‘Determination of sample size for testing the relation between an incident and a set of random variables in a sample survey’

Abstract

SUMMARY It is often necessary to determine if, and to what extent, an incident A is related to a set of environmental random variables X = (Xl, ..., Xk)'. In this paper we assume that in the general population, X is normally distributed with mean ,u and covariance matrix E. A sample of X will be taken from the incident and nonincident groups, and, assuming that the incident rate p is approximately a linear function of X1, ..., Xk, we can determine the sample sizes for detecting the dependence between A and X without any prior knowledge of the unknowns , and E. Let Pi be the average incident rate in the population and 0 and po be two given numbers with po <Pl. The sample size is then determined so that the dependence relation between A and X will be detected with small error if a fraction 0 or more of the population live in an environment which has incident rate no greater than po. Some key worde: Correlation analysis; Hotelling's T2 test; Selection of sample size.