STRATIFIED RANDOM SAMPLING ; RANK CORRELATION COEFFICIENTS, TESTS OF INDEPENDENCE AND RANDOM CONFIDENCE INTERVALS

The problem of giving reasonable measures of association when a population is °stratified was first investigated by Aoyama [1] . Recently Wakimoto [3] considered the problem more extensively. He gave an estimator of the correlation coefficient based on a stratified random sample and showed it to be superior to the one given by Aoyama. The purpose of this paper is to propose new measures of association, test of independence and confidence intervals based on a stratified random sample. These measures are stratified version of Kendall and Speaman rank correlation coefficients. Throughout this paper we assume that each size of stratum is sufficiently large compared with that of sample taken from it so that the finite correction term may be neglected. In section 2 measures of association, tests of independence and confidence intervals based on a stratified random sample is given. A stratified version of Kendall rank correlation coefficient is discussed in section 2.1 and then in section 2.2 the one of Speaman type is discussed. In section 3 gains in efficiency due to stratification is demonstrated in the case of proportional allocation by comparing proposed measures with respect to Kendall and Speaman rank correlation coefficient based on a simple random sample.