Correlation analysis - one of the main methods of statistical processing of research results in the field of psychology, biology, medicine, etc. - all those sciences that study what already exists in nature, and a person is trying to understand what laws it obeys.
The correlation analysis method allows you to detect linear (forward and backward) connections between two variables.
What is Linear Communication? In simple terms, this is a relationship between two measured variables, which can be denoted by the words “the more one, the more the other” (direct relationship) or “the more one, the less the other” (feedback).
A simple example of a direct relationship is the relationship between age and height of children. We all know well that the relationship between age and height of children is as follows: the older the age, the greater (higher) height. A small child is short, a larger child is taller, and a large child is very tall, almost like an adult.
For clarity, we find on the Internet the corresponding table reflecting the relationship between the age and height of children:
Since the table is only needed for an example, we will not dwell on the question of how reliable it is. Let's be satisfied with the fact that the data in the table is similar to the real one.
For even greater clarity, let's build a graph: the X scale reflects the child's age in years, the Y scale - the child's height in centimeters.
Both the table and the graph clearly show that as one indicator (age of children) increases, the values \u200b\u200bof the second indicator (height of children) also increase. Our own experience tells us the same: we all know that children grow taller with age. The older the child is, the higher his height. That's what it is direct link between two variables (in this case, age and height).
What other simple examples of direct communication can you give from life? The more books a person reads, the more well-read he becomes. The more highly paid a job is, the more people who want to get a job. The more we use our refrigerators, the wider our faces. The further into the forest, the more firewood. And so on. One thing increases, the other increases.
It also happens vice versa: one increases - the other decreases. The more often a child is scolded, the lower his self-esteem. The more our attention is focused on one thing, the less we notice another. "The less we love a woman, the easier she likes us." The quieter you go, the further you'll get. it feedback between two variables.
Feedforward and feedback are two types of linear relationship between variables. It is these connections that correlation analysis reveals.
In practice, the answer is not always as obvious as in the case of the relationship between age and height of children. Very often there are cases when it is impossible to say with confidence whether there is a linear relationship between two variables or not. Therefore, mathematicians have come up with a way to reliably determine its presence or absence - correlation analysis... And we use this method in our research.
We do not need to remember the formulas by heart and be able to derive them - this is the task of mathematicians. Our task is the correct application of correlation analysis in our research, correct
At the first stage of the diagnostic study, we processed all the results obtained according to the "Sincerity" scale, the results of which are presented in Table 1 of Appendix 3.
Based on the results obtained, we can say the following. The data obtained in 64% of cases can be confidently trusted, since the subjects are not inclined to give socially desired answers, but answered the test questions frankly. For 24% of the respondents, situational sincerity is characteristic, that is, in various life situations they behave sincerely or deceitfully due to circumstances, when, as 12% of those who took part in the diagnosis, are not inclined to openly answer the proposed questions. Subsequently, the subjects who received high scores on the scale of "deceit" were excluded from the study, and we did not take their answers into account.
At the second stage of diagnostics, we calculated how many points each subject scored on the scales "Extraversion - Introversion", "Neuroticism", as well as what interpretation corresponds to the given number of points. The results obtained are shown in Table 2 of Appendix 3.
Based on the data obtained, we can say that in the group of respondents, 23% can be attributed to extroverts, and 31.5% to potential extroverts. Such people are initially oriented towards the outside world. They build their inner world in accordance with the outer one. Extroverts and potential extroverts are mobile, talkative, quickly establish relationships and attachments, external factors are the driving force for them. Outwardly, they usually give the impression of cold and dogmatic people living in accordance with the established rules. Certain accentuations of characters are associated with extraversion, in particular exaltation, demonstrativeness, excitability, hyperthymia, and sensitivity. All these character traits, taken together, usually form a single complex and are found in a person together. A person with such a complex of characterological traits is distinguished by increased activity and attention to what is happening around him. He responds vividly to the relevant events and, as it were, lives by them.
23% of those surveyed are potential introverts, 9% are introverts. These people are initially self-absorbed. For them, the most important thing is the world of inner experiences, and not the outer world with its rules and laws. In the case of an introvert, we notice that all of a person's attention is directed to himself and he becomes the center of his own interests. Introversion correlates with the totality of personality traits, primarily with anxiety, pedantry. People who have this complex of characterological features are distinguished by their detachment from what is happening around, alienation, independence.
13.5% are ambiverts. People prone to ambivalence have absorbed the traits of introverts and extroverts. In different life situations, they tend to manifest themselves in different ways, in other words, they are unpredictable.
At the third stage of diagnostics, based on the results already obtained, we looked at what type each subject corresponds to. The data obtained are shown in Table 3.
The table shows that in this group of subjects 32% of the respondents correspond to the choleric personality type. Choleric is characterized by high mental activity, vigor of actions, sharpness, impetuosity, strength of movements, their fast pace, impetuosity. In a choleric temperament, activity is fast, but short-lived. From active, but reluctant to take on business precisely because he does not have endurance.
Sanguine people include 36% of the subjects. Sanguine people, like choleric people, have a strong nervous system, which means good working capacity, he easily moves on to other activities, to communicate with other people. A sanguine person strives for a frequent change of impressions, easily and quickly responds to events that occur, and experiences setbacks relatively easily. They are characterized by high mental activity, quickness and liveliness of movements, energy, efficiency, variety and richness of facial expressions.
R.M. Granovskaya believes that choleric and sanguine people are united by a similar feature - impulsivity. Choleric and sanguine people are mobile and impulsive and therefore more effective in showing initiative, in the speed of establishing interpersonal contacts (Granovskaya R.M., 1997). However, they work in fits and starts, quickly lose interest in their own proposals, if their implementation is delayed, do not pay attention to details.
14% of the respondents correspond to the phlegmatic type. Phlegmatic people have a strong, efficient nervous system, but it is difficult for him to engage in other work and adapt to the new environment. They have a calm, even mood. Feelings are usually constant. The phlegmatic personality type is characterized by a low level of mental activity, slowness, inexpressive facial expressions, a tendency to inactivity and the ability to get into motion, although not easily and not quickly, but for a long time.
The melancholic type includes 18% of the subjects. Such people are characterized by a low level of mental activity, slowness of movements, restraint of motor skills and speech, and rapid fatigability. The melancholic is distinguished by a high emotional sensitivity to everything that happens around him. Sensitivity to others makes them universally accommodating (compatible) with other people, but the melancholic himself tends to experience problems within himself and, therefore, is prone to self-destruction.
Phlegmatic and melancholic people are restrained and balanced, they perform work more accurately and economically, and plan it better.
Thus, the hypothesis of the study that representatives of the profession "advertising agent" have pronounced traits of extraversion and emotional stability, has found its factual confirmation, but only partially.
According to our data, more than a third of the subjects, advertising agents (36%), who took part in the study, can be classified as "sanguine", which characterizes them as people with pronounced extraversion and stability of the nervous system. However, 32% of the respondents belong to the "choleric" type, which corresponds to a high level of extraversion, but an unstable type of nervous system.
findings
1. In the course of the study, the following theoretical problems were consistently solved: the analysis of the problem of personality traits and types was carried out, the basic concepts and principles of the theory of personality types were identified, personality types in the theory of G.Yu. Eysenck.
