THE METHODS OF INDIRECT SCALING
As a result of studying this chapter, students will:
• the basic principles of building psychophysical and psychometric scales on the basis of indirect scaling;
• the basic mathematical models underlying the various empirical procedures for indirect scaling;
• the main systematic errors that threaten the reliability of psychological measurements;
be able to
• Evaluate the reliability of the measurement procedure in one-dimensional scaling and correct measurement results;
• skills of constructing ordinal and interval scales based on methods of indirect scaling.
Threshold scaling and the Weber-Fechner law
As we have already noted, for the first time the task of quantitative assessment of sensations was formulated at the very beginning of the 19th century. German thinker and teacher I. Herbart. However, the first practical methods of scaling sensations were developed somewhat later. Special merit in this matter belongs to the outstanding German researcher, the creator of sensory psychophysics G. Fechner.
Fechner's methodology consisted in evaluating the sensation in terms of the threshold. At the same time, the zero point of the psychophysical scale is taken to be the sensation corresponding to the lower absolute threshold, and the unit of measurement of sensation is the magnitude of the subtle difference (ESR) of the stimuli. However, such a methodology encounters a number of difficulties.
First of all, it should be noted that sequential calculation of stimulus thresholds on the whole range of its sensation on one subject is practically impossible because the threshold values themselves are subject to instantaneous fluctuations. This problem was solved by Fechner by appealing to the results of experimental studies of light sensitivity, which were obtained by the famous German physiologist E. Weber in the 1930s. XIX century, and even before the French physiologist P. Bouger.
Investigating the differences in brightness, Weber discovered that adding one candle to 60 candles causes an increase in the sense of brightness of light. But if
one candle is added to 120 candles, no such increment occurs - two candles are required. Similarly, it turns out that in order to feel the brightness gain at 180 candles, you need three candles already.
These experiments show that, despite the fact that the absolute value of the increment of the stimulus that causes the increment of the sensation changes, the ratio of this quantity to the initial value of the stimulus remains unchanged. We know that such a value is usually called the differential threshold. Thus, taking into account the constancy of the magnitude of the differential threshold over the whole range of sensations of the given stimulus, it is sufficient to estimate only three values for the scale construction: the lower absolute threshold, the differential threshold, and the upper absolute threshold. Note, however, that more recent studies have shown that the constancy of Weber's relationship is valid far from the entire range of sensations, characterizing only the sensations of average magnitude.
Another difficulty of scaling sensations in units of threshold is that we do not know whether the values of ESR taken as units of measurement are constant or they can also change as the sensation increases. Fechner's approach, which does not presuppose an immediate evaluation of the sensation, does not provide an opportunity for a practical answer to this question. We only note that Fechner himself postulated the equality of these quantities.
The postulate of the equality of the values of ESR and the values of the differential threshold allowed Fechner to formulate a logarithmic law according to which the magnitude of the sensation E is proportional to the value of the logarithm of stimulation S :
This law was called the Weber-Fechner law.
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