Journal of Dental Research, Vol 65, 1346-1348, Copyright © 1986 by International & American Associations for Dental Research Online Journals
Interpreting the correlation coefficient when one of the variables is discrete
D. R. Appleton, A. J. Rugg-Gunn and A. F. Hackett
Department of Medical Statistics, Dental School, University of Newcastle-upon-Tyne, England.
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 bivariate
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.
