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 = ( X 1 , …, X k )'. In this paper we assume that in the general population, X is normally distributed with mean μ and covariance matrix σ. 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 X 1 …, X k , we can determine the sample sizes for detecting the dependence between A and X without any prior knowledge of the unknowns μ and σ. Let p 1 be the average incident rate in the population and θ and p o be two given numbers with p o < p 1 . The sample size is then determined so that the dependence relation between A and X will be detected with small error if a fraction θ or more of the population live in an environment which has incident rate no greater than p o .