General characteristics of quantitative methods of psychological research
As a result of mastering the material of the chapter, students should:
know
• regulatory requirements for the development, adaptation and use of techniques, the structure of the research process, the principles of psychological research and interpretation of data;
• the main sources and opportunities for the appearance of errors and distortions inherent in the methods of researching the personality, activity, group, organization, management system, ways and ways of preventing and compensating them;
be able to
• apply standard research techniques;
• consider the factors that affect the variability of the empirical data and their interpretation;
own skills
• Optimal selection and development of psychological measurement procedures;
• Evaluation of the degree of applicability of specific techniques, the choice of the most appropriate methods of analysis and resolution of psychological problems;
• Developing psychologically sound recommendations to staff and team leaders and organizations.
Measurement in Psychology
In contrast to qualitative research, the experimentalquantitative procedure is subordinated to a technical measuring scheme borrowed from the natural sciences. When this scheme begins to act in the process of psychological research, it becomes the subject of the cognitive process and ceases to depend on the subjectivism of the researcher, the results of the psychological experiment become objective.
The measurement procedure in quantitative research can evolve in at least three ways. The first way is based on the reduction of the measured quality to the experimental variable. The second is to maintain a known distance between operational constructs and "true" parameters of the measured object, where true psychological qualities only suggest a similarity to mathematical dependencies. The third one is characterized by an amazing and bizarre occurrence of psychological quality from the "factorization of variables" as a consequence of their psychological interpretation.
All three cases to some extent reflect the connection of statistical factors to psychological factors. This is the ratio and is the content of the measurement procedures in psychology, in the basis of which is the comparison operation.
The theory of psychological measurement allocated three types and four levels of measurement.
The type of measurement defines the comparison object, which for the psychological variable under study is the reference ( reference point).
The first view is the normative dimension, whose content is the comparison of the values of a particular experimental variable with the normative level (or estimate). The normative measurement at nominal level uses a percentage scale that is not due to the type of distribution of the empirical variables. It differs in that arithmetically identical differences in the percentage of test evaluations may not correspond to equal differences in the intensity of the estimated variable. The modal characteristic of a variable is the norm. The essence of the nominal measurement is the comparison of the experimental variable with the mode. The normative measurement at ordinal level uses the rank and percentile (percentile) scales, which are also not conditioned by the type of empirical variables distribution. The only condition is the ability to rank indicators by value. In this case, the median may be the norm. The normative measurement at the interval level uses the assumption of the equality of the units of measurement of the psychological indicator throughout the range of its variation. The norm here is, as a rule, the average value of the experimental variable.
The second kind of psychological dimension is criterial (V. Pofam, 1978), based on a direct evaluation of the performance of the test subjects without comparison with other subjects, but only in the ratio with a certain objective (or optimal) level (criterion) for the development of the measured property, quality, attribute, action, function, etc.
Finally, the third type of measurement is the Ipsative dimension (D. Broverman, 1962). It can be aimed at evaluating intraindividual relationships and is not related to the study of interindividual differences, and also to comparison of psychological indicators in different situations. An example of an aspiration measurement may be a study using the RouffierDickson test of cardiovascular activity (by pulse rate) before and after exercise with an indicator in the normal state.
The level of statistical measurement determines the methods and procedures for the mathematical evaluation of experimental data (Table 4.1).
Table 4.1
Measurement levels (S. Stephens, 1946)
Measurement level 
The basic operation that determines the level 
Allowable conversion 
Statistical values for a given level 
Examples 
Nominal 
Assigning the same numbernames to objects that have a common feature 
X '= f (x), where f (x) is the replacement of one numbername by another 
The number of objects in the class (category); association coefficient 
Assigning a numeric code to persons with specific character traits 
Ordi native 
Ranking objects by the severity of a certain characteristic 
X  f (x), where f (x) is Any monotone incremental function 
Median; percentiles 
Ranking of specialists in terms of professional qualifications 
Inter real 
Determining the difference between objects 

The arithmetic mean; dispersion; correlation coefficient 
Celsius temperature scale 
Measuring Relationships 
Definition Equations Relationships values 

Coefficient of variation 
Measuring length, masses 
In accordance with the level of psychological measurement, measurement scales of experimental variables are determined.
