Category Archives: Important Numbers

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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IMPORTANT NUMBER IN STATISTICS: .6745

In a picture of the normal distribution, the baseline is usually marked off with numbers. The centered baseline number is the mean score. Other baseline numbers, to the right and to the left of the mean, typically correspond to scores that lie 1, 2, and 3 standard deviations away from the mean. If the picture were to show the scores positioned .6745 of a SD to right and left of the mean, we’d see the upper and lower quartile points, respectively. These points correspond to the 75th and 25th percentile points.

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