2. Theoretical analysis showed that Eysenck's theory of personality types is based on factor analysis. His hierarchical model of personality structure includes types, personality traits, habitual reactions, specific reactions. Types are continua on which characteristics of individuals are located between two extremes. Eysenck emphasizes that personality types are not discrete and that most people do not fall into extreme categories.
3. Eysenck sees only two main types (subfeatures) underlying the personality structure: introversion-extraversion, stability-neuroticism. According to Eysenck and other followers of the dispositional approach to personality, the basic structure of personality traits affects the observed behavioral responses of the individual. And, accordingly, according to Eysenck, the obvious features of human behavior are the result of combinations of two main personality sub-traits. Eysenck argues that individual differences in these two subfeatures are closely related to the neurophysiological characteristics of the human body, he attaches much more importance to the genetic foundation of personality traits than other personologists.
Eysenck, in addition to the EPi questionnaire, several more questionnaires to assess the main subfeatures that underlie his hierarchical personality model.
4. In the empirical study, the task was to conduct a diagnostic study of personality traits and types according to the method of G.Yu. Eysenck Epi. The hypothesis of the study was put forward that representatives of the profession "advertising agent" have pronounced traits of extraversion and emotional stability. This hypothesis has found its factual confirmation, but only partially. More than a third of the advertising agents we surveyed have pronounced features of extraversion and stability of the nervous system. However, another third of the respondents with the same high level of extraversion is characterized by an unstable nervous system.
The theory of correlation research, based on the concept of measures of correlation, was developed by K. Pearson and is described in detail in textbooks on mathematical statistics. Only the methodological aspects of correlational psychological research are considered here.
The strategy for conducting a correlation study is similar to a quasi-experiment. The only difference from quasi-experiment is that there is no controlled impact on the object. The correlation study plan is simple. The researcher puts forward a hypothesis about the presence of a statistical connection between several mental properties of an individual or between certain external levels and mental states. However, the assumptions about causality are not discussed.
Correlation is a study conducted to confirm or disprove the hypothesis of a statistical relationship between several (two or more) variables. In psychology, mental properties, processes, states, etc. can act as variables.
"Correlation" literally means "ratio". If a change in one variable is accompanied by a change in another, then we can talk about the correlation of these variables. The presence of a correlation between two variables does not say anything about the cause-and-effect relationship between them, but it makes it possible to put forward such a hypothesis. The lack of correlation allows us to reject the hypothesis of a causal relationship between variables. There are several interpretations of the correlation between the two dimensions:
1. Direct correlation. The level of one variable directly corresponds to the level of another. An example is Hick's law: the speed of information processing is proportional to the logarithm of the number of alternatives. Another example: the correlation of high personal plasticity and a tendency to change social attitudes.
2. Correlation due to the 3rd variable. Two variables (a, c) are related to one another through the third (c), not measured during the study. By the rule of transitivity, if there is R (a, b) and R (b, c), then R (a, c). An example of such a correlation is the fact, established by US psychologists, of the connection between the level of intelligence and the level of income. If such a study were conducted in today's Russia, the results would be different. Obviously, it's all about the structure of society. The speed of image recognition during rapid (tachistoscopic) presentation and the subjects' vocabulary also positively correlated. The hidden variable driving this correlation is general intelligence.
3. Random correlation not due to any variable.
4. Correlation due to sample heterogeneity. Let's imagine that the sample that we will survey consists of two homogeneous groups. For example, we want to find out if belonging to a particular gender is associated with the level of extraversion. We believe that “measuring” sex does not cause difficulties, while extraversion is measured using Eysenck's ETI-1 questionnaire. We have 2 groups: male mathematicians and female journalists. It is not surprising if we get a linear relationship between gender and the level of extraversion-introversion: most men will be introverts, most women will be extroverts.
Correlation links differ in their form. If an increase in the level of one variable is accompanied by an increase in the level of another, then we are talking about a positive correlation. The higher the personal anxiety, the greater the risk of developing stomach ulcers. An increase in the volume of a sound is accompanied by a sensation of its rising tone. If an increase in the level of one variable is accompanied by a decrease in the level of another, then we are dealing with a negative correlation. According to Zayonts, the number of children in a family is negatively correlated with the level of their intelligence. The more fearful an individual is, the less likely it is to take a dominant position in the group.
Correlation is called zero if there is no connection between variables.
In psychology, there are practically no examples of strictly linear relationships (positive or negative). Most connections are non-linear. A classic example of nonlinear dependence is the Yerkes-Dodson law: an increase in motivation initially increases the effectiveness of learning, and then a decrease in productivity occurs (the “re-motivation” effect). Another example is the relationship between the level of achievement motivation and the choice of tasks of varying difficulty. Persons motivated by the hope of success prefer tasks of the middle range of difficulty - the frequency of elections on the scale of difficulty is described by a bell-shaped curve.
Pearson developed the mathematical theory of linear correlations. Its foundations and applications are described in the corresponding textbooks and reference books on mathematical statistics. Recall that Pearson's linear correlation coefficient r varies from -1 to +1. It is calculated by normalizing the covariance of the variables by the product of their standard deviations.
The significance of the correlation coefficient depends on the accepted significance level a and on the sample size. The greater the modulus of the correlation coefficient, the closer the relationship of the variables to a linear functional dependence.
Planning a correlation study
The correlation study design is a kind of quasi-experimental design in the absence of the influence of the independent variable on the dependent. In a stricter sense: the test groups must be in equivalent unchanged conditions. In a correlation study, all measured variables are dependent. The factor determining this dependence can be one of the variables or a hidden, unmeasured variable.
The correlation study is divided into a series of independent measurements in the group of subjects R. There are simple and comparative correlation studies. In the first case, the group of subjects is homogeneous. In the second case, we have several randomized groups that differ in one or more specific criteria. In general, the plan of such a study is described by a matrix of the form: P x O (subjects x measurements). The result of this study is a correlation matrix. Data processing can be carried out by comparing the rows of the original matrix or columns. By correlating the lines with each other, we compare the subjects with each other; correlations are interpreted as coefficients of similarity-differences between people. Of course, P-correlations can be calculated only if the data are reduced to one scale dimension, in particular, using the Z-transformation:
By correlating the columns with each other, we test the hypothesis about the statistical relationship of the measured variables. In this case, their dimension does not matter.
Such a study is called structural, since in the end we get a correlation matrix of measured variables, which reveals the structure of the relationships between them.
In research practice, the task often arises to identify temporal correlations of parameters or to detect changes in the structure of correlations of parameters in time. Longitudes are an example of such research.
A longitudinal study design is a series of individual measurements of one or more variables at regular intervals. A longitudinal study is an intermediate option between a quasi-experiment and a correlation study, since the researcher interprets time as an independent variable that determines the level of addicts (for example, personality traits).
The complete plan of the correlation study is a parallelepiped P x O x P, the edges of which are designated as "subjects", "operations", "time stages".
