Methods of scaling - methods of subjective quantitative assessment (measurement) of the properties of various objects (physical, aesthetic, social, mental, etc.).
To measure the intensity of sensation, classical psychophysics used Fechner's law, which was the first to establish a quantitative relationship between physical and subjective quantities (the so-called basic psychophysical law). According to this law, the perceived intensity of a sensation is proportional to the logarithm of the magnitude of the stimulus. However, the basic psychophysical law formulates a certain relationship between the values ​​of sensation and stimulus only for cases when the parameters of the object related to the intensity characteristic (weight, brightness, etc.) are studied. More often there are complex, multidimensional objects, the features of which do not have physical measures. Such signs of multidimensional objects, as well as phenomena of an aesthetic and social nature, are outside the scope of Fechner's law, but can be. quantitatively expressed using the methods of modern psychophysics (S. Stevens, L. Thurstone). Studies by many authors have shown the possibility of new methods to quantitatively characterize any perceived, imagined or conceivable stimulus. These methods (which, unlike the "indirect" methods of classical psychophysics, are called "direct") include: equalization of intervals, direct numerical evaluation, pairwise comparison, ranking (for the last 2 methods, see Measurements in Psychology).
1. The method of direct subjective assessment of the magnitude of the stimulus using a standard stimulus and a number of variables. The standard (module) is denoted by some convenient number (1, 10 or 100). The task of the subject is to designate the variable stimuli with numbers so that these numbers reflect the magnitude of the relationship between the standard and the variable.
2. The method of selecting from a number of stimuli a subjectively half or doubled stimulus compared to some original standard stimulus, then half or doubled compared to the just selected stimulus, etc.
3. Method of equal intervals. This method is used in the case when it is required to find a 3rd stimulus for 2 given stimuli, which should be in the middle between these stimuli, i.e., subjectively, it should be as different from the 1st as it is from the 2nd. It is possible to carry out the division further: between one of the original data and the stimulus found, find an intermediate one.
Based on these methods, subjective scales have been developed for loudness, pitch, duration of sound, the strength of pain stimulation, for weight, brightness, smell, taste, temperature, etc. But these same methods, with some tricks, can be used to build subjective scales, for example. , for works of art or literature, fairy-tale characters, writers, cities, etc. See also Crossmodal comparison, Multidimensional scaling, Non-metric scaling.

This method, borrowed from classical psychophysics: [see: 51], is a simple and direct method for obtaining a semantic similarity matrix. The subjects are tasked with assessing the similarity of values ​​using a certain gradient scale. For example, in the experiments of Rubinstein and Goodnow (see: 339] it was a five-point scale, where 0 denoted the lowest degree of similarity, and 4 the highest; in the experiments of A.P. Klimenko, a ten-point gradual scale was used [see: 100]. Miller, the direct scaling method gives the most accurate results compared to the indirect assessment technique, but is characterized by significant laboriousness [see: 330]. n(n-1) /2 pairwise comparisons.

As an example of the use of the subjective scaling method for the semantic analysis of adjectives and: verbs, but without subsequent mathematical processing of data and the construction of semantic spaces, one can cite the works of Mosier and Cliff. An example of the use of the subjective scaling method with subsequent data processing using multidimensional scaling is the work of Rips, Shobin, Smith, devoted to the reconstruction of the semantic space of bird and animal names. In this work, the subjects were asked to rate, on a four-point scale, the degree of subjective similarity of 12 bird names, as well as the words bird and animal. The average group distance matrix (which is inversely proportional to the object similarity matrix) was subjected to a multivariate analysis procedure. Its essence is as follows: based on the matrix of subjective similarity (the distance between the analyzed objects), such a geometric space of the smallest possible dimension is reconstructed, in which the distances between the coordinate points corresponding to the analyzed objects are similar to the subjective distances of the similarity matrix. Mathematically, the multidimensional scaling procedure consists in determining the coordinate projections of points on some coordinate axes, based on the known distances between these points.

