Interpretation of the correlation coefficient

Steve Simon

2006-04-04

Categories: Blog post Tags: Linear regression

[StATS]: Interpretation of the correlation coefficient (April 4, 2006)

There are many "rules of thumb" about how to interpret a correlation coefficient. They vary slightly from one to another, but all say about the same thing. Here's a couple of interpretations I found on the web today:

One old classic and typical interpretation of "r" uses five easy "rules of thumb" to answer the question "When is a correlation coefficient "high" and when is it "low"? as follows:
"r" ranging from zero to about .20 may be regarded as indicating no or negligible correlation.
"r" ranging from about .20 to .40 may be regarded as indicating a low degree of correlation.
"r" ranging from about .40 to .60 may be regarded as indicating a moderate degree of correlation.
"r" ranging from about .60 to .80 may be regarded as indicating a marked degree of correlation.
"r" ranging from about .80 to 1.00 may be regarded as indicating high correlation.
[A. Franzblau (1958), A Primer of Statistics for Non-Statisticians, Harcourt, Brace & World. (Chap. 7)]

Other more recent scholars explain, simply, "as a rule of thumb, we can say that correlations of less than .30 indicate little if any relationship between the variables." [See: Hinkle, Wiersma, & Jurs (1988), Applied Statistics for the Behavioral Sciences, 2nd ed., Houghton Mifflin Co.]

http://irp.savstate.edu/irp/glossary/correlation.html

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regression](../category/LinearRegression.html). for pages similar to this one at [Category: Linear with general help resources. You can also browse Children's Mercy Hospital website. Need more information? I have a page reproducing it here as a service, as it is no longer available on the Hospital. Although I do not hold the copyright for this material, I am This page was written by Steve Simon while working at Children's Mercy