Estimation of correlation for a finite universe

Summary The formula for thePearsonion correlation coefficient, based on a simple random sample, is a consistent estimator of the parent correlation between two given measurable characteristics of the elements of a finite universe. However, when the universe is stratified, and the elements in each stratum are drawn without replacement and with equal probabilities at each draw, the formula for a consistent estimator is much more complex. Generally speaking, the formula for a consistent estimator of the parent correlation varies with the sampling design. The results of this paper are relevant to the analysis of sociological data obtained through sample surveys. In the literature of the theory of statistical sampling the problem of estimating the correlation between pairs of variate values of the identifiable elements constituting a universe has so far not been considered. Needless to say the solution of this problem has an important bearing on sociological studies based on sample surveys.