Research results can be analyzed in different ways. In addition to calculating P- and O-correlations, it becomes possible to compare the P x \u200b\u200bO matrices obtained in different periods of time by calculating a two-dimensional correlation - the relationship of two variables with a third. The same applies to the matrices P x T and T x O.
But more often, researchers limit themselves to processing of a different type, testing hypotheses about the change in variables over time, analyzing the P x \u200b\u200bT matrices for individual dimensions.
Let's consider the main types of correlation research.
1. Comparison of the two groups. This plan can only conditionally be attributed to correlation studies. It is used to establish the similarity or difference between two natural or randomized groups in terms of the severity of a particular psychological property or condition. Let's say you want to find out if men and women differ in terms of extraversion. To do this, you must create two representative samples, equalized by other parameters that are significant for extraversion-introversion (by parameters that affect the level of extraversion-introversion), and measure using the EPQ test. The mean results in the 2 groups are compared using the Student's t-test. If necessary, the variances of the extraversion indicator are compared according to the F.
The simplest comparison of the 2 groups contains the sources of a number of artifacts characteristic of the correlation study. First, there is a problem of randomization of groups - they should be clearly divided according to the chosen criterion. Secondly, real measurements do not take place simultaneously, but at different times:
Thirdly, it is good if testing within the group is carried out simultaneously. If individual subjects are tested at different times, then the result may be affected by the influence of the time factor on the value of the variable.
It is impossible to change the gender today without much effort (including without surgical intervention), but you can move from one study group to another, as well as from class to class.
If a researcher sets out to compare two study groups in terms of performance, he / she should take care not to “mix” them during the study.
The effect of non-simultaneous measurements in two groups (in the case of an assumption about the significance of this factor) could be “removed” by introducing two control groups, but they will also have to be tested at another time. It is more convenient to divide the initial groups in half and test (if possible) according to the following plan:
__________________
The processing of the results to identify the effect of the sequence is carried out by the method of two-factor analysis 2 x 2. Comparison of natural (non-randomized) groups is carried out according to the same plan.
2. One-dimensional study of one group, in different conditions. The design of this study is similar to the previous one. But in essence, it is close to an experiment, since the conditions in which the group is located differ. In the case of a correlation study, we do not control the level of the independent variable, but only state the change in the behavior of the individual under new conditions. An example is the change in the level of anxiety of children during the transition from kindergarten to the 1st grade of school: the group is the same, but the conditions are different.
The main artifacts of this plan are the cumulation of sequencing and testing effects. In addition, the time factor (the effect of natural development) can distort the results.
The scheme of this plan looks very simple: A O1 B O2, where A and B are different conditions. Subjects may be randomly selected from the general population or represent a natural group.
Data processing is reduced to assessing the similarity between test results in conditions A and B. To control the effect of consistency, you can counterbalance and go to a correlation plan for two groups:
In this case, we can consider A and B as influences, and the plan as a quasi-experiment.
3. Correlation study of pairwise equivalent groups. This design is used when studying twins using the intra-pair correlation method. Dizygotic or monozygotic twins are divided into two groups: each contains one twin from a pair. Mental parameters of interest to the researcher are measured in twins of both groups. Then the correlation is calculated between the parameters (O-correlation) or twins (P-correlation). There are many more sophisticated versions of twin psychogenetic research plans.
4. To test the hypothesis about the statistical relationship of several variables characterizing behavior, a multivariate correlation study is carried out. It is implemented according to the following program. A group is selected, which is either the general population or the population of interest to us. Tests are selected that are verified for reliability and internal validity. Then the group is tested according to a specific program.
R А (О1) В (О2) С (О3) D (О4) .... N (Оn),
where А, В, С ... N - tests, Оi - testing operation.
The research data are presented in the form of a matrix: mxn, where m is the number of subjects, n - tests. The raw data matrix is \u200b\u200bprocessed, and the linear correlation coefficients are calculated. It turns out a matrix of the form m x n, where n is the number of tests. In the cells of the matrix - the correlation coefficients, along its diagonal - units (correlation of the test with itself). The matrix is \u200b\u200bsymmetric about this diagonal. Correlations are assessed for statistical differences as follows: first, r is converted to Z-scores, then Student's t-test is used to compare r. The significance of the correlation is assessed by comparing it with the table value. When comparing rexp. and rtheor. the hypothesis is accepted that the correlation is significantly different from the random one for a given value of accuracy (a \u003d 0.05 or a \u003d 0.001). In some cases, it becomes necessary to calculate multiple correlations, partial correlations, correlation ratios, or dimension reduction - reducing the number of parameters.
Various methods of latent analysis are used to reduce the number of measured parameters. Many publications are devoted to their application in psychological research. The main reason for artifacts that appear during multivariate psychological testing is real physical time. When analyzing the data of the correlation study, we abstract from the non-simultaneity of the measurements. In addition, it is assumed that the result of the subsequent measurement is independent of the previous one, i.e., there is no carryover.
Let's list the main artifacts that arise during the application of this plan:
1. Effect of consistency - the previous execution of one test can affect the result of the execution of another (symmetric or asymmetric carryover).
2. Learning Effect - By performing a series of different tests, the test subject may be more competent in testing.
3. The effects of background influences and "natural" development lead to uncontrolled dynamics of the subject's state during the study.
4. The interaction of the testing procedure and the composition of the group is manifested in the study of a heterogeneous group: introverts pass exams worse than extroverts, "anxious" ones cope worse with speed tests of intelligence. To control the effects of sequencing and transference, use the same technique as when planning experiments, namely counterbalancing. Only instead of impacts, the order of the tests is changed.
Table 5.14
For 3 tests, the complete design of the counterbalanced correlation study is as follows:
1st group: А В С
2nd group: C A B
3rd group: B C A
where A, B, C are various tests. However, I do not know of a single case when the effects of testing and transfer were controlled in Russian correlation studies.
Let me give you one example. We needed to find out how the type of task affects the success of completing tasks replacing one another. We assumed that the subjects were not indifferent to the sequence in which they were given the tests. The tasks for creativity (from the Torrance test) and for general intelligence (from the Eysenck test) were selected. The tasks were given to the subjects in a random order. It turned out that if the task for creativity is completed first, then the speed and accuracy of solving the task for intelligence decreases. The opposite effect was not observed. Without going into the explanation of this phenomenon (this is a difficult problem), we note that here we are faced with the classic effect of asymmetric transfer.
5. Structural correlation research. This scheme differs from the previous variants in that the researcher reveals not the absence or presence of significant correlations, but the difference in the level of significant correlations between the same indicators measured in representatives of different groups.
Let us illustrate this case with an example. Let's say we need to test a hypothesis about whether the gender of the parent and the gender of the child influences the similarity or difference in their personality traits, for example, Eysenck's level of neuroticism. To do this, we must conduct a study of real groups - families. Then the coefficients of correlation of the levels of anxiety of parents and children are calculated. 4 main correlation coefficients are obtained: 1) mother-daughter; 2) mother-son; 3) father-daughter; 4) father-son, and two additional ones: 5) son-daughter; 6) mother-father. If we are only interested in comparing the similarities-differences of the first group of correlations, and not in the study of assortativity, then we build a 4-cell table 2 x 2 (Table 5.14).
