Strength of Association. Report 2. Graduations of Correlation Size

Abstract

Purpose: To summarize data on graduation of the effect size on the base of Hill’s first causality criterion ‘strength of association’ on the magnitude of the correlation coefficient (mainly Pearson r). Material and methods: Survey of published sources: monographs, handbooks, papers, educational material on statistics in various disciplines (including on-line), etc. (121 references; of which more than 20 textbooks on statistical methods and statistics in psychology and 8 textbooks on epidemiology). Results: Estimation of the strength of association by the correlation size is most common in psycho-sociological disciplines and is almost never used in epidemiology (since the establishment of a fact of statistically significant association/correlation in epidemiology is only the initial stage of evidence, unlike the experimental and named disciplines). A number of known scales for r were obtained: the Chaddok scale (R.E. Chaddock) from 1925, which is now apparently not used abroad, but widely represented in the countries of the former USSR, the Cohen scale (J. Cohen) from 1969–1988, reflecting the ‘soft’ criteria of causality in psychology, D.E. Hinkle with co-authors scale (1979–2003) and the Evans scale (J.D. Evans) from 1996. A number of other graduations, published in the singular, are also given. A total of at least 16 different scales of varying degrees were collected for the correlation coefficient r (1925–2019). The information about the value of r for correlations, which should be neglected was presented. Depending on the source, this is r <0.1; r <0.2 or r <0.3. The data on the possibility of transferring graduations from the Pearson coefficient r to the Spearman correlation coefficient and other parameters of the effect size are given. The question of the difference between estimation of strength of association in epidemiology and medicine and in psycho-sociological disciplines is considered. Unlike the second, in epidemiology and medicine a small value of the correlation coefficient does not necessarily mean a small effect size. Conclusions: To estimate the value of r one should use the most common and officially established scales, with the exception of the strongly ‘soft’ Cohen scale. The present study can be used as a reference guide on the graduations of effect size on r for a wide variety of observation disciplines.