As a result of studying this chapter, the student must:


• Conditions for causal inference in experimental, quasi-experimental and correlation studies;

• The role of statistical analysis in providing conditions for causal inference;

• concepts of complex linear regression, multiple and partial correlation, coefficient of determination;

be able to

• construct linear regression equations for two or more independent variables;

• correctly interpret the coefficients of regression, the coefficient of determination, multiple and partial correlation coefficients;


• the basic conceptual apparatus of multivariate regression analysis;

• Data processing skills using complex linear regression using standard statistical packages.

Causal analysis in the experimental study

An experiment in the exact sense of the word assumes the study of cause-effect, or causal, dependencies. In order to determine whether the variable X causes Y, to change, three conditions must be met (T. Kornilov [11], J. Cohen et al. [211].

1. The events and facts associated with the X variable must precede the events and facts associated with the Y variable.

This condition can obviously be satisfied only for those variables that the experimenter is able to control. This can be, for example, different ways of teaching, tasks of varying degrees of difficulty, words that the subject must remember. All these effects can be determined directly by the experimenter. Therefore, such variables are usually called manageable. However, often the experimenter is forced to investigate the effect of variables that he can not control. Such variables can, for example, reflect the various individual characteristics of the subjects, their personal or individual properties, such as gender, type of character, temperament, level of development of abilities. Strictly speaking, even if the experimenter uses standard experimental schemes that presuppose direct control, such variables can only perform the role of analogs of the independent variable, and in the standard experimental scheme the conclusion about the influence of such variables on any other variables remains open.

2. The change of X must be accompanied by a change in the variable Y.

Methods of statistical data analysis, be it dispersion, covariance, correlation or regression analysis, are just designed to statistically evaluate this relationship. As we have already seen, far from always the relationships that we observe between independent and dependent variables are reliable in themselves. Estimating the relationship between them, we correlate the observed patterns with a possible experimental, or statistical, error.

3. The influence of the third variable, which implies an alternative, competing, explanation of the empirically observed and statistically confirmed relationship between the variables X and Y should be excluded.

The problem of excluding the possibility of competing explanation of empirically observed regularities is one of the main tasks of experimental research in the exact sense of the word. It is here that the fundamental boundary separates the experiment and other experimental methods, such as observation or interrogation. This task is being solved as a result of special experimental control procedures. If these procedures are directly included in the experimental plan and are its integral part, then such control, as we already know, is called direct, or direct. If, however, for any reason, for example, due to the use of uncontrolled independent variables in the experiment, such control is impossible or impractical, the experimental control is transferred from the planning stage of the experiment to the stage of statistical analysis of the obtained data. We know that such a control option is called indirect, indirect, or statistical.

In Ch. 8 we examined how statistical control can be performed in a quasi-experimental study using covariance analysis procedures. In this chapter, we consider another possibility of statistical control, which makes it possible to extend the possibilities of causal analysis to correlation research.

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