple physical dimensions, for example, food preferences.
In 1860, G. Fechner designed psychophysical methods to measure the absolute threshold, defined as the minimum stimulus energy that an organism can detect, and the differential threshold, defined as the minimum detectable change in a stimulus. Both quantities had to be defined as statistical averages. To obtain reliable measurements for these averages, Fechner devised the method of limits (also called the method of minimal changes) and the method of constant stimuli.
In the method of limits, the experimenter begins with a stimulus which is too weak for the subject to detect. In successive presentations, the stimulus intensity is increased in small, equal steps, the subject reporting after each presentation whether the stimulus was perceived until it has been detected. The descending series is then begun, the stimulus intensity beginning at an above-threshold value and decreasing in steps until the subject signals the disappearance of the stimulus. Many such series are given.
In measuring the difference threshold, essentially the same procedure is involved, except that the subject now signals the relation of a comparison stimulus to a standard stimulus. After a large number of such trials, the average of each of these four threshold values is computed.
To measure the absolute threshold by the method of constant stimuli, the experimenter selects a small number of stimulus values in the neighborhood of the absolute threshold (previously roughly located by informal use of the method of limits) and presents them to the subject a large number of times each, in an irregular order unknown to the subject. Each time a stimulus is presented, the subject reports the presence or absence of sensation.
The data provide the proportion of times that each stimulus resulted in a report of sensation by the subject. One can then estimate the stimulus value that has a probability of .50 of producing sensation, this value being defined as the absolute threshold. An analogous procedure is followed in obtaining difference thresholds.
Fechner proposed to use the results of threshold measurement in developing a subjective metric or scale. He defined the difference threshold, or just noticeable difference (jnd), as the subjective unit and the absolute threshold as the zero point of the subjective scale. Thus the subjective intensity of a particular brightness of light, for example, would be specified when it was given as 100 jnd's above threshold. The subjective scale so defined is not a linear function of the physical stimulus scale since jnd's , though defined as subjectively equal units, are not of physically equal magnitude throughout the intensity scale. The size of the jnd is approximately proportional to physical stimulus intensity. To the extent that this relation holds, Fechner deduced that subjective intensity should be proportional to the logarithm of the stimulus intensity.
Rather than requiring of the subject merely either yes-no or ordinal judgments, some methods require the subject to make direct-ratio discriminations. For instance, he or she may be presented with a moderately loud tone, and then required, by turning a knob, to adjust the loudness of a comparison tone until it is half as loud, or twice as loud, as the first. The first case illustrates the method of fractionation, the second the method of multiplication. In the method of magnitude estimation, the subject is given a stimulus, such as the brightness of a light, to serve as a modulus with a value assigned to it, for example, 10. The task, as other lights of different intensities are presented, is to assign them numbers which shall stand in the same ratio to 10 as their brightness stands to that of the modulus. One twice as bright is given the designation 20; one half as bright is 5. In these and other similar methods, whether the subject's task is to estimate or to produce the prescribed ratio or the prescribed fraction, there are certain common characteristics. Direct-ratio assessments are obtained from the subject; there can be experimental checks on internal consistency of the results, and since the individual judgments are not of high precision, repetition is required if stable averages are to be obtained.
The empirical results obtained by the various methods are in fairly good agreement. They agree in that, to at least a first approximation, subjective magnitudes on a variety of dimensions are found to be power functions of suprathreshold stimulus intensity; that is to say, subjective magnitude is proportional to the suprathreshold stimulus magnitude raised to a power. The powers have a range from 0.3 for auditory loudness to 3.5 for subjective intensity of alternating current that is applied to the skin.
In direct-matching methods the subject is not required to produce or assess the ratio of one subjective magnitude to another, but only to adjust a comparison stimulus until some attribute appears to match that of a standard stimulus. For example, the subject might be asked to adjust the physical intensities of tones of various frequencies until their loudness matched that of a 1000-Hz tone of fixed intensity. The result would be an equal-loudness contour, showing the intensities to which tones of various frequencies must be set to produce sensations of equal loudness. These data are of use in acoustics. See Loudness
The method of average error, the third of the three methods devised by Fechner, is a special application of direct-matching methods to cases in which the point of interest is in discrepancies between perception and stimulation. The subject adjusts a comparison stimulus to match a standard stimulus; the average of a number of such settings gives the point of subjective equality, and the difference between this point and the standard stimulus is the average error. Two illustrative uses of the method are the measurement of accuracy of distance perception and the measurement of the magnitude of so-called optical illusions. See Hearing (human), Psychology