A Generalization of the Intraclass Correlation in Cluster Sampling

다국어 초록 (Multilingual Abstract)

This article is concerned with the intraclass correlation in survey sam-pling. From a design-based viewpoint the intraclass correlation is general-ized to a nite population with unequal sized clusters. Under simple randomcluster sampling the intraclass correlation is given in an explicit form, whichis a generalization of the usual one. The range of it is found and the designeect is expressed by means of it. An example is given to compare the intr-aclass correlation with the homogeneity measure numerically, which showsthat two measures are not the same except some limited cases.AMS 2000 subject classications.Primary 62D05.Keywords.Design-based intraclass correlation, Design eect, Homogeneity measure.1. IntroductionThe eciency of cluster sampling in a nite population is aected by twosources of variation : a selection method and the population structure. When asample of clusters is chosen by simple random sampling the variance of the clustersample mean could be represented by the sample size as well as the measure ofpopulation structure. In this situation two measures for the population structurehave been commonly used : one is the intraclass correlation and the other one isthe homogeneity measure.The intraclass correlation is a measure of the correlation between two elementsin the same cluster. In a xed nite population with equal sized clusters letyijis the value of thejth element in theith cluster then the intraclass correlationofyij and yij 0 is dened asReceived July 2004; accepted August 2005.

참고문헌 (Reference)

1 "？The effect of using household as a sampling unit？" 70, . : 289？-314, 2002