In the experiment under consideration, a two-dimensional semantic space was identified that satisfactorily describes the original data matrices. Based on the found loads of each word for each of the selected factor-axes of the semantic space, the coordinates were reconstructed

Rice. 3. Semantic space of bird names

these words in the semantic space (Fig. 3). The horizontal axis of the semantic space - Ф 1 - was interpreted by the authors as the "size" factor (eagle, goose "=> robin, sparrow, blue parrot), and the vertical axis - Ф 2 - as the "wildness" factor (eagle, jay, sparrow, robin) in opposition to poultry (chicken, duck, goose). The constructed space is not only a compact form of description and differentiation of the analyzed vocabulary, but also has the status of a model representation of verbal semantic memory, which makes it possible to predict some patterns of its functioning. According to this model, the meanings of words are recorded in memory as sets of their semantic characteristics, and the closer the words are located in the semantic space, the closer they are in content. Indeed, if we use the word birds(bird), then more frequent associations will be words robin, sparrow, jay etc., having smaller distances with this word in the semantic space.

Multidimensional scaling as a procedure for mathematical data processing is most typical of the subjective scaling method. But it is possible to apply to the matrix data obtained using subjective scaling, factorial and cluster analysis procedures. For example, in our study, the behavior similarity matrix was built both by subjective scaling and by assigning a set of given motives to the actions of the subjects, where the similarity of their motives served as a measure of the similarity of actions [see: 186]. Factorization of the data obtained in the group of adult subjects highlighted the similarity of the factor structures of the matrices constructed by both procedures. These results indicate that the subjective similarity of actions is based on their motivational aspect.

Methodically factorization of similarity matrices constructed using subjective scaling can be carried out in two ways: 1) when the normalized coefficient of subjective similarity is considered as an approximation to the correlation coefficient; 2) when, based on estimates of the subjective similarity of each pair of objects with all other objects, the correlation coefficient of this pair of objects is calculated, which is considered as a measure of their similarity. These assumptions make it possible to move from the subjective similarity matrix to the correlation matrix, which is subjected to factor analysis.

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methods that ensure the use of quantitative indicators to assess the attitude of the subjects to certain objects, which can be physical or social processes. To carry out subjective scaling, there are a number of methods characterized by certain rules, according to which numerical estimates are attributed to certain qualities of objects. Within the framework of classical psychophysics, the following are used: the method of mean error; method of minimal changes; constant stimulus method. New methods include:

1) direct methods - such as equalization of intervals, numerical straight line estimation, pairwise comparison, ranking;

2) indirect methods - for example, Fechner's method of scaling subtle differences (-> microscaling).

SCALING METHODS

English methods of scaling) - methods of subjective quantitative assessment (measurement) of the properties of various objects (physical, aesthetic, social, mental, etc.).

To measure the intensity of sensation, classical psychophysics used Fechner's law, which was the first to establish a quantitative relationship between physical and subjective quantities (the so-called basic psychophysical law). According to this law, the perceived intensity of a sensation is proportional to the logarithm of the magnitude of the stimulus. However, the basic psychophysical law formulates a certain relationship between the values ​​of sensation and stimulus only for cases when the parameters of the object related to the intensity characteristic (weight, brightness, etc.) are studied. More often there are complex, multidimensional objects, the features of which do not have physical measures. Such signs of multidimensional objects, as well as phenomena of an aesthetic and social nature, are outside the scope of Fechner's law, but can be. quantitatively expressed using the methods of modern psychophysics (S. Stephens, L. Thurstone). Studies by many authors have shown the possibility of new methods to quantitatively characterize any perceived, imagined or conceivable stimulus. These methods (which, unlike the "indirect" methods of classical psychophysics, are called "direct") include: equalization of intervals, direct numerical evaluation, paired comparison, ranking (for the last 2 methods, see Measurements in Psychology).

