On large-scale sample surveys

In sample surveys the final estimate is prepared from information collected for sample units of definite size (area) located at random. Large-scale work involves journeys from one sample unit to another so that both cost and precision of the result depend on size (area) as well as the number (density per sq. mile) of sample units. The object of planning is to settle these two quantities in such a way that (a) the precision is a maximum for any assigned cost, or (b) the cost is a minimum for any assigned precision. The present paper discusses the solution for (1) uni-stage sampling (with randomization in one single stage) both in the abstract and in the concrete; and for (2) multi-stage sample (with randomization in more than one stage) mostly in the abstract. The whole area is considered here as a statistical field consisting of a large number of basic cells each having a definite value of the variate under study. These values (with suitable grouping) form an abstract frequency distribution corresponding to which there exists a set of associated space distributions (of which the observed field is but one) generated by allocating the variate values to different cells in different ways. This raises novel problems which are space generalizations of the classical theory of sampling distribution and estimation. On the applied side it also enables classification of the technique into two types: (a) 'individual' or (b) 'grid' sampling depending on whether each sample unit consists of only one or more than one basic cell. For most space distribution precision of the result is nearly equal for both types of sampling; these are called fields of random type. For certain fields (including those usually observed in nature) precision depends on sampling type; these are fields of non-random type. Application to estimating acreage under jute covering 60,000 sq. miles in Bengal in 1941-2 is described with numerical data. The margin of error of the sample estimate was about 2%, while cost was only a fifteenth of that of a complete census made in the same year by an official agency