The effects of age grouping on the estimate of a correlation coefficient.

Healy (1962) showed that the variance of a growth measurement was inflated when calculated from a sample spanning an age range during which the average value of the measurement changed. Using a reasonable set of assumptions, he showed how a correction factor could be calculated in order to obtain an unbiased estimate of the ' instantaneous' variance. The present note extends Healy's results to the calculation of covariances and correlations. Healy used the characteristic function to obtain his results and although this is a simple way of obtaining estimates of the skewness and kurtosis, the basic results on the variance and covariance can be obtained using simpler expectation methods and these are used here. Consider two measurements x, y taken over a unit (say one year) interval, whose mean and variance change with age over the interval. Following Healy, for age t, let