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Letters to the Editor
May 2001

The Use and Abuse of Correlation Coefficients

Arch Neurol. 2001;58(5):833-834. doi:

Khoury et al1 report significant correlations between peripheral blood T-cell activation markers and disease activity in multiple sclerosis (MS). Indeed, they find a number of statistically significant correlations between changes in percentages of T cells expressing CD25+ or CD4+ and magnetic resonance imaging measures of disease activity and even disability measurements. However, in placing emphasis on the statistical significance (P value) of the test result, they make the classic error of ignoring the actual magnitude of the observed correlation. Most of their conclusions about relationships between T-cell activation and disease activity are based on correlations with r values between 0.16 and 0.33 (with 0.0 representing no correlation at all and 1.0 a perfect correlation). To put the magnitude of the observed correlations into perspective, the observed relationship can only explain (r2) 2.5% to 11% of the variability in the selected parameters!2 Conversely, other parameters must explain the remaining 89% to 97.5% of variability. The low P value of the correlation coefficients only indicates that the chance that the actual correlation coefficient is very different from the observed value is small.

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