The Correlation Coefficient: Its Values Range Between Plus/Minus 1, or Do They?

The “correlation coefficient” was coined by Karl Pearson in 1896. Accordingly, this statistic is over a century old, and is still going strong. It is one of the most used statistics today, second to the mean. The correlation coefficient’s weaknesses and warnings of misuse are well documented. As a fifteen-year practiced consulting statistician, who also teaches statisticians continuing and professional studies for the Database Marketing/Data Mining Industry, I see too often the weaknesses and warnings are not heeded. Among the weaknesses/uses, there is one that is rarely mentioned: the correlation coefficient interval [-1, +1] is restricted by the individual distributions of the two variables being correlated. The purpose of this article is: 1) to introduce the affects the distributions of the two individual variables have on the correlation coefficient interval; and 2) thusly, to provide a procedure for calculating an adjusted correlation coefficient, whose realized correlation coefficient interval is often shorter than the original one.

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