On the Two Different Aspects of the Representative Method: The Method of Stratified Sampling and the Method of Purposive Selection

Abstract

In planning an investigation of a population by sampling the samples may be chosen in 2 different ways (1) at random either from the population as a whole or from each of several strata into which it is divided (stratified sampling). It is often convenient to choose for each sample a group of individuals, e.g., a census district. (2) Groups are chosen so that the weighted mean of some control character y, known for the whole population and assumed to be linearly correlated with the character x to be investigated, has the same value as in the total population (purposive selection). Bowley''s estimate of the mean of x is inconsistent. (In the discussion Bowley pointed out that Neyman had misunderstood his method, which is really consistent). The method of Gini and Galvani is consistent if the regression of x on y is linear not only for the whole population but for each group of districts composed of a fixed number of individuals. The applicability of this hypothesis can only be tested by an extensive enquiry. On the other hand the method of stratified sampling does not depend on any hypothesis about the stratified population and is therefore preferable except in special cases. If groups are used as elements of sampling they should be as small as possible.