Relationships and relationship variables. Normalization of relations. Six normal forms

Relationship. Variable relationships. Meaning of relation variables. Basic relation variables and their representations. Predicates and propositions

Computer science, cybernetics and programming

Relationship. Variable relationships. Meaning of relation variables. Basic relation variables and their representations.

Relationship. Variable relationships. Meaning of relation variables. Basic relation variables and their representations. Predicates and statements.

Definitions

n -ary relation R, or R power ratio n , called a subset of the Cartesian product of sets D 1, D 2, D 3... Dn (n >=1), not necessarily different. Source sets D 1, D 2, D 3...are called domains in the model (in the DBMS the concept of data type is used).

The relationship is simple graphic interpretation, it can be presented in the form of a table, the columns (fields, attributes) of which correspond to occurrences of domains in the relation, and the rows (records) to sets of values taken from the source domains. The number of rows (tuples) is called the cardinal number of the relation (cardinality), or the cardinality of the relation.

This table has a number of properties:

There are no two identical rows in the table.
The table has columns corresponding to the attributes of the relationship.
Each attribute in a relation has a unique name.
The order of rows in the table is arbitrary.

An attribute here refers to the occurrence of a domain in a relation. The rows of a relation are called tuples.

The header Hr (or schema) of the relation r a finite set of ordered pairs of the form , where A is called the name of the attribute, and T denotes the name of some base type or previously defined domain, that is, the set of valid values. By definition, all attribute names in the header of a relationship are required to be distinct.

Tuple tr corresponding to header Hr set of ordered triplets of the form , one such triplet for each attribute in Hr. Third element of the v triplet must be a valid value for the data type or domain T. Note: Since attribute names are unique, specifying the domain in the tuple is unnecessary.

The body Br of the relation is an unordered set of distinct tuples tr.

The value Vr of a relation r is a pair of sets Hr and Br.

The concept of a primary key is also useful - this is a set of attributes that uniquely defines a tuple and is minimal among all its subsets (that is, none of the attributes can be removed). When adding new records, the primary key must remain the primary key (for example, it would be incorrect to use the set First Name + Patronymic + Last Name of an employee as the primary key, even if at the time the table was created there were no full namesakes among the people entered in it).

Basic concepts:

An object a domain element that can be clearly identified.

The properties of an object are displayed using variables, which are elementary units of information within the database, and are called attributes.

Attribute/field/columna logically indivisible element related to the properties of some object or process.

Attributes are divided into attributes-signs and attributes-bases.

Attributes signsare a qualitative characteristic of the object.
Attributes basecharacterize the quantitative side of the object.

Attributes have many valid values.

The set of all possible values of an attribute is called domain.

The set of attributes characterizing one object is calledrecord/tuple/string.

The record type is determined by the properties of the object.

Key an attribute or a set of attributes that uniquely define an object.

Potential Keya key that can identify an object.

From the set of potential keys, one primary key is selected. Otheralternative keys.

Surrogate keyan attribute that is created to uniquely identify an object.

Secondary key an attribute that assigns an object to a certain group.

Table indexingthe process of creating an index file, which describes how to sort a table by a selected field or expression.

In modern DBMSs, several indexes can be stored in one index file.

A filter can be applied to the table.

Filter logical condition that allows you to display only those records that are satisfactory. this condition.

In the database noun. concept representation virtual table , which can display data from one or more tables.

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The basis for the construction of modern experimental psychology is the formula K. Levina- behavior is a function of personality and situation:

B =f(P;S).

Neobehaviorists put in the formula instead R(personality) O (organism), which is more accurate if we consider not only people, but also animals as test subjects, and reduce the personality to the organism.

Be that as it may, most specialists in the theory of psychological experiments, in particular McGuigan, believe that in psychology there are two types of laws:

1) “stimulus-response”;

2) “organism-behavior*.

First type of laws discovered during experimental research, when the stimulus (task, situation) is an independent variable, and the dependent variable is the response of the subject.

Second type of laws is the product of a method of systematic observation and measurement, since the properties of the body cannot be controlled by psychological means.

Are there "crossovers"? Of course. Indeed, in a psychological experiment, the influence of so-called additional variables is often taken into account, most of which are differential psychological characteristics. Therefore, it makes sense to add to the list "system" laws, describing the influence of a situation on the behavior of a person with certain properties. But in psychophysiological and psychopharmacological experiments, it is possible to influence the state of the body, and during a formative experiment, it is possible to purposefully and irreversibly change certain personality properties.

