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Random sample

Any method of taking a sample by which each member of the population of items has a known chance of being included in the sample. A special case of a random sample is a simple random sample, whereby each item in the population has an equal chance of being included in the sample, and therefore all possible samples of a given size (number of items) have an equal chance of being selected. It is important to distinguish between the meaning of random here and its meaning in everyday usage. An intuitive interpretation of the phrase ‘a random sample of voters’ would be that one goes out on to the street and questions the first, say, twenty people one meets or picks out twenty people ‘at random’. This is not, however, a random sample, since we do not know what chance each member of the population (the people of voting age in a particular constituency) had of being chosen, and it is quite possible that many of them had no chance at all. A random sample, properly defined, may well be the result of a careful calculation, and there may be a very precise specification of how many of which types of item are to be included in the sample. The word ‘random’ is not being used in the sense of ‘haphazard’ or ‘fortuitous’, but rather in the more specialized sense of ‘probabilistic’ (in fact probabilistic sample is the term often used in the U.S. for random sample). The importance of devising a random sample is that only if a definite probability of being included in the sample is assigned to each item in the population can the probable error in using the information derived from the sample to make statements about the population be estimated. An incidental but important advantage of random sampling is that by specifying beforehand which types of item, or even exactly which items, are to be included in the sample on the basis of an objective procedure, the inevitable biases which arise from an on-the-spot choice of the sample are avoided. Thus an interviewer may unconsciously select better-dressed people, or flats on lower floors, in a sample which is supposedly to be chosen without bias, and such unconscious biases may influence the results in ways which cannot be estimated. For particular types of sampling procedure based on the idea of random sample.

Reference: The Penguin Dictionary of Economics, 3rd edt.