## Sampling

Some so-called census information is in fact obtained by sampling. Computerassisted statistical procedures make it possible to obtain useful information about many characteristics of the population by questioning only a selected sample of persons. Samples cost only a fraction of what it would cost to interrogate everyone.

To sample something is to examine a small portion of it, usually for the purpose of judging the nature or quality of the whole. In statistics, a collection of elements that have one or more specified characteristics is called a population. A sample, then, is some portion of a population. Because many populations of interest are too large to work with directly, techniques of statistical sampling have been devised to obtain samples taken from larger populations.

Unless a sample is chosen by a random mechanism, however, the results that are obtained from a study are likely to be biased in some direction. It is for this reason that methods of random sampling have been devised. A random sample can be chosen, for example, by throwing dice. Most commonly, however, when a list of names exists from which a sample can be chosen, the actual technique is to use random numbers generated by a computer. The list is numbered, and the computer provides a string of numbers from this list in such a way that various batches of entries in the list have an equal chance of being drawn.

Suppose that a market survey is being taken. A sample group is chosen from the population in the above manner, and the individuals who make up the sample are then interviewed. For example, an individual may be asked about washing powder brand choice. The arithmetic mean of the total answers provided by the individuals yields the proportion preferring one brand or the other. Any statistical population asked this question will also have an average response to it. The responses of the individuals in the population vary about this average response. The variability of the response is described by a quantity called the population variance. The arithmetic mean varies from one sample to the next, but it varies about the average response. In addition, the bigger the sample relative to the population size, the more accurate is the estimate determined by sampling.

Some situations permit the population to be split into a few very homogenous groups or strata. The sample may then consist of a random sample taken within each stratum. Such a sample is called a stratified random sample.

Thus far we have assumed that a list, or sampling frame, is available. This is not true, however, in all cases. For example, no list exists of the pony population of Dartmoor. Thus the important topic of estimating the size of some populations must be handled differently. Areas are usually chosen at random.

THE BASIC NOTION OF A RANDOM SAMPLE

If the population is (1,2,3), there are three possible two-member samples: (1,2), (2,3), and (1,3).

Each of them has a one in three chance of being drawn. This is called random sampling.

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