In a classic psychological behavioral experiment, it is established functional dependence kind

R = f(S) ,

Where R- answer, a S- situation (stimulus, task).

The variable S is systematically varied, and the changes in the subject's response determined by it are recorded. During the study, the conditions under which the subject behaves in one way or another are revealed. The result is recorded in the form of a linear or nonlinear relationship.

Other type dependencies are symbolized as the dependence of behavior on the personal properties or states of the subject’s body:

R = f(O) or R = f(P).

The dependence of the subject's behavior on a particular state of the body (illness, fatigue, level of activation, frustration of needs, etc.) or on personal characteristics (anxiety, motivation, etc.) is studied. Research is conducted with the participation of groups of people that differ in a given characteristic: property or current condition.

Naturally, these two strict dependencies are the simplest forms of relationships between variables. More complex dependencies established in a specific experiment are possible; in particular, factorial designs make it possible to identify dependencies of the form R = f (S 1, S 2), when the subject’s answer depends on two variable parameters of the situation, and behavior is a function of the state of the organism and the environment.

Let's focus on Levin's formula. In general form, it expresses the ideal of experimental psychology: the ability to predict the behavior of a specific individual in a specific situation. The variable “personality”, which is part of this formula, can hardly be considered only as “additional”. The neo-behaviourist tradition suggests using the term “intervening” variable. IN Lately for such “variables” - personality traits and states - the term “moderator variable”, i.e., mediator, was assigned.

Let's look at the main possible options relationships between dependent variables.

There is at least six types, variable connections.

First, he is the simplest, - no dependency , Graphically, it is expressed in the form of a straight line parallel to the x-axis on the graph, where along the x-axis (X) levels of the independent variable are plotted. The dependent variable is not sensitive to changes in the independent variable (see Figure 4.8).

Monotonically increasing dependence is observed when an increase in the values of the independent variable corresponds to a change in the dependent variable (see Fig. 4.9).

Monotonically decreasing dependence is observed if an increase in the values of the independent variable corresponds to a decrease in the level of the independent variable (see Fig. 4.10).

Nonlinear dependence– The U-shaped type is found in most experiments in which features of the mental regulation of behavior are revealed: (see Fig. 4.11).

Inverted U-shaped relationship obtained in numerous experimental and correlational studies in both personality psychology, motivation, and social psychology(see Fig. 4.12).

The last variant of dependence is not detected as often as the previous ones - complex quasiperiodic dependence the level of the dependent variable from the level of the independent one (see Fig. 4.13).

When choosing a description method, the “principle of economy” applies. Any simple description is better than a complex description, even if they are equally successful. Therefore, arguments common in domestic scientific discussions like “Everything is much more complicated in reality than the author imagines” are, to say the least, meaningless. Moreover, no one knows how “in reality”.

The so-called “complex description”, “multidimensional description” is often simply an attempt to avoid solving a scientific problem, a way of disguising personal incompetence, which they want to hide behind a tangle of correlations and complex formulas where everything is equal to everything.

Parameter name	Meaning
Article topic:	Relationships between variables
Rubric (thematic category)	Psychology

At the root of the construction of modern experimental psychology lies the formula K. Levina- behavior is a function of personality and situation:

B =f(P;S).

Neobehaviorists put in the formula instead R(personality) O (organism), which is more accurate, if we consider not only people but also animals as test subjects, and the personality is reduced to the organism.

Be that as it may, most specialists in the theory of psychological experimentation, in particular McGuigan, believe that in psychology there are two types of laws:

1) “stimulus-response”;

2) ʼʼorganism-behavior*.

First type of laws is discovered during an experimental study when the stimulus (task, situation) is an independent variable, and the dependent variable is the response of the subject.

Second type of laws is the product of a method of systematic observation and measurement, since the properties of the body cannot be controlled by psychological means.

Are there “intersections”? Of course. Indeed, in a psychological experiment, the influence of so-called additional variables is often taken into account, most of which are differential psychological characteristics. Therefore, it makes sense to add to the list “systemic” laws, describing the influence of a situation on the behavior of a person with certain properties. But in psychophysiological and psychopharmacological experiments it is possible to influence the state of the body, and in the course of a formative experiment - to purposefully and irreversibly change certain personality properties.

