INTERPRETING CORRELATIONS

Important Number (.7071)

If data exist on 2 variables (X & Y), the square of the correlation coefficient is called the “coefficient of determination.” This latter coefficient, if multiplied by 100, indicates the % of variability in either variable that’s associated with (or explained by) variability in the other variable.

For example, if r = .80, 64% of the variability in X is associated with variability in Y. Or, if r = –.40, 16% of the variability in X is associated with variability in Y.

To have at least 50% “explained variability,” the correlation must exceed ±.7071.

This number, .7071, is worth remembering because many researchers report that a correlation is “moderate” or has “medium strength” if r is near ±.50. In reality, such correlations are not so strong; they indicate that only about 25% of the variability in Y is associated with variability in X.

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