1. The method of direct subjective assessment of the magnitude of the stimulus using a standard stimulus and a number of variables. The standard (module) is denoted by some convenient number (1.10 or 100). The task of the subject is to designate the variable stimuli with numbers so that these numbers reflect the magnitude of the relationship between the standard and the variable.

2. The method of selecting from a number of stimuli a subjectively half or doubled stimulus compared to some original standard stimulus, then half or doubled compared to the just selected stimulus, etc.

3. Method of equal intervals. This method is used when it is required to find a 3rd stimulus for 2 given stimuli, which should be in the middle between these stimuli, i.e., subjectively, it should be as different from the 1st as it is from the 2nd. It is possible to carry out the division further: between one of the original data and the found stimulus, find an intermediate one.

Based on these methods, subjective scales have been developed for loudness, pitch, duration of sound, the strength of pain stimulation, for weight, brightness, smell, taste, temperature, etc. But these same methods, with some tricks, can be used to build subjective scales, for example. , for works of art or literature, fairy-tale characters, writers, cities, etc. See also Crossmodal comparison, Multidimensional scaling, Non-metric scaling.

Scaling methods

Word formation. Comes from lat. scala - ladder.

Kinds. To implement the process of subjective scaling, there are a number of methods characterized by certain rules, according to which numbers are assigned to certain qualities of objects. Within the framework of classical psychophysics, methods of average error, minimum measurements, constant stimuli are used. New psychological methods include, firstly, direct methods, such as equalization of intervals, direct numerical evaluation, pairwise comparison, ranking, and secondly, indirect methods, for example, Fechner's method of scaling subtle differences.

SCALING, METHODS

Simply, scaling procedures. Although a century of research into the construction of psychological scales has yielded dozens of variations, the most common procedures can be classified into three general classes. 1. Scaling intervals. Subjects are asked to rate stimuli based on intervals or differences. In bisection, the subject must set the stimulus so that it is midway between the other two stimuli; in categorical evaluation, he must distribute various stimuli into a small number of categories; in the method of equal-looking intervals, stimuli must be distributed among groups so that the intervals between them are subjectively equal. 2. Scaling relationships. The subject evaluates the subjective experience by assigning numbers, either directly or indirectly, to the stimuli so that they reflect their perceived magnitude. When assessing the magnitude, each stimulus is assigned a number that reflects its proportional intensity with respect to some standard; for example, if the standard is assigned the number "10", then a stimulus that is subjectively twice as large is assigned "20", one half as small is assigned "5", and so on. In the production (reference) method, the subject is asked to produce a stimulus that corresponds to some proportional value of the standard, for example, twice as bright, corresponding to one third in loudness, etc.; this procedure is also called the adaptation method. In the mutual comparison of modalities, the quantities are obtained indirectly; for example, the volume of a tone is adjusted so that it sounds as loud as a given weight feels heavy. 3. Non-metric scaling. These are procedures for scaling psychological variables that are non-metric, that is, that simply cannot be dealt with in the form of scale intervals. This group includes scales of preferences, tastes, judgments about values, etc. The typical technique here is that the subject is presented with pairs of stimuli and asked to rate them in terms of desirability or preference; for example, the subject would rather choose a cheese sandwich or a ham sandwich. There are several mathematically complex procedures by which these ordered judgments can be represented as true interval scales. See multidimensional scaling.

Stevens has developed a group of methods (direct scaling methods) that allows one to obtain an estimate of the magnitude of sensation on an interval or ratio scale as a direct result of the measurement procedure. Stevens argued that it is possible to directly evaluate sensations, for this it is only necessary to use certain methods that allow observers to "translate" their sensations into the language of numbers. Using similar scaling methods, Stevens and his followers found an equation that describes the relationship between the magnitude of a signal and the magnitude of the sensation it causes, called a power law. In accordance with this law, the magnitude of the sensory sensation increases in proportion to the physical intensity of the signal raised to a power.

