Sampling

In one line

Sampling is studying a part in order to say something about the whole, and it works only if the part was chosen in a way that gives every member of the whole a known chance of being in it.

In the wording a student can write in an exam: sampling is the process of selecting a portion of a population, called the sample, for study, in such a manner that the characteristics of the whole population may be inferred from it. The population or universe is the entire set of units about which conclusions are to be drawn; the sampling frame is the list from which the sample is actually drawn; the sampling unit is the element selected; and the sample size is the number selected.

Why sample at all

Cost and time. A complete enumeration of a large population is prohibitive, which is why a census is conducted once in ten years and surveys continuously.

Feasibility. Some populations cannot be fully enumerated at all.

Destructive or intrusive study, where examining every unit is impossible or unacceptable.

Speed, since results are needed while they are still useful.

Accuracy, paradoxically. A well-designed sample can be more accurate than a complete enumeration, because a small number of units can be studied with trained investigators and careful supervision, while a complete count must use a large and less well-supervised field force. This is the point students find surprising and examiners like: the errors of measurement in a census can exceed the sampling error of a good survey.

The two families

Probability or random sampling

Every unit in the population has a known and non-zero chance of selection. This is the only family from which the accuracy of the estimate can be calculated, and therefore the only one that supports statements about the population with a stated margin of error.

Simple random sampling. Every unit has an equal chance; selection by lottery or by random numbers. It requires a complete frame and gives no assurance that subgroups will be represented in proportion.

Systematic sampling. Every kth unit from a list after a random start. If a population of 2,000 is to yield a sample of 100, k is 20: a random start between 1 and 20 is chosen and every twentieth unit taken thereafter. Simple and convenient. Its danger is periodicity: if the list has a cycle matching k, the sample is systematically distorted.

Stratified sampling. The population is divided into strata that are internally homogeneous, and a sample is drawn from each. Proportionate stratification takes from each stratum in proportion to its size; disproportionate stratification over-samples small strata so that they can be analysed separately. Its merit is that it guarantees representation of every stratum and generally produces a more precise estimate than simple random sampling. In Indian work strata are typically rural and urban, region, and social group.