As a result of studying this chapter, students will: know

• the main tasks of general and differential psychometrics;

• types and types of measuring scales; be able to

• correctly determine the type of the measuring scale, corresponding to the measured psychological characteristics;


• the basic apparatus of general psychometrics.

General and differential psychometrics

In the previous part of the general psychological workshop, the main emphasis was placed on the procedures for data collection and the qualitative characterization of the results obtained. Nevertheless, modern psychology has a number of procedures that allow us to express the investigated patterns not only qualitatively, but also quantitatively, i.e. in the form of a number or an array of numbers. We already know that for these purposes, the methods of mathematical statistics are used, which are widely used at the stage of processing the newly obtained data. Such quantitative procedures can significantly enrich the research procedures already discussed by us, connected with the use of methods of observation and conversation. Some of these features have already been discussed in previous chapters.

Nevertheless, the question of a quantitative description of psychological facts and regularities turns out to be much broader. This question concerns the fundamental possibilities of mathematical representation and modeling of psychological phenomena. In this case, it is customary to talk about measurement procedures as part of the experimental work of the researcher. A special section of psychology, called the psychometrics, deals with the solution of such questions in the general methodological plan.

The main task of psychometrics is the development of methodological procedures that ensure the possibility of psychological measurements, determine the boundaries of such opportunities and create specific measuring tools.

Although the term measurement seems familiar and understandable to practically everyone, its formal definition may seem complicated, especially if it is a question of psychological facts and patterns. It is not surprising that discussions on this subject continue in psychology so far.

One of the most famous experts in the field of psychometrics and psychophysics, American psychologist S. Stevens, has contributed to the development of the very understanding of what measurements represent. He defined measurement as an expression of relations existing between objects, facts, or phenomena of relations with the help of numbers. "We can say," wrote Stevens, "that the measurement, in a broad sense, is defined as assigning numbers to objects or events in accordance with the rules . In this case, the system of relations and the range of possible operations that the researcher determines for a given set of numerical values ​​must correspond to those relations that exist for the measured facts or phenomena. In this, from the point of view of Stevens, is the essence of any measurement procedures of varying degrees of complexity. This point of view on the subject of measurements is the most common in modern psychology in general and psychometrics in particular.

For example, by determining the temperature outside the window and expressing it in numerical form, we can correlate the result obtained with those indications that we already have. We can tell if the temperature outside the window is different from the temperature in the room, and where it is warmer or colder - at home or on the street. If, for example, we recorded the thermometer reading outside the window at 5 ° C and the room thermometer shows 20 ° C, we can say that the temperature level is not the same, because 5 ≠ 20. We can also make a clarification in our judgment, saying that the room is warmer, as 5 & lt; 20. We can also judge how warmer the room is: 20 - 15 = 5.

However, the rules system, which is set for the temperature scale of Celsius, does not allow us to carry out another empirical operation: say how many times the room is warmer than outside it. Thus, the system of rules that sets the temperature scale of Celsius provides us with a number of possibilities, but at the same time limits us in our judgments.

Let's note further that similar relationships can be assigned with some degree of accuracy not only for those facts that we have available at the moment, but also in relation to the data for some past period of time or for different geographical places. We can compare them, accumulating statistics, calculating the average values ​​over a certain time interval, determining the ranges of temperature variability, applying some statistical criteria to the data obtained.

Note that, although we usually strive to express temperature using various physical instruments, this can be done without their participation, relying solely on our sensations. It is not by chance that recently, more often in weather reports, one can find such an indicator as the effective temperature that determines how we perceive weather conditions.

When we feel any objects, they can be perceived by us as warmer or less warm, no matter how it really is. The same is true of other modalities of sensations, such as sight, hearing, smell, awareness, sensations of taste, pain, etc.

All this suggests that sensations have not only qualitative, but also quantitative characteristics. Thus, these quantitative characteristics of sensations can and should be expressed with the help of numbers. But for the numbers themselves, which can be used to describe our sensations, appropriate rules must be established in the same way as for numbers expressing physical relationships. These rules will allow us to establish mutual correspondences between our sensations and the numbers used for the measurement. In this case, we can answer the same questions as we ask about the temperature expressed in physical units: are our sensations equal, which is greater or less, how different are the sensations from each other, and even how many times does one sensation exceed the other .