- relationship evaluation method: it was proposed to explain how many times the proposed sensation is more or less than the previous one (the subject is presented with 2 (or more) stimuli and he must evaluate the relationship between the stimuli according to a given parameter and express this in numerical order);

- relationship method: it was proposed to select for the reference stimulus one that is more or less than it in a certain number of times (fractionation - division or multiplication multiplication).

- magnitude estimation method: it was proposed to evaluate the magnitude of the sensation in units of the standard (there is a standard (it has a numerical value, for example, this is 1), then a stimulus is presented in random order, which must be evaluated in accordance with the standard. The subject must assign numbers to the sequence of stimuli (example: evaluation of emotions) );

- method of setting values: it was proposed to choose a sensation equal to a certain number of units of the standard (inverse to the method of estimating the magnitude). Here the experimenter names the values ​​(numbers) and asks the subject to arrange a number of stimuli in accordance with the presented numerical axis.

Direct methods leading to the interval scale (methods based on the construction of equal distance scales, interval scales):

· Method of equal sensory distances. There are a number of methods in which the subject attempts to select or match a series of stimuli so that they mark subjectively equal distances on a continuum.

The first one "halving the interval". Plateau in 1850 asked artists to recreate a gray tone that is somewhere between black and white. The subjective distance between white and gray was the same as between black and gray. The main goal was to test the validity of Fechner's law. If the midpoint coincided with the geometric mean, not the arithmetic mean, then Fechner would be right. Sometimes the point fell on one mean, sometimes on another; it also happened that she was somewhere between them. It is clear that this method is subject to the same errors as the fractionation method. Indeed, the method of bisecting an interval is very similar to the method of bisecting a quantity. The only difference is that the bisection method can give a true zero for the scale.

Sanford experiment. Of course, there is no reason to limit experiments to bisection. You can split the subjective distance into any number of equal intervals. In the Sanford weighing experiment, 108 bags, ranging from 5 to 100 g, are arranged into five piles with approximately equal sensory distances between them. If the average of all the weights placed in each pile is applied to the ordinate on a logarithmic scale, and the subjective values ​​on a linear scale to the abscissa, then according to Fechner's law, the points should lie on a straight line.

The subject is presented with a set of stimuli and is asked to correlate them all with a certain number of categories. From 3 to 20 categories. Numbers or adjectives are usually used as categories. One simple procedure for categorical scaling is the apparent equal interval method. It is assumed that when a person assigns stimuli to categories, he is able to take into account the intervals between the boundaries of the categories used. Based on this, the experimenter considers the categories as values ​​on a scale of intervals. To obtain reliable data, you need to average a large number of judgments. In modern practice, verbal labels are often used for each numerical category, indicating the degree of expression of the measured feature. These labels help the subject make more accurate and consistent judgments about the magnitude of the stimulus. The influence of the context is great - the values ​​of other stimuli.

Method of cross-modal comparisons.

For a more detailed verification of the power law, experiments were carried out with cross-modal comparison of stimuli. The task of the subject in the experiment was to equalize the intensity of sensations of different modalities. For example, he had to equalize the strength of sensation from the vibration sensor placed on the finger and the volume of the sound. After some adaptation of the subjects to the experimental situation, they become quite stable.

If the power law is indeed true, then there must be a relationship between stimuli and sensations:

Let there be two sensory modalities: Sn and Sm, associated with the corresponding stimuli In and Im by power dependences:

S1= I1 ^n S2= I2 ^m

If we take into account that the subject equalizes the intensities of S1 and S2:

The criterion of equality means that stimuli are equal because they lead to sensory outcomes of the same intensity. In addition, when taking a logarithm, the stimulus intensities are linearly related, which means that this confirms the power law (tgL=m/n, where L is the angle between the straight line and the abscissa axis).

indirect scaling.

Three Methods for Measuring Fechner Thresholds:

1) Method of boundaries (minimum changes): what minimal changes in stimulus cause the difference in sensations.

