By Rao C.R., Krishnaiah P.R.

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The problem of non-response The relative simplicity of this problem makes it reasonable to deal with it in some detail even in a First Course. 42 T. 1. The notion of non-response A sample of n elements have been selected for a survey. Data is to be collected for several characteristics, which in this context often are referred to as 'items'. There may be two kinds of non-response: (i) element non-response: no data is collected for some elements; and (ii) item non-response: for some elements, no data is collected for one or more item~.

M/m) Z, N i , The estimator 9~ is clearly a radio-type estimator: both the numerator and the denominator are random variables. Hence, in the general case, the expression for V a r y will differ from that for Var f. The discussion of the general theory may be supplemented by some considerations of the variance properties of cluster sampling. This may be carried out by comparing for example the estimator y for simple random sampling of n = m N 35 First course in survey sampling elements with replacement, for which the variance is: Varp= 1 _ : 0 -2 mN with the expression for the variance of cluster sampling using the estimator f as given above.

Sales may be expected to have a markedly skewed distribution: a small number of large stores contribute heavily tO the total; at the same time, there are many small stores which together contribute much to the total. Experience from previous surveys may show that data from the large stores may be collected by mail, while data from the small stores must be collected by interviews. Consequently, it is reasonable to use a combination of 'element sampling' and 'multi-stage sanlpling'. Thus, element sampling Would be applied to a directory of large stores, which, while not comprising all large stores, comprises a substantial fraction of these stores.