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# Simple random sample

A random sample in which each item in the population has an equal chance of being included in the sample. Suppose the population to be sampled consists of twelve students and that we wish to find, by taking a sample of three students, the average annual expenditure on books. If we want to take a simple random sample, we could number the students from one to twelve, write each number on a separate piece of paper, put them into a bag and draw out three pieces. The numbers on them would then identify the three students for our sample. Each piece of paper has the same chance of being selected; any other procedure which has the property of giving the items in the population an equal chance of being included would be suitable, and choice of a procedure depends on its cost and convenience. A simple random sample shares the general properties of random samples in being independent of human judgement and therefore of the biases this might impart, and in permitting the size of the likely error in generalizing from sample to population to be estimated. However, there may well be situations in which, although we wish to retain the properties of the random sample, we do not want each item in the population to have the same chance of being selected – we may wish to have consistently more of one type of item than another in our sample. This then requires a stratified sample.

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