In a classic psychological behavioral experiment, a functional dependence of the form

R = f(S) ,

Where R- answer, a S- situation (stimulus, task).

Other type dependencies are symbolized as the dependence of behavior on the personal properties or states of the subject’s body:

R = f(O) or R = f(P).

Let's focus on Levin's formula. In general form, it expresses the ideal of experimental psychology: the ability to predict the behavior of a specific individual in a specific situation. The variable “personality”, which is part of this formula, can hardly be considered only as “additional”. The tradition of neobehaviorism suggests using the term “intermediate” variable. Recently, the term “moderator variable,” i.e., mediator, has been assigned to such “variables” - personality traits and states.

Let's consider the main possible relationships between dependent variables.

There is at least six types, variable connections.

Monotonically increasing dependence is observed when an increase in the values of the independent variable corresponds to a change in the dependent variable (see Fig. 4.9).

Monotonically decreasing dependence observed if an increase in the values of the independent variable corresponds to a decrease in the level of the independent variable (see Fig. 4.10).

Nonlinear dependence– The U-shaped type is found in most experiments in which features of the mental regulation of behavior are revealed: (see Fig. 4.11).

Inverted U-shaped relationship obtained in numerous experimental and correlational studies in both personality psychology, motivation, and social psychology (see Fig. 4.12).

When choosing a description method, the “principle of economy” works. Any simple description is better than a complex description, even if they are equally successful. For this reason, arguments common in domestic scientific discussions like “Everything is much more complicated in reality” than the author imagines are at least meaningless. Moreover, no one knows how it really is.

The so-called “complex description”, “multidimensional description” is often simply an attempt to avoid solving a scientific problem, a way of masking personal incompetence, which they want to hide behind a tangle of correlations and complex formulas where everything is equal.

Relationships between variables - concept and types. Classification and features of the category "Relationships between variables" 2017, 2018.

Concept and principles of database construction.

A database is a set of independent materials presented in an objective form (articles, calculations, regulations, court decisions and other similar materials), systematized in such a way that these materials can be found and processed using electronic computer(COMPUTER)

2. Relational model. Three aspects of the model. Basic concepts underlying the relational model.

The relational data model is a logical data model, an applied theory of database construction, which is an application to data processing problems of such branches of mathematics as set theory and first-order logic.

The relational data model includes the following components:

Structural aspect (component) - the data in the database is a set of relationships.

An aspect (component) of integrity - relationships (tables) meet certain integrity conditions. RMD supports declarative integrity constraints at the domain (data type) level, relation level, and database level.

Aspect (component) of processing (manipulation) - RMD supports relation manipulation operators ( relational algebra, relational calculus).

Relationship. Relational variables. The meaning of relationships, properties of relationships. Domains.

Domain

The concept of a domain is more specific to databases, although there are analogies with subtypes in some programming languages (in fact, in their Third Manifesto, Christopher Date and Hugh Darwen eliminate the distinction between domain and data type altogether). IN general view a domain is defined by specifying some base data type to which the elements of the domain belong, and an arbitrary logical expression applied to an element of this data type (domain constraints). A data element is a domain element if and only if the evaluation of this Boolean expression returns true (for boolean values we will alternately use the notation true and false or true and false). Each domain is associated with a name that is unique among the names of all domains in the corresponding database.

The most correct intuitive interpretation of the concept of a domain is its perception as an acceptable potential, limited subset of values of this type. For example, the domain NAMES in our example is defined on the base type character strings, but its values can only include those strings that can represent names (in particular, to be able to represent Russian names, such strings cannot begin with a soft or hard character and cannot be longer than, for example, 20 characters). If a certain attribute of a relationship is defined on a certain domain (as, for example, in Fig. 3.1 the SLU_NAME attribute is defined on the NAMES domain), then the domain constraint subsequently plays the role of an integrity constraint imposed on the values of this attribute.

It should also be noted the semantic load of the domain concept: data are considered comparable only if they belong to the same domain. In our example, the values of the domains PASS NUMBER and DEPARTMENT NUMBER are of the type integer, but are not comparable (allowing them to be compared would be pointless)

Relationship concept is the most fundamental in the relational approach to organizing databases, since the n-ary relation is the only generic data structure stored in a relational database. This is reflected in the general name of the approach - the term relational comes from relation. However, the term relation itself is extremely imprecise, because when we talk about any data that is stored, we must mean the type of that data, the values of that type, and the variables in which the values are stored. Accordingly, to clarify the term relation, the concepts of relation header, relation value and relation variable are distinguished. In addition, we need the auxiliary concept of a tuple.

