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Summer/May 2012 MB0051-Q1. a. Distinguish between Double sampling and multiphase sampling.

Answer :

DOUBLE SAMPLING :A standard form of sample design for industrial inspection purposes. In accordance with the characteristics of a particular plan, two samples are drawn, n1 and n2, and the first sample inspected. The batch can then be accepted or rejected upon the results of this inspection or the second sample be inspected and the decision made upon the combined result.

Context:

The term has also been used somewhat loosely for what is called multi-phase sampling and the two-stage version of multi-stage sampling. There is a further usage whereby a first sample provides a preliminary estimate of design parameters which govern the size of the second sample to achieve a desired overall result.

MULTI-PHASE SAMPLING: It is sometimes convenient and economical to collect certain items of information from the whole of the units of a sample and other items of usually more detailed information from a sub-sample of the units constituting the original sample. This may be termed two-phase sampling, e.g. if the collection of information concerning variate, y, is relatively expensive, and there exists some other variate, x, correlated with it, which is relatively cheap to investigate, it may be profitable to carry out sampling in two phases.
At the first phase, x is investigated, and the information thus obtained is used either (a) to stratify the population at the second phase, when y is investigated, or (b) as supplementary information at the second phase, a ratio or regression estimate being used.
Two-phase sampling is sometimes called "double sampling".

Context:

Further phases may be added if desired. It may be noted, however, that multiphase sampling does not necessarily imply the use of any relationships between variates x and y. The expression is not to be confused with multi-stage sampling.

b. Replicated or interpenetrating sampling: Interpenetrating Sampling: interpenetrating sampling (IPS), also known as interpenetrating sub sampling and replicated sampling. IPS was introduced in the pioneering contribution of P.C. Mahalanobis. It was originally proposed in assessing the non sampling errors as the so-called “interviewer errors”. IPS provides a quick, simple, and effective way of estimating the variance of an estimator even in a complex survey. In fact, IPS is the foundation of modern re-sampling methods like Jackknife, bootstrap, and replication methods. In IPS, three basic principles of experimental designs, namely, randomization, replication, and local control, are used. IPS is used extensively not only in agriculture, but also in social sciences, demography, epidemiology, public health, and many other fields.

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