The scaling model captures the principle of deriving instrumental scores, the level of the measurement obtained (type of scale), and the choice of ways to evaluate the functional unity of the obtained measurement instrument. In the practice of psychological research, various measuring scales are used. We will review the basic scales and their modifications.
1. Description in natural language. An example of practical application of this scale of measurement is the compilation of the psychological characteristics of a person who consulted or undergoes psychological examination in the process of solving personnel tasks. It, as a rule, is a textual material that characterizes a particular individual and distinguishes him from other people. This description of the characterological and behavioral characteristics of the subject makes it possible speculatively compare its psychological signs with signs of another person. Strictly speaking, the measurement procedure is started.
It should be borne in mind that in a strict sense the psychological dimension is based on the methods of parametric and nonparametric statistics. Although already within the framework of nonparametric scales, mathematical methods are actively used, they are limited in the possibilities of applying the entire breadth of the spectrum of statistical tools.
2. Nonparametric scales.
2.1. Scale of titles. Unclear (blurry) classification. The content of the dive scale is the comparison of the features of real objects with the "standard", the search for the degree of similarity to the standard (A). The standard can be an ideal object (for example, a list of professionally significant qualities, a characteristic of the psychotype) or a real object (the best in the profession, a separate subject).
There is no absolute similarity (identity) to the standard. Therefore, the similarity is determined by the degree of coincidence of the characteristics. In practice, a situation is common where the ratios of psychological objects under investigation are based on logical formulas: "B is similar to A; C is similar to A; but B is not like C .
If some features (characteristics) of one person (A) take place in the characteristic of the other (B), then these people have similar and distinctive features in individual characteristics ("A" like "B"). If B and C there are no similar traits, then "B" not like C & quot ;. However, in individuals "A and C there may be similar characterological features (Figure 4.1).
Fig. 4.1. Illustration of the fuzzy (blurred) classification
If, in the course of diagnostic studies, the "similarity" score is " psychological characteristics of people with the help of mathematical calculations is quite rare, then in the psychology of occupations, the identity of specialties is often computed using the coupling coefficient.
The coefficient of conjugation of specialties (professions) is calculated by the formula:
where Cn is the conjugacy coefficient of specialties,  the total number of identical attributes (qualities),  the total number of all professionally significant attributes (qualities), S  the number of specialties.
2.2. Scale of titles. Strict classification. The content of this scale is described by the logical rule: A  is not In & quot ;; In  not C & quot ;; C  not D etc. Scale Strictly determines the difference of one measured characteristic (or subject) from another. Often in questionnaires works dichotomic scale "yesno", which is interpreted in the form of the presence or absence of the trait being examined ("this attribute is or is not"). For example, the Differential Diagnostic Questionnaire EA Klimova is interpreted within the framework of this scale as the presence in a subject of attributes belonging to five categories (types of personality orientation): "man", "technique", "sign system", "nature" and art image & quot ;. Nominal affiliation of the subject to one of the areas determines the absence of attributes of other categories.
2.3. Scale of orders (rank scale) (strict ordering). In the ordinal scale of strict ordering, the logical scheme A & gt; In & quot ;; In & gt; C & quot ;; C & gt; D etc. The main content of the scale is characterized by a situation of differentiation of subjects according to the degree of increase or decrease in the sign or quality.
2.4. Scale of orders (rank scale) (nonstrict ordering). In the ordinal scale of nonstrict ordering, the logical scheme is "more or equal to  less than or equal to" ( A & gt; In & quot ;; In C & quot ;; C & gt; D etc.). An example of rank scales are the different rating scores of subjects or experimental groups. A nonordered ordered rank scale occurs in cases of equality of rank grading, when subjects are assigned the same rank score.
3. Parametric scales.
If the investigated psychological phenomena differ among themselves by a certain number of conventional units, then a new level of measurement based on the parameter appears.
Parametric scales include interval, ratios and absolute scales.
3.1. Interval scale (interval ). The difference of a scale of this type from other parametric scales is that the origin (zero) and intervals are chosen conditionally. Here the logical rule is that between the psychological signs A and B there is a difference, measured by conditional units N (interpreted as A more (or less) N The calculated standardized interval allows us to assume that at a confidence level (95%) the difference between A and B is constant and is equal to a certain value.
