How an almost absent correlation becomes «meaningful» and the research is effective
Authors: Basimov M. M. 
Published: June 2023

Introduction. The analysis of statistical relationships between the studied characteristics is found in almost any dissertation psychological research, so the problem of traditional errors in interpreting the results of correlation analysis becomes extremely relevant. This is manifested in the fact that the concepts of “strength of connection” and its “significance” are in no way related to each other, and the strength of the connection is considered regardless of the size of the sample. All this leads to either considering “significant”, but at the same time very weak and weak correlations, as results worthy of attention, or to considering strong correlations for small samples. It becomes necessary when analyzing the results of correlation analysis to take into account both the strength of the connection and its “significance”, so that only connections that are objectively worthy of attention when describing the results of the study remain.

Materials and Methods. Tables of critical values of the Pearson (Spearman) correlation coefficient for three significance levels (0.05, 0.01, 0.0001). Transformation of the intervals of the correlation coefficient by the strength of the relationship, taking into account the significance and size of the sample.

Results. The article provides a detailed analysis of literary sources on statistics with a demonstration of the problems of interpreting the results of correlation analysis. An attempt is made to objectively estimate the correlation coefficient, taking into account independent characteristics: the absolute value of the correlation coefficient, the significance level and the sample size, which must be considered simultaneously, without ignoring any of them. A sample of 150 objects is taken as some ideal for interpreting the values of the correlation coefficients in the framework of the classification by the strength of the connection. In order for users to have a single rule for interpreting the absolute value of the correlation coefficient, the article provides tables for users of the transformed correlation strength intervals at significance levels of 0.05, 0.01, 0.001 for different sample sizes. The problems under consideration are discussed on the example of two dissertation studies, when the authors follow the rules for interpreting the results of correlation analysis set out in the educational literature and offer very strange interpretations in the framework of their research.

Discussion and Conclusions. The proposed scheme for interpreting the results of correlation analysis both in terms of strength and significance makes it possible to describe statistical relationships much more objectively when the strength of the relationship is considered with reference to the sample size. This prevents numerous interpretive errors that occur when unilaterally interpreting the results of correlation analysis either by the strength of the relationship or by the level of significance, when numerous results of psychological research in articles and dissertations are very doubtful within the linear paradigm.