Correlations are z-transformed and compared using the Student's t-test.
Here is the simplest example of a structural correlation study. In research practice, there are more complex versions of structural correlation studies. Most often they are carried out in the psychology of individuality (B.G. Ananiev and his school), the psychology of work and education (V.D.Shadrikov), the psychophysiology of individual differences (B.M. Teplov, V.D. Nebylitsyn, V.M. Rus-salov and others), psychosemantics (V.F.Petrenko, A.G. Shmelev, etc.).
6. Longitudinal correlation study. Longitudinal research is a variant of quasi-experimental research plans. The longitudinal psychologist considers time to be the influencing variable. It is analogous to a test plan for one group in different conditions. Only conditions are considered constant. The result of any time study (including a longitudinal one) is the construction of a time trend of the measured variables, which can be analytically described by various functional dependencies.
A longitudinal correlation study is built according to a time series plan with group testing at specified time intervals. Apart from learning effects, consistency, etc. In a longitudinal study, the dropout effect should be taken into account: not all subjects who initially took part in the experiment can be examined after a certain time. Possible interaction between dropout and testing effects (refusal to participate in a follow-up survey), etc.
Structural longitudinal research differs from simple longitude in that we are interested not so much in the change in the central tendency or the spread of any variable, as in the change in the relationships between the variables. This kind of research is widespread in psychogenetics.
Processing and interpretation of correlation research data. The data of the structural correlation study are one or more matrices of "subjects" x "tests". Primary processing consists in calculating the coefficients of the statistical relationship between two or more variables. The choice of the measure of connection is determined by the scale with which the measurements were made.
1. If the measurements are made on a dichotomous scale, then the coefficient j is used to calculate the closeness of the relationship of signs. The dichotomous scale is often confused with the naming scale (even in textbooks on statistics; see, for example, J. Glass and J. Stanley. Statistical Methods in Pedagogy and Psychology, 1976). The dichotomous scale is a degenerate version of the interval scale; all statistical methods of the interval scale are applicable for it. The data for calculating the coefficient (φ are presented in the contingency table (Figure 5.19).
2. Data are presented on an ordinal scale. The measure of the relationship that corresponds to the scale of order is the Candell coefficient. It is based on counting mismatches in the order of rankings X and Y. There are a number of subjects: first we build this series in decreasing order of body weight, and then in decreasing order of height. For each pair, the number of matches and inversions is counted: match, if their order in X and Y is the same; inversion if the order is different. The difference between the number of "matches" and the number of "inversions" divided by n (n – 1) / 2 gives the coefficient t. The counting algorithm is given in the manuals on statistics [see. J. Glass and J. Stanley, 1976] and in any statistical package for personal computers.
Spearman's rank correlation coefficient is often used to process data obtained using the order scale, which is a modification of Pearson's coefficient for a natural series of numbers (ranks). It has nothing to do with the ordinal scale. But it is recommended to use it if one measurement is made on a scale of orders, and the other on a scale of intervals.
3. Data are obtained on a scale of intervals, or ratios. In this case, the standard Pearson correlation coefficient or Spearman's rank correlation coefficient is applied. In the event that one variable is dichotomous and the other is interval, the so-called biserial correlation coefficient is used.
Finally, if the researcher believes that the relationships between the variables are nonlinear, he calculates the correlation ratio characterizing the magnitude of the nonlinear statistical dependence of the two variables.
The correlation study ends with the conclusion about the statistical significance of the established (or unidentified) relationships between the variables. However, the researchers are not limited to such a statement. One of the main tasks that psychologists face is to find out if the connections between individual parameters (psychological properties) are due to hidden factors? For this purpose, an apparatus for reducing the number of variables is used: methods of multivariate data analysis, which are studied by psychologists in the course "Mathematical Methods in Psychology".
Planning correlation studies in cross-cultural psychology and psychogenetics
Everything said in this chapter refers to general psychological research. There are at least 4 areas of research planning that are rarely addressed in the psychological science methodology literature.
The first area is a multidimensional experiment. The plans for a multivariate study, in particular an experiment, are a generalization of traditional schemes for the case of n-dependent variables. In a typical experiment, we examine the effect of one independent variable on one dependent. A multilevel factorial experiment is carried out to study the influence of 1, 2, ..., m independent variables on one dependent variable as well. A multidimensional experiment assumes the scheme mxn, where m is the number of independent variables, n is the number of dependent variables. Even the application of the design for 2 independent and 2 dependent variables requires the identification of relationships between each pair of independent - dependent variable, i.e. building 4 tables of average results 2 x 2 (if the averages are compared). In addition, it is required to identify the influence of the level of each independent variable, as well as the influence of their interaction on the correlation between the two dependent variables.
More complex plans for a multidimensional psychological experiment are very laborious and require automated planning and implementation of the experiment, as well as special computer programs for processing the results. At the very least, planning for multidimensional experiments provides researchers with ample room for creativity.
The second area of \u200b\u200bresearch planning is an experiment in differential psychology or an individual psychological experiment. The purpose of this experiment is to identify individual differences in behavior in homogeneous situations. Even in an ordinary multidimensional study, the main hypothesis is not the unconditional propositions “If A, then B”, but the conditional proposition “If A, then B - subject to C1, B - subject to C2 ... etc.”. Additional variables - individual psychological differences - act as a condition.
In a differential psychological experiment, these additional variables become the main ones: we investigate personality as a determinant of behavior. The main statistical indicator in this study is not a measure of central tendency, but indicators of variation in the values \u200b\u200bof the dependent variable. The independent variable (tasks for the subject, experimental influence) turns into an additional one. Varying the independent variable turns into a fitting procedure using a method that combines stratification and randomization, for example, when developing tests, groups are selected by gender and age, but they are equalized for other indicators.
The planning of differential psychological research is another important and underdeveloped area of \u200b\u200bexperimental psychology.
The third area is cross-cultural research. Any cross-cultural research is carried out to compare the behavior of individuals who grew up in different socio-cultural conditions. The factors of natural development and background (history), which in the usual general psychological research act as sources of artifacts, in cross-cultural research are analogous to the independent variable.
At its core, cross-cultural research is a variant of an ex-post-facto experiment (the experiment referred to). Therefore, all the requirements for ex-post-facto, as well as restrictions on the interpretation of the results obtained, apply equally to cross-cultural research.Interest in a comparative study of the patterns of mental development of representatives of different cultures is very great, and therefore the planning of cross-cultural research is one of the most intensively developing areas of experimental psychology.
Fourth, a special direction - research plans in psychogenetics. Let's take a closer look at the last 2 areas.
Cross-cultural research
Cross-cultural research is, in fact, a special case of the group comparison plan. Moreover, the number of compared groups may fluctuate (minimum - 2 groups).
Conventionally, there are 2 main plans used in cross-cultural research.
First plan: comparison of 2 or more natural or randomly selected groups of 2 populations.
Second plan: a combination of a comparison plan for 2 or more groups with a longitude, in which not only differences in the behavioral features of these groups are compared, but the process of changing these features under the influence of time or time and additional external factors is studied.
The main feature of cross-cultural psychology is the subject that determines the specifics of the method.