3.2. Scale of relations. The application of the relationship scale is carried out in psychophysiological studies. Its content is the presence of an absolute reference point, from which a relatively equal countdown takes place. A living example of such a measuring scale is the measurement of length and weight, where the reference point (no weight or length) takes place, and intervals are generally accepted units. In physiology, the scale of relationships measures the activity of the heart (heart rate  heart rate).
3.3. The absolute scale (F. Lord, M. Novik, 1968) is applied in a situation where there is zero (absence of a sign or quality) from which the absolute values are counted. Examples are physical measurements (recording the number of electrons in an atom, the charge of a nucleus, etc.).
The abovementioned onedimensional scales can be converted to other scales of a lower level (scale power can be reduced). So, the interval scale can be represented quite easily in the form of a rank (by rating of a score), and in the presence of a criterion (the value of a feature or its boundaries)  in a nominal scale. Onedimensional psychological scales obtained by measuring the same feature in the same object using different instruments can also be transformed into multidimensional scales by constructing functional relationships between them.
For processing and analysis of empirical data, obtained as a result of the experiment, psychologists apply various methods of mathematical calculus.
The first step is to test the hypothesis of the form of statistical data distribution. This is necessary to determine the acceptable level of psychological measurements. As is known, if the experimental data are distributed according to the normal distribution law (the GaussLaplace law), then in the process of mathematical analysis it is correct to use the methods of parametric statistics, if not, then nonparametric. The contentprincipal difference between parametric calculus and nonparametric calculus is that in the latter case the results obtained should be considered as facts only for a specific sample. In the parametric measurement, the result becomes a fact for the entire population under study.
In each metric scale, certain statistical methods are applied. Methods of nonparametric statistics are applicable in the nominal and ordinal scales. Parametric statistics are used in interval and more powerful scales.
Any social research related to the application of statistics and probability theory is aimed at studying a large number of people, their feature space, for generalizations and typological conclusions about all or part of the observed population. In psychometry (and also other mathematical disciplines) this population is called the general population. The psychologist is not able to study the properties of the whole population, so he works with the sample (part of the population, the group), and draws conclusions based on certain procedural rules for the entire population. Thus, the researcher, studying the properties of a relatively small group, obtains knowledge about the properties of the general population. The characteristics of the distribution of the general population are called parameters, and the characteristics of the sample distribution are called parameter estimates. For the possibility of applying parametric statistics methods, a procedure is used to determine the type of statistical distribution of empirical data.
According to Bernoulli's theorem (1713), with an infinite increase in the sample size, the empirical probability distribution tends to the theoretical distribution (the more the number of observations, the greater the probability of their coincidence and the "smoother" is the data distribution schedule). Theoretically, under uncertainty, the results of psychological variables depend on the randomness and are determined by a large number of independent factors, the influence of which can not be taken into account. But, the larger the volume of empirical data, the closer the real distribution to the theoretically expected normal probability. The graph of the normal distribution was first constructed by mathematicians P. Laplace and K. Gauss as a result of research in the field of game theory. In the XIX century. the Belgian statistician A. Kutetlet was the first to apply the notion of a normal distribution of empirical data to the study of human anthropometric qualities. In particular, noticing the similarity of the normal distribution curve to the variability of anthropometric features, he put forward a hypothesis that the researchers' desire for an experimental "ideal" or the norm, due to various circumstances, meets with failure. Kuthelet's experience in applying the normal distribution was rethought and developed by F. Galton, who actively applied the normal distribution graph for quantifying and transforming data of individual and group differences. However, it should be remembered that the assumptions about the normal distribution of data are model character and can not be fulfilled absolutely accurately.
Therefore, the statistical conclusions drawn on the basis of a model approximating to the normal distribution are also more or less approximate. Estimate the proximity practical curve to the parameters of the normal is realized by calculating: a) the frequency distribution of the data in a proportion of 16.5%  67%  16.5%, b) asymmetry and kurtosis, and c) Pearson's (Chisquare), Kolmogorov's (1933) ), Yastremskii (1949), etc. In the first case, the structure of the accumulated data is evaluated, in the second case, the position of the top of the empirical curve with respect to the theoretical curve is characterized, and finally the position of certain "patches" (frequency groups) of the practical curve relative to the theoretical normal.
