As a result of studying this chapter, students will:


• the main purpose and types of methods for multidimensional data representation in general psychometrics;

• Basic procedures and basic varieties of factor analysis, multidimensional scaling and cluster analysis;

be able to

• apply factor analysis to solve the problem of reducing the dimensionality of data;

• apply various multidimensional scaling procedures in the analysis of complex stimuli;

• Classify the excess amount of data based on standard cluster analysis procedures;


• Basic skills in multidimensional analysis and presentation of psychological properties and characteristics.

Data Dimension Reduction Capability

Factor analysis

The formation and development of the method of factor analysis is closely related to the formation of an industry of psychology, such as differential psychometrics, or psychodiagnostics.

The task of differential psychometrics is to measure individual differences. It is assumed that personality, individuality is a set of stable individual responses to the environment in which it operates and with which it interacts. Such individual reactions, which possess the property of a super-situation, are usually called personality traits. If these features are associated with the success of performing certain types of activities, they are called abilities.

To test personality traits and abilities in differential psychometrics, various tests and questionnaires are developed. Their purpose is to quantify various aspects of the manifestation of personality as an individual. But since the personality itself is a complex phenomenon, it is initially incomprehensible which individual characteristics are truly unique, and which are the manifestation of its other characteristics, perhaps even hidden from direct observation. It is difficult to immediately choose the necessary number of characteristics essential for the description of the person: as a rule, there are more than necessary. Many repeat one another in part or in full, give excessive information. For example, the talkative and sociable not completely identical, but close in meaning. Are two such characteristics important, or can they be combined into one?

Thus, the problem arises of reducing redundancy in the description of personality traits or the structure of abilities. This problem consists in that from a set of characteristics of a complex research object (which is not only a person, but also many other things in psychology - for example, professional identity, general intelligence, emotional sphere structure, and much more) to identify a minimal set of characteristics by means of which it would be possible to fully and comprehensively describe and explain the complex object of research. It is impossible to solve this problem at random, because any knowledge claiming the status of a scientific one should be justified. This means that the researcher should always be able to answer the question of why he chose precisely so many characteristics for describing or explaining, for example, the structure of the personality or the structure of the emotional sphere, and not more and not less, and why these, and not other characteristics, were chosen .

Precisely for these purposes the method of factor analysis was developed. Such famous representatives of differential psychology and psychometrics as Ch. Spearman, L. Thurstone, R. Cattell and some other researchers have contributed to its development.

Currently, factor analysis is considered as an important method of mathematical statistics, representing one of the variants of common linear models. Its use in psychology has long gone beyond the research of individual differences and the construction of psychological tests. It finds application in many branches of modern psychology, as well as in other natural and social sciences for solving a variety of problems.

As part of the course of the general psychological workshop, we will not dwell in detail on the mathematical foundations of factor analysis of data, but consider only a general description of this method, its varieties and procedures. A more detailed analysis of this method can be found in specialized manuals on the application of mathematical methods in psychology and in the manuals on the most factor analysis.

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