It is worth emphasizing here that any database update operation accepted in practice - INSERT (inserting a tuple into a relation variable), DELETE (removing a tuple from a relation value by a relation variable) and UPDATE (modifying a relation value tuple of a relation variable) - from a model point of view is the operation of assigning a relation variable some new relation value. This does not mean at all that the listed operations should be performed in exactly this way in the DBMS: the main thing is that the result of the operations corresponds to this model semantics. Note that in classical relational databases data, once the database schema was defined, only the values of relationship variables could be changed. However, now in most implementations it is also possible to change the database schema: defining new and changing the headers of existing relationship variables. This is commonly called database schema evolution.

Relationship variable keys. Types of keys.

A-priory, primary key a relation variable is a subset5) S of the set of attributes of its header such that at any time the value primary key(composite if the primary key includes more than one attribute) in any tuple of the body of the relation differs from the value of the primary key in any other tuple of the body of this relation, and no proper subset6) S has this property. In the next section we will show that the existence of a primary key for any relation value is a consequence of one of fundamental properties relations, namely the property that the body of a relation is a set of tuples. The usual everyday representation of a relation is a table, the header of which is the schema of the relation, and the rows are the tuples of the instance relation; in this case, the attribute names correspond to the names of the columns of the given table. Therefore, people sometimes talk about “table columns”, meaning “relationship attributes”.

Independent variable. The researcher should strive to operate only on the independent variable in the experiment. An experiment where this condition is met is called pure experiment. But more often than not, during an experiment, by varying one variable, the experimenter also changes a number of others. This change can be caused by the action of the experimenter and is due to the relationship between two variables. For example, in an experiment on developing a simple motor skill, he punishes the subject for failures electric shock. The size of the punishment can act as an independent variable, and the speed of skill development can act as a dependent variable. Punishment not only reinforces the appropriate reactions in the subject, but also gives rise to situational anxiety in him, which affects the results - it increases the number of errors and reduces the speed of skill development.

The central problem in conducting experimental research is identifying the independent variable and isolating it from other variables. As independent variables in psychological experiment may act:

characteristics of tasks;

· features of the situation ( external conditions);

· controlled characteristics (states) of the subject.

The latter are often called “organism variables.” Sometimes isolated fourth type variables - constant characteristics subject (intelligence, gender, age, etc.), but, in my opinion, they belong to additional variables, since they cannot be influenced, but can only take into account their level when forming experimental and control groups.

The characteristics of the task are something that the experimenter can manipulate more or less freely. According to the tradition coming from behaviorism, it is believed that the experimenter varies only the characteristics of the stimuli (stimulus variables) but he has much more options at his disposal. The experimenter can vary the stimuli or task material, change the type of response of the subject (verbal or nonverbal response), change the rating scale, etc. He can vary the instructions, changing the goals that the subject must achieve during the task. The experimenter can vary the means that the subject has to solve the problem and put obstacles in front of him. He can change the system of rewards and punishments during the task, etc.

The features of the situation include those variables that are not directly included in the structure of the experimental task performed by the subject. This could be the temperature in the room, the environment, the presence of an external observer, etc.

Experiments to identify the effect of social facilitation (amplification) were carried out according to the following scheme: the subject was given any sensorimotor or intellectual task. He first performed it alone, and then in the presence of another person or several people (the sequence, of course, changed depending on different groups). The change in the productivity of the subjects was assessed. In this case, the subject’s task remained unchanged, only the external conditions of the experiment changed.

What can the experimenter vary?

Firstly, these are the physical parameters of the situation: the location of the equipment, appearance rooms, lighting, sounds and noises, temperature, placement of furniture, painting of walls, time of the experiment (time of day, duration, etc.). That is, all the physical parameters of the situation that are not stimuli.

Secondly, these are socio-psychological parameters: isolation - work in the presence of an experimenter, work alone - work with a group, etc.

Thirdly, these are the features of communication and interaction between the subject(s) and the experimenter.

Judging by publications in scientific journals, in recent years there has been a sharp increase in the number of experimental studies that involve varying external conditions.

