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JN SAMPLING, the sampling-units are usually chosen so as to be similar in size and structure. With some types of population, however, it is convenient or necessary to use sampling-units that differ in size. Thus the farm is often the sampling-unit for collecting agricultural data, though farms in the same county may vary in land acreage from a few acres to over 1,000 acres. Similarly, when obtaining information about sales or prices, the sampling-unit may be a dealer or store, these ranging from small to large concerns. In such cases the question arises: Should differences between the sizes of the sampling-units be ignored or taken into account in selecting the sample and in making estimates from the results of the sample? This paper contains a preliminary discussion of the problem, though further research is needed, many of the results given below being only large-sample approximations. It is convenient to consider first the problem of estimation, since it appears that the best method of distributing the sample depends on the process of estimation that is to be used.
W. G. Cochran (Mon,) studied this question.