Wanted: guidelines for reporting correlations.

Recently (1–3), there have been guidelines published for authors regarding what and how statistics should be reported when describing the differences between groups of observations. There seems to be a paucity of such guidance with respect to describing the correlation between groups of observations. Of particular concern to me is the way in which Pearson product-moment correlations are reported in many journals. Consider a trial where variable x is fixed (for example, by the researcher) and variable y is free to vary. Least squares regression is used to identify the line of best fit, and the residuals determine the value of the Pearson product-moment statistic, “r.” r can range from 1.0 (a perfect positive correlation) to 1.0 (a perfect negative correlation). An r value of 0 indicates no correlation whatsoever. I have two concerns regarding the use and reporting of such correlations. First, r indicates association, which may be coincidence or causal; however, the shared variance between x and y is inferred using the coefficient of causality, “R” (equal to r r). This means that one could assert that if r 0.7, then merely 49% of the variance in y can be attributable to variance in x. Of course, as the value of r decreases, say to 0.6, then the explanatory value of x is reduced to 36%. Furthermore, if r 0.5, then the predictive value of x 25%. Even at the r 0.7 level, this level of correlation is likely to be of no utility in most physiological studies, where required precision in assertion making is far higher than these values. Moreover, an r value also has an attendant P value, which indicates the likelihood that this correlation (whatever its value) is not due to chance, i.e., is statistically significant. Any value for r can be shown to be statistically significant if the sample size is large enough, and so it is reasonably common (5–7) to see very low correlations reported, i.e., “there was a significant correlation between x and y, r 0.3, P 0.05.” Just a few examples from physiological and medical journals in 2008 where correlations of 0.3 and below are given above to support the point, but there are many available examples. It is my contention, for debate, that for such a finding to be published, authors should either 1) justify the real-world utility of such a low predictive value or 2) explicitly state that the predictive value is very low, and its utility is therefore low. Second, Ludbrook (4) has indicated that the use of the Pearson-product moment in comparing x values between measurement methods or between investigators is “. . .not only wrong, but dangerous. . .rather than looking for agreement, what we should look for is disagreement or bias.” I wonder, therefore, whether we might soon see guidelines for reporting correlations penned by an appropriate authority in Advances in Physiology Education. Such guidelines will help clarify our discourse and help further standardize our communication.