Cross-cultural psychology has its origins in the works of W. Wundt [Wundt V., 1998] and French sociologists of the early XX century: G. Lebona [Lebon G., 1998], A. Foulier [Foulier A., \u200b\u200b1998], G. Tarde [Tarde G., 1998].
However, these scientists did not conduct empirical studies. Wilhelm Wundt became the methodologist of cross-cultural psychology (as well as of empirical psychology). In 1900-1920. he undertook the publication of the grandiose, 10-volume "Psychology of Nations". He considered the main manifestation of the "national spirit" to be linguistic activity (in contrast to the linguistic system - the subject of linguists' research). This work, along with the "Foundations of Physiological Psychology", became the main contribution of W. Wundt to psychology. The work "Problems of the Psychology of Peoples" is a collection of articles that are a summary of the research program of W. Wundt, and serves as an introduction to the multivolume "Psychology of Peoples".
Wundt singled out at least two disciplines in the science of the "national spirit": "the historical psychology of peoples" and "psychological ethnology". The first is an explanatory discipline, the second is descriptive.
The laws of the "psychology of peoples" are the essence of the laws of development, and its basis is 3 areas, the content of which "exceeds the volume of individual consciousness: language, myths and customs." Unlike French psychologists and Austrian psychoanalysts, W. Wundt was least of all interested in mass behavior and the problem of "personality and mass", and more in the content of the "national spirit" (Volksgeist), which, incidentally, corresponded to the idea of \u200b\u200bpsychology as a "science of consciousness" ... He emphasizes the genetic priority of the “national spirit” over the individual: “In the history of human society, the first link is not the individual, but precisely their community. From the tribe, from the circle of relatives, through gradual individualization, an independent individual personality is distinguished, contrary to the hypotheses of the rationalistic Enlightenment, according to which individuals partly under the yoke of need, partly through reflection, united into society. " A latent polemic with French social psychologists is also present in the interpretation of the role of imitation. V. Wundt, using the examples of the assimilation of two languages \u200b\u200bby individuals, shows that imitation is not the main, but only an accompanying factor in social interactions, and he subjects the "theory of individual invention" to similar criticism. In place of these theories, he puts the processes of "general creativity", "assimilation" and "dissimilation", but does not fully disclose their nature.
The main method of the "psychology of peoples", according to W. Wundt, was understanding, a comparative interpretation of the elements of culture.
In modern cross-cultural psychology, the empirical method dominates.
The subject of cross-cultural research is the characteristics of the psyche of people from the point of view of their determination by socio-cultural factors specific to each of the compared ethnocultural communities.
This implies that for the correct planning of cross-cultural research, one should, firstly, at least determine which features of the psyche can potentially be influenced by cultural factors, and also identify many parameters of behavior corresponding to these features. Second, it is required to give operational, rather than theoretical, definitions of the concepts of "culture" and "cultural factor", as well as describe the many of these factors, which can presumably affect the differences in mental characteristics and behavior of people belonging to different cultural communities.
Thirdly, one should choose an adequate research method and an adequate methodology for measuring the characteristics of the behavior of people belonging to different cultures.
Fourthly, you should decide on the object of research. It is necessary to select for the study such populations that clearly represent the subjects of different cultures. In addition, selection or selection of groups from populations that are representative in terms of belonging to the compared crops is critical.
Let's consider these issues in more detail.
Cross-cultural psychology begins where psychogenetics ends. The result of psychological research is the determination of the relative contribution of the genotype and environment to the determination of individual differences in people by any psychological property.
Cultural factors are also part of environmental determination. Consequently, at first glance, the hypothesis of any cross-cultural research should relate to those properties of the psyche that are more dependent on the environment than on heredity, or significantly depend on the environment.
However, there is not a single individual psychological parameter that, to one degree or another, would not be subject to environmental influences. Therefore, hypotheses about the cultural determination of psychological properties cover their entire spectrum: from psychophysiological parameters to the value orientations of the individual.
Among the factors of culture that can potentially affect individual psychological differences, there are universal and specific [Lebedeva NM, 1998].
There are many classifications that characterize the psychological characteristics of cultures.
The most popular classification is H. S. Triandis, who formulated the concept of "cultural syndrome" - a certain set of values, attitudes, beliefs, norms and behaviors that distinguish one cultural group from another.
He considers the main dimensions of culture to be “simplicity-complexity”, “individualism-collectivism”, “openness-closeness”. A number of researchers [in particular, J. Hofstede, 1984] identify such parameters as: 1) power distance - the degree of uneven distribution of power from the point of view of a given society, 2) uncertainty avoidance, and 3) masculinity-femininity.
Of course, these parameters are extremely primitive. Even an "inveterate" ethnopsychologist will never consider them sufficient and even necessary to describe a particular culture.
The very term "culture" is extremely vague. Following K. Popper, one can consider the “third world” culture, the system of “transformed reality” created by people.
Most often, cultural differences are reduced to ethnic ones, and by cross-cultural research is meant ethnopsychological research. Sometimes cultures (more precisely, groups of people belonging to different cultures) are distinguished according to other criteria: 1) place of residence - we are talking about “urban” and “rural” culture; 2) religious affiliation - they mean Orthodox, Muslim, Protestant and other cultures; 3) familiarity with European civilization, etc.
Hypotheses that are formed during cross-cultural research express the causal relationship between cultural factors and mental characteristics. Cultural factors are considered to be the reason for the differences in the mental properties of individuals belonging to different cultures.
There is a reasonable assumption about the reverse influence of the mental characteristics of individuals on the nature of the culture of the peoples to which these peoples belong.
In particular, such hypotheses can be put forward in relation to temperamental, intellectual and a number of other mental characteristics, the hereditary determination of which is very significant. In addition, biophysical factors also contribute to individual psychological differences. However, classical cross-cultural research is carried out within the framework of the paradigms: "culture is the cause, mental characteristics are the effect."
Obviously, any cross-cultural research is built on a non-experimental plan, the experimenter cannot control cultural factors. Consequently, there are no methodological grounds to consider the relationship "culture - psyche features" causal. It would be more correct to speak of a correlation dependence.
Cross-cultural research is divided into several types depending on the methodological focus and subject matter of content.
F. Van de Weiver and K. Leun (1997) proposed to classify cross-cultural studies depending on two reasons: 1) confirmatory (aimed at confirming or refuting a theory) - exploratory (exploratory) research, 2) the presence or absence of contextual variables (demographic or psychological).
A generalizing study is carried out when there is a possibility of transferring or generalizing the results obtained in the study of one cultural community to others. These studies are based on some theory and do not take into account the influence of context variables, therefore, in a strict sense, they cannot be classified as cross-cultural. They are conducted to confirm universal hypotheses for all members of the species Homo sapiens and to clarify the external validity.
Theory-based research includes factors of cross-cultural context. They test hypotheses about specific relationships between cultural and mental variables. In the strict sense of the term "cross-cultural research" only they can be considered as such. But more often there are studies of psychological differences. Typically, a standard measurement procedure is applied and the existence of significant differences in the mean or standard range of measured mental properties of 2 or more groups belonging to different cultures is determined. Cultural factors are not taken into account when planning research, but are only used to interpret the differences obtained.