“Organismal variables,” or uncontrollable characteristics of the subjects, include physical, biological, psychological, socio-psychological and social characteristics. They are traditionally referred to as “variables,” although most are constant or relatively constant throughout life. The influence of differential psychological, demographic and other constant parameters on an individual’s behavior is studied in correlation studies. However, the authors of most textbooks on the theory of psychological method, for example M. Matlin, classify these parameters as independent variables of the experiment.

As a rule, in modern experimental research, the differential psychological characteristics of individuals, such as intelligence, gender, age, social status(status), etc., are taken into account as additional variables that are controlled by the experimenter in a general psychological experiment. But these variables can turn into a “second main variable” in differential psychological research, and then a factorial design is used.

Dependent variable. Psychologists deal with the behavior of the subject, so parameters of verbal and nonverbal behavior are selected as the dependent variable. These include: the number of mistakes the rat made while running the maze; the time the subject spent solving the problem, changes in his facial expressions when watching an erotic film; motor reaction time sound signal etc.

The choice of behavioral parameter is determined by the initial experimental hypothesis. The researcher must specify it as much as possible, i.e. ensure that the dependent variable is operationalized - amenable to registration during the experiment.

Behavior parameters can be divided into formal-dynamic and substantive. Formal-dynamic (or spatio-temporal) parameters are quite easy to record with hardware. Let's give examples of these parameters.

1. Accuracy. The most frequently recorded parameter. Since most of the tasks presented to the subject in psychological experiments are achievement tasks, then accuracy or the opposite parameter - the error of actions - will be the main recorded parameter of behavior.

2. Latency. Mental processes occur hidden from the outside observer. The time from the moment the signal is presented to the choice of response is called latent time. In some cases, latency time is the most important characteristic process, for example when solving mental problems.

3. Duration, or speed, execution. It is a characteristic of executive action. The time between the selection of an action and the end of its execution is called the speed of action (as opposed to latent time).

4. Pace, or frequency of actions. The most important characteristic, especially when studying the simplest forms of behavior.

5. Productivity. The ratio of the number of errors or the quality of execution of actions to the execution time. It serves as the most important characteristic in the study of learning, cognitive processes, decision-making processes, etc. Contentful parameters of behavior involve categorizing the form of behavior either in terms of ordinary language or in terms of the theory whose assumptions are tested in a given experiment.

Recognizing different forms of behavior is the job of specially trained experts or observers. It takes considerable experience to characterize one act as a manifestation of submission, and another as a manifestation of servility.

The problem of recording qualitative features of behavior is solved through: a) training observers and developing observation cards; b) measuring formal dynamic characteristics of behavior using tests.

The dependent variable must be valid and reliable. The reliability of a variable is manifested in the stability of its recordability when experimental conditions change over time. The validity of a dependent variable is determined only under specific experimental conditions and in relation to a specific hypothesis.

Three types of dependent variables can be distinguished: 1) simultaneous; 2) multidimensional; 3) fundamental. In the first case, only one parameter is recorded, and it is this parameter that is considered a manifestation of the dependent variable (there is a functional linear relationship between them), as, for example, when studying the time of a simple sensorimotor reaction. In the second case, the dependent variable is multidimensional. For example, the level of intellectual productivity is manifested in the time it takes to solve a problem, its quality, and the difficulty of the problem solved. These parameters can be fixed independently. In the third case, when the relationship between individual parameters multidimensional dependent variable, the parameters are considered as arguments, and the dependent variable itself is considered as a function. For example, a fundamental measurement of the level of aggression F(a) is considered as a function of its individual manifestations (A) facial expressions, pantomimes, swearing, assault, etc.

F(a) =f(a 1,a 2,...,a n).

There is one more important property dependent variable, namely, the sensitivity (sensitivity) of the dependent variable to changes in the independent one. The point is that manipulation of the independent variable affects the change in the dependent variable. If we manipulate the independent variable, but the dependent variable does not change, then the dependent variable is non-positive with respect to the independent one. Two variants of manifestation of non-positivity of the dependent variable are called “ceiling effect” and “floor effect”. The first case occurs when the task presented is so simple that the level of its implementation is much higher than all levels of the independent variable. The second effect, on the contrary, occurs when the task is so difficult that the level of its performance is below all levels of the independent variable.

So, like other components psychological research, the dependent variable must be valid, reliable, and sensitive to changes in the level of the independent variable.