The standard stimulus is not presented to the subject, and his task is to answer whether he detects a stimulus or. Here, 2 quantities are determined: the magnitude of the stimulus that is first felt by the subject when a series of stimuli of increasing intensity is applied, and the magnitude of the stimulus that he does not feel for the first time when the order of stimuli decreases in intensity. The absolute threshold is taken as the average value of the absolute thresholds of each column.

habituation error- the tendency to keep the answer "yes" in the descending ranks and the answer "no" in the ascending ranks. anticipation error has the opposite character. Associated with the expectation of a change - a change in the answer to the opposite.

the experimenter changes the compared stimulus in small steps in ascending and descending rows. The subject at each change in stimulus must say<, = или >variable stimulus compared to standard. As a result of the experiment, the values ​​of the variable stimulus corresponding to the change in the response category are determined. To determine the values ​​of L, it is recommended to take into account only the 1st transition from + to = (L+, upper difference threshold) and the 1st transition from = to - (L-, lower difference threshold) in the descending series. In the ascending row, the 1st transition from - to = and the 1st transition from = to + are taken into account. Uncertainty interval(IN) - where estimates = are most often found. SI covers a zone with a size of 2 difference thresholds or s.r.p.: from – to = and from = to +. difference threshold= IN/2.

2) Installation method (medium error): the stimulus is trimmed until it subjectively matches the standard.

When determining the difference threshold the subject, as a rule, himself adjusts the compared stimulus, which can continuously change, to the standard, i.e. sets the variable stimulus to such a value that it appears to be equal to the standard. This procedure is repeated several times, and then the average value and the variability of the subject's attitudes are calculated. The mean of the trims (sets) is a direct measure of the TCP (Subjective Equity Point), and the variability of the trims allowed by the subjects can be used to calculate the difference threshold.

When determining the absolute threshold the subject repeatedly sets the value of the variable stimulus, which, in his opinion, is the lowest among the stimuli he detects. The average of these settings is taken as the absolute threshold.

The difference between the TCP and the observer's setting in each individual sample is called variable error(SD), which is measured by the standard deviation.

3) Constant method(comparison of pairs of stimuli, one of which is constant for all pairs).

The method is as follows. Stimuli of varying intensity are presented to the subject in random order. When it comes to determining the difference threshold, stimuli are presented alternating with the normal one. The subject is required to evaluate whether the variable stimulus seems to him more or less than the normal one (in some experiments, the answer is “equal”). In the case of determining the absolute threshold, the subject simply has to say whether he feels or does not feel the irritation presented to him.

If a stimulus or a difference between stimuli is perceived in 50% of cases, then they respectively indicate the position of the absolute and difference thresholds. Note that the stimulus value corresponding to 50% in the transition zone of the absolute threshold corresponds to the point of subjective equality in the transition zone of the difference threshold.

§Adopted from classical psychophysics (Woodworth and Schlosberg, 1974). This is a method of directly obtaining the matrix of semantic similarity of objects. §The subject is tasked with assessing the similarity of values ​​using a certain gradient scale. For example, a scale from 0 to 5, where 0 is no similarity, 5 is almost a match. §This is a fairly accurate method (Miller, 1971), but laborious. The study of the semantic relations of objects requires n(n–1)/2 pairwise comparisons to construct the similarity matrix.

Next, a multivariate analysis procedure was applied. Its essence is as follows. Based on the matrix of subjective similarity (the distance between the analyzed objects), such a geometric space of the minimum possible dimension is reconstructed, in which the distances between the coordinate points corresponding to the analyzed objects are similar to the subjective distances of the similarity matrix.

Mathematically, the multidimensional scaling procedure consists in determining the coordinate projections of points on some coordinate axes, based on known distances between points. Based on the found loads of each word for each of the selected factors-axes of the semantic space, the coordinates of these words in the semantic space were reconstructed.