The last type of research - "special studies of external validity" (it would be more accurate to say - environmental) are aimed at identifying differences in the manifestation of mental properties under the influence of cultural factors. The influence of a number of factors on 1 (less often 2 or 3) mental characteristics is investigated. The technique of regression analysis is used for data processing. As a rule, researchers do not have any preliminary considerations about which cultural variables and to what extent affect mental characteristics.
The main problem of planning a cross-cultural study is the design or choice of a methodology for recording behavior parameters that are valid in description for the studied mental characteristics. Any psychological measurement technique is a product of culture, most often - Western, and can have an adequate meaning only in the context of this culture. The first task of the researcher is to achieve high (meaningful) validity of the method, otherwise the subjects will simply not be "included" in the research process.
What many authors consider to be the achievement of constructive (conceptual) validity is nothing more than evidence that the generalized ideas about the studied mental phenomenon in persons belonging to the studied cultural groups correspond to the theoretical ideas of the researcher.
And in the "cross-cultural triangle" (not to be confused with Bermuda), it is necessary to achieve the universality of behavioral traits, measured properties and their high validity (Fig. 5.20).
Although many researchers consider the procedure for finding “cultural and behavioral analogues” to be the main one, I am not inclined to share their positions. In the end, a theoretical physicist has the right to his own judgment about the reasons for the fall of bodies to the ground, different from the concept adopted in a particular tribe or social group. This also applies to psychology as a natural science. If someone interprets the concept of "intelligence" as social intelligence or reduces it to the success of solving educational problems, and does not consider it theoretically as a general ability for mental activity, then this is his problem. Another question is, to what extent does the author of the study influence the theoretical understanding of his belonging to a particular culture? Is his view universal?
In order to avoid “cultural one-sidedness”, two approaches have been proposed: convergent and divergent. The convergent approach is that the research is carried out by representatives of all cultural groups that are the object.
Each researcher develops his own test, which is then presented to each group.
Thus, the study plan can be displayed in the following diagram (for 2 groups):
Group I O1 (I) O2 (II)
Group II O3 (I) O4 (II)
Obviously, the results of comparing O1 and O3 and also O2 and O4 will indicate intergroup differences. Moreover, the comparison of DO13 and DO24 will become an indicator of the differentiating strength of the O (I) and O (II) techniques.
Differences in the results of O1 and O2, as well as O3 and O4 will be indicators of the influence of the measurement method on the manifestations of behavior in different groups. Comparison of DO12 and DO34 provides information on the bias effect: the effect of the interaction of measurement technique and group composition.
The divergent approach is to take into account the ideas about the nature of the phenomenon, prevailing among researchers belonging to different cultures, when drawing up one methodology. This approach is possible only when developing a methodology where the diversity of tasks will not affect its reliability and validity (for example, when compiling questionnaires on value orientations).
Otherwise, this approach is no different from the converged one.
Yet the ideal for most Western scholars is to create universal or culture-free methods.
A technique developed by a researcher belonging to the same cultural background as the test group is likely to produce different results when applied to a group of persons belonging to a different culture.
In particular, the test for social intelligence, developed on the basis of studies of the life and customs of one of the nomadic tribes of Northeast Africa, will be more successfully solved by representatives of this tribe than the test developed by a Russian psychologist based on the material of the life of workers and engineers of the Middle Urals.
The effects of consistency can influence the results of a study conducted with a converged design. Therefore, it is recommended to double the number of groups and test each group in a specific sequence.
An improved plan for a convergent cross-cultural study for 2 cultural communities is as follows:
Culture Group 1 O1 (I) O2 (II)
Group 2 O3 (I) O4 (II)
Culture II Group 3 O5 (I) O6 (II)
Group 4 O7 (I) O8 (II)
But even this plan is not enough. It is necessary to control the influence of the researcher. In most cross-cultural studies, testing is carried out by a psychologist who belongs to one of the 2 tested cultural communities, or to the third - most often Western European or North American. Communication problems can be a major source of bias. It is not only a matter of the subject's knowledge of the language that the researcher speaks, or, on the contrary, of the researcher's knowledge of the language of the studied national group. Differences in behavioral stereotypes, attitudes, communication methods, etc. can be so large that they will lead to a violation of the entire testing procedure and a complete distortion of the results. Therefore, it is advisable that cross-cultural studies are carried out by representatives of both tested cultural groups. Of course, the use of balancing, taking into account the personality of the experimenter, dramatically increases the number of tested groups. In this case, you should abandon the full plan and use the Latin square plan.
Verbal test scores are most influenced by cultural factors. It is required to assess the adequacy of the studied psychological constructs in each study group, the method of presenting the material and the content of questions or statements.
D. Campbell and O. Werner proposed a double translation technique. The test is translated from the original language into the language of the cultural group, and then another translator independently translates that text into the original language. Mismatches are used to correct deficiencies in the wording of statements. The second technique, proposed by the same authors, is "decentration", namely, the exclusion from the original text of the technique of concepts and expressions that are difficult to translate or specific to the culture to which the author of the technique belongs.
However, until now, only a few techniques have been developed that meet the criterion of cultural universality.
American ethnopsychologists divide all methods into "culture-specific" and "universal".
Among the tests "free from the influence of culture" (and even then - in the opinion of the authors) are "progressive matrices" by J. Raven, "Cultural-free test" (CFT) by R.B Cattell, questionnaires by G. Yu. Eysenck EP1 and EPQ, McCrae and Costa's Big Five test and others.
Most ethnopsychologists believe that attempts to create methods that are free from the influence of culture are akin to searching for a "perpetual motion machine."
Table. 5.15
Form of the methodology "Cultural and value differential"
Instructions for the subject. How do you think these qualities are characteristic for your people (for another people)? The qualities are assessed on a 4-point scale: 1 - this quality is absent, 2 - the quality is poorly expressed, 3 - the quality is moderately expressed, 4 - the quality is expressed in full.
Among the specialized methodological properties is the Atlas of Affective Meanings, created by Charles Osgood and his collaborators in 1975. The Atlas contains over 620 objective indicators of subjective cultures. It is the result of a generalization of cross-cultural studies of psychosemantic structures of young men and adolescents. However, even this atlas was created on the basis of a "universal" psychological concept - the theory of the "semantic differential" method by C.E. Osgood.
The process of developing a measurement methodology for cross-cultural research can be divided into 3 stages: 1) selection of a group of "supercultural" (universal) variables and the creation of a culturally universal methodology; 2) highlighting culturally specific variables and complementing the methodology; 3) correction of the methodology by means of its cross-cultural validation. This cross-cultural validation and modification was carried out by E.S.Bogardus' method of measuring social distance.
In Russia, there are very few methods developed specifically for cross-cultural research. Modifications of the "Semantic Differential" method by Ch. E. Osgood (VF Petrenko), modifications of the test of personality constructs by J. Kelly (G. U. Soldatova) are often used.
Among the original ones should be attributed the methodology "Types of personal identity", developed by G.U. Soldatova and S.V. Ryzhova, as well as the methodology - "Cultural and value differential" (G.U. Soldatova, I.M. V. Ryzhov). Consider the latter as an example. The purpose of this methodology is to measure group value orientations: towards the group, towards power, towards each other and towards social change.