For the first time the task of measuring sensations, i.e. their expression with the help of numbers, followed by the possibility of applying mathematical procedures to these numbers, was posed by the famous German philosopher and pedagogue I. Herbart in his famous work "Psychology as a science once again based on experience, metaphysics and mathematics" light in 1824

Agreeing with the opinion of I. Kant, who considered the existence of experimental psychology as an industry of scientific knowledge impossible, Herbart noted the important role of mathematics, which it can play in the development of psychological knowledge. Herbart designated his psychological system by the terms "statics of the spirit" and spirit dynamics & quot ;. The statics of the spirit, according to Herbart, must explore the quantitative properties of sensations, and the dynamics of the spirit - the forces acting between them.

The whole psychic experience, in accordance with this system, consists of three parts: a region of clear consciousness, a region of unclear consciousness and a region of the unconscious. Between these areas there are non-rigid boundaries, which Herbart designated by the term threshold & quot ;. And if the transition from the field of clear consciousness to the domain of an obscure consciousness is determined only by the static characteristics of the representations that Herbart considered necessary to measure, then he associated the output of representations in the unconscious area with a process such as "displacement."

It occurs every time the repulsive forces between the two representations are so great that it inevitably either one or at once

Both of these representations are unable to remain in the realm of consciousness and become unconscious. For example, this happens if sensations of blue and yellow appear simultaneously in the area of ​​consciousness. The result of their displacement is the feeling of white. Herbart believed that with the help of mathematics, all the laws of this kind should be described and understood. However, his conception was nevertheless mostly speculative.

Further development of Herbart's ideas can be found in the works of his follower, another outstanding German philosopher - G. Fechner. Creatively developing Herbart's notions of thresholds of consciousness, Fechner developed a specific empirical methodology for their measurement. That's why Fechner is rightfully considered the creator of psychometrics - the science of psychological dimensions.

Fechner described his approach in the framework of the science he developed, called psychophysics. The foundations of this science were presented to scientists in a work published by him in 1860, which was called - "Elements of psychophysics".

According to Fechner's plan, psychophysics was to become a science offering a specific scientific solution to one of the fundamental metaphysical problems known since the time of R. Descartes - the problem of the correlation of matter and spirit. On the path to the creation of such a science, Fechner elaborated in more detail a more particular aspect of this problem-the problem of the relationship between the physical stimulus that acts on the sense organ and the sensation arising under its action. Such a science Fechner called small, internal, or sensory psychophysics. His development of the foundations of sensory psychophysics is considered an important stage in the development of scientific psychology in the second half of the nineteenth century.

It should be noted that Fechner's approach excluded the possibility of a direct evaluation of the sensation. To assess the sensation, the scientist believed, can only be indirectly, i.e. Only in units of a physical stimulus-stimulus. The minimum necessary stimulus value, or the minimum necessary difference in the physical magnitude of the two stimuli that can cause a sensation, Fechner called the sensory threshold. Thus, in order to measure the sensation, it is necessary to express it in terms of the threshold.

By postulating the equality of the values ​​of subtle differences between the two stimuli throughout the continuum of change and building on the work of the German physiologist E. Weber, who studied light discriminating thresholds Fechner theoretically come to the conclusion that there is a logarithmic relationship between the physical energy of the stimulus and the value of experience.

That's why Fechner's approach is called indirect. It does not imply the possibility of a direct evaluation and comparison of the magnitude of the sensation. These values ​​are expressed through an external criterion, in which quality different characteristics of physical stimulation act. For example, the physical correlation of loudness of perceived sound is the amplitude of a sound wave, and the physical correlation of its height is the frequency of sound vibrations. Knowing the physical values ​​of these quantities and the corresponding values ​​of the thresholds of consciousness, we can express the values ​​of the sensations we experience.

Later, already at the beginning of the last century, the American psychologist L. Thurstone developed Fechner's approach, going beyond the psychophysical framework. The methodology proposed by him made it possible to abandon the need to correlate the magnitude of the sensation with any clearly expressed physical characteristic of the object of measurement. This methodology is reflected in the proposed by Thurston in 1927 the law of comparative judgments. This law made it possible to assess quantitatively even those sensations that do not have immediate physical correlates, such as the sense of danger of various offenses or the aesthetic value of works of art. This is achieved on the basis of a statistical analysis of the number of preferences of each stimulus of a given set for their pairwise comparison.