The most developed technique of semantic analysis. Discussed in detail in the works of J. Deese (1962), Dixon and Horton (1968), Creelman (1965). Analysis of the psychological nature of the processes underlying associations is given in the works of A.A. Leontiev, L.B. Itelson, A.A. Brudny, B.A. Ermolaeva, V.F. Petrenko and others.

The measure of semantic proximity (distance) of a pair of words is the degree of coincidence of the distribution of answers. That is, the degree of similarity of the objects of analysis is established through the similarity of the associations given to them. This value in the works of different authors can be called: the coefficient of intersection, the coefficient of association, the measure of overlap.

Associations are divided into paradigmatic (reaction words and stimulus words from the same grammatical class: father-mother, chair-table, etc.) and syntagmatic (stimulus words and reaction words from different grammatical classes: car-drives, smoke -bad, etc.)

Advantages - simplicity, ease of use, because. can be simultaneously carried out on large groups of subjects; - the ability to identify unconscious components, tk. the subjects work with the value in the mode of use; - associative technique reflects both the cognitive structures behind the linguistic meanings and the individual characteristics of the subjects, their personal meanings.

Designed in 1955. a group of American psychologists led by C. Osgood. It was originally used to study the mechanisms of synesthesia. It has been widely used in studies related to the perception and behavior of a person, with the analysis of social attitudes, personal meanings. The SD method is a combination of scaling procedures and the controlled association method.

The SD method measures the connotative meaning. These are states that follow the perception of the stimulus symbol and necessarily precede meaningful symbol operations (Osgood, 1957). An analogue of this in Soviet psychology is the concept of “personal meaning”, as the meaning of meaning for the subject (A.A. Leontiev, 1965; A.N. Leontiev, 1975).

Advantages of the SD method ¦Compactness (unlike the associative method). ¦ Ease of data processing (numerically presented standardized data are easily amenable to statistical processing). ¦The possibility of associations on the principle of rhyming stamps, rhyming associations, i.e. associations due not to the proximity of the content plan, but to the similarity of the expression plan.

Estimates of concepts on separate scales correlate with each other. With the help of factor analysis, it is possible to single out bundles of highly correlated scales and group them into factors. C. Ozgood considered the phenomenon of senesthesia to be the psychological mechanism that provides the interconnection and grouping of scales into factors. The American psychologist L. Marx (1975) considered synesthesia as a universal form of pre-linguistic categorization that provides generalization at the level of the organism.

A measure of the proximity of the objects under study in the SD method is the similarity of assessment profiles, data on SD scales. For example, let's consider three profiles obtained using the SD method "Assessment of speech properties" according to the factor of emotional expressiveness, expression. It can be seen from the figure that the first profile (*) differs significantly from the second and third profiles +). And the last two profiles are similar to each other.

Factors are a form of generalization of antonym adjectives. The grouping of scales into factors makes it possible to move from the description of objects using the features specified by the scales (the polar profile method) to a more capacious description using a smaller set of categories-factors.

Geometrically, the axes of the semantic space are categories-factors (orthogonal, independent of each other). The connotative meanings of objects (emotionally rich, poorly structured and little realized forms of generalization) are given as coordinate points or vectors within this space. These points are restored based on the knowledge of their projections on the axis of factors (in other words, these are the factor loadings of the object for each factor).

In his research, Ozgood (1962) scaled concepts from a wide variety of conceptual classes and identified three universal categorization factors that are identical in representatives of different linguistic cultures, people of different educational levels, and even in patients with schizophrenia compared with healthy subjects. 42 In the development of the SD method, the following trends can be distinguished: The transition from the construction of universal semantic spaces that differentiate vocabulary from the most diverse concepts of classes, to the construction of private semantic spaces. Expansion of the means of describing the analyzed objects, the use of non-verbal, in particular visual, oppositions for building scales. The transition from constructing spaces based on average group data of randomly selected subjects to constructing semantic spaces that characterize a group of subjects united by a controlled attribute (gender, age, social class, etc.), or to constructing semantic spaces that reflect the differential psychological aspects of personality the subject, his cognitive style.