There are two main techniques for recording changes in the dependent variable. The first is used most often in experiments involving one subject. Changes in the dependent variable are recorded during the experiment following changes in the level of the independent variable. An example is the recording of results in learning experiments. The learning curve is a classic trend - changes in the success of completing tasks depending on the number of trials (time of the experiment). To process such data, the statistical apparatus of trend analysis is used. The second technique for recording changes in the level of an independent variable is called delayed measurement. A certain period of time passes between the impact and the effect; its duration is determined by the distance between the effect and the cause. For example, taking a dose of alcohol increases the time of the sensorimotor reaction not immediately, but after a certain time. The same can be said about the effect of memorizing a specific number of foreign words on the success of translating a text into a rare language: the effect does not appear immediately (if it does).

Relationships between variables. The construction of modern experimental psychology is based on K. Lewin’s formula - behavior is a function of personality and situation:

Neobehaviorists put in the formula instead R(personality) ABOUT(organism), which is more accurate if we consider not only people but also animals as test subjects, and the personality is reduced to the organism.

Be that as it may, most specialists in the theory of psychological experimentation, in particular McGuigan, believe that there are two types of laws in psychology: 1) “stimulus-response”; 2) “organism-behavior”.

The first type of laws is discovered during experimental research, when the stimulus (task, situation) is an independent variable, and the dependent variable is the response of the subject.

The second type of laws is a product of the method of systematic observation and measurement, since the properties of the body cannot be controlled by psychological means.

Are there "crossovers"? Of course. Indeed, in a psychological experiment, the influence of so-called additional variables is often taken into account, most of which are differential psychological characteristics. Therefore, it makes sense to add to the list "system" laws, describing the influence of a situation on the behavior of a person with certain properties. But in psychophysiological and psychopharmacological experiments it is possible to influence the state of the body, and in the course of a formative experiment - to purposefully and irreversibly change certain personality properties.

In a classic psychological behavioral experiment, a functional dependence of the form

Where R- the answer is a S- situation (stimulus, task). Variable S varies systematically, and the changes in the subject’s response determined by it are recorded. During the study, the conditions under which the subject behaves in one way or another are revealed. The result is recorded in the form of a linear or nonlinear relationship.

Another type of dependency is symbolized as the dependence of behavior on the personal properties or states of the subject’s body:

R = f (O) or R = f (P).

The dependence of the subject's behavior on one or another state of the body (illness, fatigue, level of activation, frustration of needs, etc.) or on personal characteristics (anxiety, motivation, etc.) is studied. Research is conducted with the participation of groups of people that differ in a given characteristic: property or current condition.

Naturally, these two strict dependencies are the simplest forms of relationships between variables. More complex dependencies established in a specific experiment are possible; in particular, factorial designs make it possible to identify dependencies of the form R = f(S 1, S 2), when the subject’s answer depends on two variable parameters of the situation, and behavior is a function of the state of the organism and the environment.

Let's focus on Levin's formula. In general form, it expresses the ideal of experimental psychology - the ability to predict the behavior of a specific individual in a certain situation. The variable “personality”, which is part of this formula, can hardly be considered only as “additional”. The neobehaviourist tradition suggests using the term “intervening” variable. Recently, the term “moderator variable” has been assigned to such “variables”—properties and states of personality—i.e. intermediary

Let's consider the main possible options for relationships between dependent variables. There are at least six types of variable relationships. The first, which is also the simplest, is the absence of dependence. Graphically, it is expressed in the form of a straight line parallel to the x-axis on the graph, where along the x-axis (X) levels of the independent variable are plotted. The dependent variable is not sensitive to changes in the independent variable (see Figure 4.8).

A monotonically increasing dependence is observed when an increase in the values of the independent variable corresponds to a change in the dependent variable (see Fig. 4.9).

A monotonically decreasing dependence is observed if an increase in the values of the independent variable corresponds to a decrease in the level of the independent variable (see Fig. 4.10).

Nonlinear dependence U-shaped type is found in most experiments in which features of mental regulation of behavior are revealed: (see Fig. 4.11).

Inverted U-shaped dependence is obtained in numerous experimental and correlational studies both in personality psychology, motivation, and in social psychology (see Fig. 4.12).

The last version of the dependence is not found as often as the previous ones - a complex quasiperiodic dependence of the level of the dependent variable on the level of the independent one (see Fig. 4.13).

Relationships and relationship variables. Normalization of relations. Six normal forms

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