Let, for example, the subject compare the social danger of two types of crimes - say, murder and rape. If, when these stimuli are compared many times, the subject does not demonstrate an obvious preference for any one variant as more dangerous, choosing, for example, in one half of cases, murder as a more dangerous crime, and in the other half - rape, we can conclude that the sense of danger for these two types of crimes in the subject do not differ. On the contrary, the preference for any choice, as suggested by Thurstone, in units of standard deviation, can be a measure of the differences in the corresponding sensations. On the basis of such values, one can construct a subjective risk scale for offenses, just as a temperature scale is constructed.

Even later, already closer to the middle of the last century, Stevens, developing the problem of psychological measurements, criticized the approach of Fechner, offering methods for direct measurement of sensations. Based on the methods developed by him, Stevens was able to collect a large array of empirical data, characterizing the quantitative sensations of a variety of modalities. The first scale, created by Stevens, was the scale of the soles, which made it possible to quantify the auditory sensations. Later, Stevens and his followers developed appropriate subjective scales for other modalities of sensations.

Stevens works allowed to overcome the limitations set in the classical Fechner psychometrics, and move on to building psychophysical and psychometric scales on the basis of direct scaling methods.

An important contribution to the development of the theory of psychological measurements was also the approach proposed in 1954 by W. Tanner and J.S.S. and in detail expounded in 1966 by D. Greene and J.S.S.S. approach, which was called the theory of signal detection. In this theory, the sensation is described as a decision-making process, based on an estimate of the likelihood ratio. It is assumed that sensation is the process of separating a signal from noise. Noise is described as a random, stochastic process that has both an internal origin (associated with the characteristics of the operation of the receptors and the perception system as a whole) and external (associated with the appearance of more or less stimulus-like interference).

Theory asserts that the observer decides each time how plausible is that this sensory impression is caused by a signal in the background of noise, and not just by noise. The task of measuring sensations in this case is reduced to constructing the operating characteristic of the receiver (observer), which reflects the ability of the sensory system to isolate the signal from noise (this indicator is treated as sensitivity) and make a decision on this subject on the basis of an established criterion based on the likelihood ratio estimate .

The considered tradition of psychological measurements does not concern the question of how diverse the individual's reactions can be. In other words, it does not concern the issue of individual differences. They are recognized as insignificant, do not change the general picture of measurements, and therefore this direction of research has received the name of general psychometrics. The issue of individual differences is considered in the framework of another direction of psychometric research - differential psychometrics. In another way, the direction of psychometrics in domestic psychology following E. Kretschmer is usually called psychodiagnostics.

The question of measuring the individual characteristics of the individual and her abilities was first investigated by the French psychologist A. Wine in 1903, although the origins of differential psychometrics should be sought in the earlier works of the famous British naturalist, creator of the eugenics F. Galton.

The problem of Wine was more practical than theoretical and methodological. It was to assess the level of development of children's mental abilities for their readiness for primary education. Initially, Vine, like Fechner, adhered to an indirect approach, trying to express mental abilities through external signs, such as, for example, the size, shape and proportions of the head. However, he soon realized that in this way it was not possible to reliably assess the child's mental abilities. Therefore, the criterion for him was the level of success in the performance of a number of typical tasks. Sets of such tasks, specially standardized by certain rules based on the use of procedures for mathematical statistics, began to be called psychological tests.

Test procedures are a way of assessing the abilities and personality traits. The collected data are subjected to a frequency estimation, and on the basis of the distribution of the probabilities of manifestation of the investigated feature. As a rule, the obtained distributions on the basis of mathematical procedures of monotone transformation are reduced to a normal distribution, for which the standard values ​​of the mathematical expectation and the standard deviation are specified. Based on these values, test scores are determined. For example, the WAIS Intelligence Scale, developed by D. Wexler, establishes the midpoint of the distribution of 100 points, and one scale point is set equal to 1/15 of the standard deviation. Thus, the assessment of intelligence on this scale, say, 105 points, will mean that the result of this subject differs from the population's average by 1/3 of the standard deviation.

The development of specific procedures for differential psychometrics (psychodiagnostics) has become one of the most notable achievements of scientific psychology. These studies change not only our notions of the nature and essence of psychological measurements, but also the entire social practice. A specific methodology for such work is presented in a separate training course, which is extremely important for the training of bachelors, specialists and masters in psychology, - the course of psychodiagnostics. However, we will not consider the questions of differential psychometrics in the course of the general psychological workshop, confining ourselves to only general questions of psychological measurements, which are mainly set out in the framework of psychophysical studies.

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