Value orientations are formulated within the psychological universal dimension of culture “individualism-collectivism”.
The scale "group orientation - self-orientation" is considered on the basis of such parameters as intragroup support (mutual assistance - disunity), subordination to the group (subordination - independence) and tradition (loyalty to tradition - destruction of traditions). Orientation to change is considered in the range of "openness to change - resistance to change" according to the parameters: openness - closed culture (openness - isolation), perspective orientation (aspiration for the future - aspiration for the past), degree of risk (inclination to risk - caution). Orientation towards each other - in the range of "focus on interaction - rejection of interaction" according to the parameters: tolerance - intolerance (peacefulness - aggressiveness), emotionality (cordiality - coldness) and achievement motivation (compliance - rivalry). Orientation towards power - in the range of “strong social control - weak social control” according to the parameters: obedience to prohibitive and regulatory standards of society (discipline - self-will, law-abidingness - anarchy) and the importance of authority (respect for power - distrust of power) (Table 5.15. ).
On the basis of "raw" data, the degree of manifestation of the measured quality and the coefficient of coincidence of the degrees of expression of qualities in different groups are calculated.
Let's move on to the crucial moment of any cross-cultural research: population selection, group formation and selection.
The researcher must first select a population that matches the hypothesis and design of the empirical study.
Several options are possible. First, the researcher chooses a population based on practical tasks: often research is carried out within the framework of programs funded by the state, scientific and public funds, as well as private individuals. Sometimes research is carried out with the aim of predicting, in particular, conflicts on interethnic grounds.
The researcher works with the population that meets the customer's requirements.
The second option: the researcher chooses a population based only on scientific prerequisites. Cross-cultural populations are selected in accordance with a scientific hypothesis that is based on psychological theory. As a rule, researchers choose populations based on their position on the continuum of a property that characterizes culture: it can be “openness-closedness”, “individualism-collectivism,” etc. The choice of two populations allows testing a qualitative hypothesis about the influence of culture on behavior. and 3 populations located, respectively, at the edges and in the center of the continuum, allow us to test the quantitative hypothesis. Less commonly, populations are selected at random for reasons of convenience or by randomization. The example of S. Schwartz's research into the structure of value orientations in representatives of 36 cultures is often cited. For this S. Schwartz invited researchers belonging to different ethnic groups and willing to cooperate with him to take part in the experiment.
Research on natural groups that "came to hand" is not welcomed in modern methodological practice, since the scientific results obtained in this way are not valid enough and are difficult to interpret theoretically.
After the selection of populations, the intercultural researcher must select a sample and assign the subjects to groups.
In the simplest case, the sample consists of two groups of subjects belonging to different cultures.
The selection of subjects into groups from the population is determined by randomization or by stratometric randomization.
But the problem is how to get the subjects to participate in the research. The researcher has a limited set of methods. He can engage in practical work, for example, in the activities of school psychological counseling, and examine those children who are brought in by parents or who themselves seek help.
In this case, the psychologist may face the problem of displacement of the surveyed groups. Suppose he needs to compare the features of communication between Russian and Armenian children. If he consults children who are experiencing difficulties in adapting to the conditions of communication in a Russian-speaking school, then it can be assumed that Armenian children will experience great problems in adaptation, but their parents will not always turn to a Russian psychologist.
The researcher can recruit volunteers (for a fee or enthusiasts). But it is known that groups of volunteers differ in their characteristics from the characteristics of the population as a whole. In addition, many volunteers can be included in research for political, ideological, and other external motives.
Also, a psychologist can persuade people to take part in the research, but at the same time he should keep in mind that people who are more likely to come into contact with a representative of the culture to which the researcher belongs to persuasion. Therefore, the sample of “recruiters” will not be representative of the population. Most likely, the results will be biased towards the similarity of the mental characteristics of the two cultural groups. This will happen even if the researcher does not belong to any of the studied cultural groups (although in this case the effect will be somewhat weakened). As a rule, people with a high level of education and income, who know foreign languages, are open and tolerant, are inclined to cooperate, come into contact with a research psychologist.
Finally, the researcher can forcefully select the subjects if the authorities are interested in this. Such research is carried out in the army, in prisons, in closed educational institutions - where people's behavior is tightly controlled.
However, in this case, the researcher may face distortion of the results, sabotage and unwillingness of the subjects to cooperate with him.
We considered the ^ -test, intended mainly for comparing the results of different groups of subjects (assuming a normal distribution and data presented in normalized scales). Another fairly common task in psychological research is to identify relationships between two or more data sets. One of the simplest forms of identifying such a connection is correlation.
Correlation analysis makes it possible a ton of quantifying the degree of consistency of changes (variation) of two or more signs. The degree of consistency of changes is characterized by the tightness of the relationship - the absolute value of the correlation coefficient.
A correlation between two outcomes essentially means that when one outcome changes, the other also changes - so there is a relationship between the results, a relationship is revealed. If the value of a certain quantity can change, then such a quantity is called variable. The correlation between the two variables can be positive or negative. Positive correlation such a relationship between variables is called when the values \u200b\u200bof both variables increase or decrease proportionally: with decreasing (increasing) one, the other decreases (increases). A simple example of a positive correlation is the relationship between height and weight of a person - as height increases, so does weight, and, as a rule, tall people have more weight than small people. When negative correlation, the relationship is inversely proportional: an increase in one variable is accompanied by a decrease in another (for example, the air temperature and the amount of clothes worn - the warmer it is outside, the less clothes we wear).
It is important to note something else: correlation does not mean there is a causal relationship. The presence of a correlation indicates that there is a relationship between two variables, but not that one of the variables is the cause, and the other is the effect. The existence of a causal relationship is established by other methods.
In this regard, a meaningful conclusion about the causal relationship between the studied phenomena is quite risky only on the basis of the statistical significance of the relationship between the corresponding signs (i.e., based on the correlation coefficient). Of course, a static relationship between signs is a necessary, but not a sufficient condition for a causal relationship between them. The statement that the phenomenon AND there is a reason for the phenomenon IN, is true if three conditions are simultaneously fulfilled:
- phenomena AND and IN statistically related;
- AND happens earlier IN;
- there is no alternative interpretation of the appearance IN besides AND (in other words, there is no common cause WITH joint variability AND and IN).
Thus, the use of the correlation method makes it possible to substantiate the presence of only statistical connection - one of three signs of causation.
But let's go back to the above example with air temperature and clothing. The connection between these variables does not mean that if we take off our clothes, then temperatureair will rise. We will have to use other methods to show that in this case the relationship is one-way and the reason for the change in the amount of clothing people wear is due to the change in air temperature. In other cases, the relationship between two variables may be due to some third variable, and the correlation simply reflects the presence of something in common between the two variables and this third. To illustrate this situation, the following example is often cited: if we had the strange desire to measure the size of the feet of students and assess their knowledge of mathematics, then we would find a positive correlation between the length of the feet and the grades in mathematics.
