Interpreting the Correlation Coefficient when One of the Variables is Discrete

Abstract

The effect on the correlation coefficient of discretizing data was investigated in two ways. First, the theoretical effect of dichotomizing data was calculated, and it was shown that the resulting correlation coefficient is considerably less than that between the underlying bi-variate normally distributed variables. Second, computer simulations were performed of a model in which a continuous variable (measured with some error) gives rise to a counting variable through a mechanism in which the count is zero below a certain threshold value for the continuous variable and then increases linearly as the continuous variable increases. It was shown that the correlation coefficient between the observed values of the continuous and counting variables decreased as (a) the measurement error increased, (b) the slope of the relationship decreased, and (c) the number of counts decreased. It is concluded that caution is required when interpreting correlation coefficients when one or both of the variables consist of a few (say only four or five) discrete scores.

Get full access to this article

View all access options for this article.

References

Casagrande, J.T. ; Pike, M.C. ; and Smith, P.G. (1978): The Power Function of the 'Exact' Test for Comparing Two Binomial Distributions, Appl Statist 27:176-180.

Diem, K. and Lentner, C. (1970): Scientific Tables. Macclesfield : Geigy Pharmaceuticals, p. 62.

Guilford, J.P. (1965): Fundamental Statistics in Psychology and Education , 4th ed. New York: McGraw-Hill, pp. 352-354.

Rugg-Gunn, A.J. ; Hackett, A.F. ; Appleton, D.R. ; Jen-Kins, G.N. ; and Eastoe, J.E. (1984): Relationship Between Dietary Habits and Caries Increment Assessed over Two Years in 405 English Adolescent School Children , Arch Oral Biol 29 :983-992.