Abstract: In the problem of discriminant analysis using Fisher's sample discriminant function W, Anderson (1973) obtained an asymptotic expansion of the distribution of W in the case of simple random samples. The approximation to the rate of misclassification resulting from this asymptotic expansion is very good. This paper examines the situation where the sample selection can depend on the values of auxiliary variables of the population under study, for example stratified random sampling. We show that Anderson's asymptotic expansion has an error of order O(1) under disproportionate stratified random sampling and we provide a reasonable correction which takes into account such sampling design effect.
Key words and phrases: Asymptotic expansion, discriminant function, sampling design effect, stratified random sampling.