Does this mean that math ability is dependent on foot size, or that those who do well in math grow their legs faster? Of course not - this correlation is explained by the influence of a third variable: namely, age (the older the child, the larger his leg and the better he understands mathematics). Therefore, caution is needed when interpreting correlation.
Once a positive or negative correlation has been identified, it is necessary to establish how close it is. This is indicated by the correlation coefficient, which is denoted by the letter r, the value of r varies in the range from -1 to +1. In the case of a directly proportional dependence of one feature on another, the correlation coefficient is equal to one (i.e., the feature is correlated (connected) with itself). A negative correlation coefficient, as mentioned above, indicates a different direction of variation of features: when one changes in the direction of increasing the other, it decreases and vice versa.
When statistical analysis is carried out on data taken from "real life", correlations are usually found with coefficients ranging between zero (no correlation) and one (perfect correlation), and the closer the value of r is to ± 1, the closer the relationship is. ... The values r expressed in decimal fractions (for example, -0.23; +0.5, etc.). At low values r (values \u200b\u200bare usually considered low if they do not exceed 0.2 at p
The zero value of the correlation coefficient indicates the absence of a relationship between signs, but this is very rare, because in the sphere of mental phenomena, all phenomena are interconnected with all (in most cases, indirectly and can manifest themselves only at the level of tendencies). This requires no proof. And the whole problem is how close this relationship is, by what and by what factors it is mediated, what it depends on, by what methods it is revealed and how it is taken into account in the practical activities of teaching, upbringing, the formation of professionally important skills, qualities, and mastery.
When considering the numerical values \u200b\u200bof the correlation coefficients, it seems that the values r are a direct indicator of the strength of the correlation. For example, one might think that since for an ideal positive correlation r (+1), then r \u003d 0.7 corresponds to 70% perfect correlation (or, exactly the same as r \u003d 0.4 corresponds to 40% perfect negative correlation). In fact, the correlation coefficient is a pretty deceiving number. To find what percentage of the ideal correlation a given value of r is, you need to square it and multiply the result by 100. If r \u003d 0.7, then this correlation is 49% of the ideal (0.7 0.7 100 \u003d 49). Likewise, the negative correlation / * \u003d -0.4 is 16% of the ideal negative correlation. Therefore, the "degree of ideality" of the correlation can be much less than one might think, judging by the value r 163, p. 2711.
Statisticians usually do not use the concept of the degree of ideality, but believe that the correlation coefficient r indicates the proportion of changes in one variable that can be predicted from changes in another variable. There are many methods for measuring correlation, and the choice of a particular method depends on the type of data being considered.
We will consider an algorithm for calculating the Pearson correlation coefficient, which is a measure of the correlation between two variables distributed according to the normal law (for example, to identify the relationship between the level of intelligence development and adaptive capabilities of a person or the relationship between academic performance in mathematics and the time it takes to solve an arithmetic problem, etc. .). The advantage of this method is that the magnitude of the correlation is not affected by the units in which the features are presented. Among the disadvantages of the method is the complexity of mathematical calculations, especially for large data sets. However, this drawback can be completely eliminated by using application programs (for example, the simplest one is Excel).
The nonparametric equivalent of this estimate is spearman's correlation coefficient(for example, to compare the order of arrival to the finish line of the same runners in two races or to identify the relationship between academic performance in mathematics and the time to solve an arithmetic problem, etc.). The advantage of the method is the ability to carry out not very complex mathematical calculations using a calculator for small samples. The disadvantage of this method is the limitation imposed by the complexity of processing large data sets and the need to rank the series of values.
Calculation algorithm in Excel.Opening the Sheet 1 consolidated statement. Choose from the menu Tools\u003e Data Analysis,the "Data Analysis" dialog box appears (Fig. 7.18).
Figure: 7.18.
We choose Correlation\u003e OK.The "Correlation" dialog box appears (Fig. 7.19).
Figure: 7.19.
We set Input interval(indicated by an arrow). For the table in Fig. 7.19 this will be the entire data array, including the scale of attribute names: from the first cell of the attribute name SZ(OL sign - column C) to the last numerical value in the rightmost column P29(sign Score - column P) diagonally.
A correlation matrix appears on a new worksheet, which has the following form (Fig. 7.20).
This correlation matrix must be printed out and, armed with pencils (felt-tip pens), proceed to its analysis.
Each row of the intercorrelation matrix presents the correlation coefficients of one feature with all the others in the order of features that was chosen when compiling the pivot data table. The matrix usually contains the correlation coefficients of one group of features with another group of features of the same space (the entire set) of features. The rows and columns of the matrix are indicated by the name of the features, the cells show the correlation coefficients of one feature with another. The subjects and their serial numbers from the table of initial data are not represented in the intercorrelation matrix in any way. Correlation coefficients carry information only about the tightness of the connection between the signs and do not give any information about any subject.
To effectively use the calculated correlation coefficients, it is necessary to present the available numerical information in a visual form. First of all, it is necessary to highlight the correlation coefficients, the value of which exceeds the critical values \u200b\u200bfor the level of confidence (statistical significance) r The critical values \u200b\u200bof the Pearson correlation coefficient are given in Appendix 6.
It is advisable to single out the correlation coefficients that exceed these significance levels. You can emphasize the coefficients with a confidence of 0.05 with one line or mark with one asterisk, with a confidence of 0.01 - two, and with a confidence of 0.001 - three. Color coding is also convenient.
If the matrix is \u200b\u200blarge, then even highlighting significant coefficients does not create sufficient clarity. Then you can add a few more rows to the bottom of the matrix and write in the corresponding cells the number of significant coefficients in this column: significant at the level r It should be noted right away that in our example, since the sample is insignificant and the number of features is limited, the tabular presentation of the data does not look quite impressive and representative. But as an example, the tabular presentation of available data can be formatted as follows (Table 7.3).
In a real psychological study and the description of its results, the visibility of the presentation of the correlation analysis data increases by several orders of magnitude.
Figure: 7.20.
Table 7.3
The results of the correlation analysis of the relationships between the personal characteristics of psychology students and the level of development of the main cognitive mental processes (P = 25)
In a number of cases, for clarity of the identified relationships, correlation pleiades are used. Both representations of correlation analysis data are quite reasonable. The form in this case depends little on the content, but the assessment and indicativeness of the content of your research largely depend on the form of presentation of the results. For example, this is how the form of representing the relationship between the components of the empathic potential of students with high and low levels of discipline looks like a galaxy of correlations (Fig. 7.21).
Figure: 7.21.
Note.-direct communication; .........- feedback; Sp- desire for acceptance;
So - fear of rejection; Rc- rational channel of empathy;
Her - emotional channel; In - intuitive channel; Us - attitudes that promote or hinder empathy; Pr - penetrating ability;
It - identification; Oi - general level of empathy; Et- empathic tendency;
Tr- tendency to join; St - sensitivity to rejection.
Let us consider what conclusions can be drawn based on the analysis of the correlations shown in Fig. 7.21 and in table. 7.3.
We see that only in relation to two signs: the level of behavioral regulation (PR) and personal adaptive potential (LAP) - we can conclude that they are associated with the functioning of some cognitive mental processes at a reliably significant level. (R
