Many reports claim serious "relationships" between variables when they find a statistically significant correlation like r = .20 (that happens often with large sample sizes), which in fact indicates not more than 4% commonality between X and Y. I feel that reporting r square would be a more informative solution and also make aware authors that in spite of statistical significance there is a weak relationship.
If strength and direction of a linear relationship should be presented, then r is the correct statistic. If the proportion of explained variance should be presented, then r² is the correct statistic. These are just different things. Unfortunately, many authors seem to give just some value because others give it or the software provides it. Often, niether of them is useful. The slope, its confidence interval and prediction intervals or the residual standard error are much more interesting and useful, but usually not provided.
If strength and direction of a linear relationship should be presented, then r is the correct statistic. If the proportion of explained variance should be presented, then r² is the correct statistic. These are just different things. Unfortunately, many authors seem to give just some value because others give it or the software provides it. Often, niether of them is useful. The slope, its confidence interval and prediction intervals or the residual standard error are much more interesting and useful, but usually not provided.
Thank You Both! I think I was referring to linear correlations, bur perhaps made it not clear. I see the point! The slope and its confidence intervals are indeed not provided in most reports.
I completely agree with both Jochen and Luis. However, if it comes down to ONLY reporting "r" or "r-squared," I'd report "r" because it contains more information (due to the sign, indicating direction of the relationship). Anybody with a paper and pencil (or a calculator) can compute "r-squared" if they know "r," but in the case of an inverse relationship they can't know "r" if all they know is "r-squared."
Dear Kenneth, - This is the most logical answer (...but you'd surprised to learn that a number of scholars are not familiar with the meaning of the r square:-(). Thanks!
@Kenneth W Wallston, @Attila Szabo
Thank u both so~O much. We have submitted a MS for publication. It gives TSH vs FT4 (both thyroid hormones) linear regression during 3 trimesters of pregnancy in total ( A n=307), Iodine-deficient (B n=279) and Iodine-sufficient ( C n=28)subjects. The p is highly significant in each trimester
I completely agree with both Jochen and Luis. However,is that logical in linear regressions and what is with the logistic regressions?
the r and r2 of the models are always very low
Thanks for the help. For my linear relationship I will go with "r" and as indicated simple multiplication will give an "r squared" if desired.
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