For example, the second option for calculating the type of data distribution assumes that the asymmetry coefficient (As) shows the magnitude of the displacement of the vertex of the empirical curve relative to the calculated vertex horizontally, and the kurtosis coefficient (Ex) determines the "slope" practical curve (Figure 4.2).
Fig. 4.2. Empirical data distribution relative to the theoretical curve (GaussLaplace distribution)
The estimation of normality of distribution of empirical data can be carried out using Pearson's agreement criterion, Chisquared (χ2). The probability of the correspondence between the practical frequency of the manifestation of the trait (in terms of the test scores) and the theoretical distribution is calculated.
As a result of the study of the parameters of the distribution of empirical data, a psychologist can make at least two practical conclusions:
1) distribution of test data close (or not) to a normal theoretical distribution and, therefore, it is possible to use parametric statistics methods;
2) the technique (or weakly) differentiates the subjects according to the structure of the measured property and, on the whole, reflects (or not) the properties of the studied population.
In the practice of studying the distribution of psychological data, at least two kinds of curves are possiblethe symmetric and asymmetric distribution of S. Poisson (Figure 4.3). The symmetric distribution of data includes the normal distribution (the GaussLaplace distribution) (Figure 4.4) and the bimodal distribution (Figure 4.5).
Fig. 4.3. Asymmetric distribution of empirical data
Fig. 4.4. Symmetric distribution of empirical data
Fig. 4.5. Bimodal distribution of empirical data
The main factors influencing the shape of the distribution of empirical data in psychological research are: the inadequacy of the sample, the use of invalid or unreliable means of measuring psychological variables and conditions directly affecting the quality studied.
It should be emphasized that the inadequacy of the sample occurs as a result of the selection of the test subjects, when in the course of diagnosis, by screening out people showing unsatisfactory results, the normal distribution curve is transformed into a Poisson Jcurve. The distribution of psychological data in the form of a Jcurve was first used by F. Allprot (1934) to study social conformism.
In conclusion, we should say a few words about the peculiarities of the psychological dimension and the application of mathematical methods in this field. Undoubtedly, the use of exact calculus in psychology raised it to the height of the natural sciences. This conclusion is made by many leading psychologists. But the merit of both experiment and mathematical methods is not that a new branch of psychological knowledge (or even industry) has appeared, but, apparently, that psychology has acquired a quantitative method that can lead to new qualitative conclusions. Traditionally, it is believed that the use of mathematics in the social sciences is expressed in obtaining only quantitative characteristics. This understanding is extremely simplistic, since quantitative determinants are always related to qualitative ones. Quantitative and qualitative procedures are one and the same process of psychological cognition of reality, one can not exist without the other.
Acceptance of mathematical and experimental procedures by psychologists and especially representatives of "humanitarian" directions is associated with at least four problems.
First is associated with nonexperimental character of empirical social sciences. The natural sciences deal with the magnitudes of the phenomena being studied. Here the experiment is the transition from the indicator to the phenomenon. Social sciences have to study only the indicators of hidden phenomena. Such latency leads not only to proving the accuracy of revealing the essence of the things themselves, but also to substantiating the validity of the instrument of this study. This is the specificity of the cognitive process in psychology, as, in this sense, the "nonexperimental" science.
The second problem is that the psychological dimension  first of all, the measurement of mass phenomena, aggregates, types, etc. In this regard, the psychologist is faced with the need to operate with different symbolic systems  the volume of the aggregate, measures of position, dispersion, communication, etc. Single, individual cases that go beyond the framework of a typical phenomenon often acquire the status of an artifact  of trust, error or error.
The third problem is related to the multidimensionality, complexity, complexity of social phenomena and the need to reflect this complexity in the development of adequate research methods, as well as with a certain system of data, characteristics, indicators, etc.
The fourth problem concerns the objectivity of the psychological experiment is that the results of social research bear the imprint of the researcher's influence. According to N. Wiener, "in the social sciences we are dealing with short statistical series and can not be sure that the significant part that we observed is not created by ourselves."
Thus, modern psychology can not imagine its existence and development outside the experimental field, without the use of statistical methods. Mathematics in psychological research is used in the process of forming an experimental sample, designing an experiment, obtaining and analyzing psychological data and modeling (S. Stauffer, 1957). It should be seen as a reliable assistant and a support in a difficult psychological investigation.
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