Random sample
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A sample is a subset chosen from a population for investigation. A random sample is one chosen by a method involving an unpredictable component, in the sense that the selection of any element of the population is independent of the selection of any other element. A more probabilistic approach to a random sample is taking n independent elements from the same probability distribution. A probability sample is one in which each item has a known probability of being in the sample.
Whenever sampling is used there is a risk that the sample will not be sufficiently representative of the population from which it was drawn—this is known as sampling error. In the case of random samples, mathematical theory is available to assess the risk associated with sampling error. Thus, estimates obtained from random samples can be accompanied by measures of the uncertainty associated with the estimate. This can take the form of a standard error, or if the sample is large enough for the central limit theorem to take effect, confidence intervals may be calculated.
Types of random sample
- A simple random sample, also known as an epsem sample, is one in which every individual, or object, in the population of interest has an equal opportunity of being selected for the sample.
- Stratified random sample, in which the population consists of a mixture of distinct subpopulations, each with its own mean and variance, and the sample is structured to make use of this fact. Great gains in efficiency are possible from stratification.
- A cluster sample, in which the sampling units are collected in groups. For example, a sample of telephone calls may be collected by first taking a collection of telephone lines and collecting all the calls on the sampled lines. The analysis of cluster samples must take into account the intra-cluster correlation which reflects the fact that units in the same cluster are likely to be more similar than two units picked at random.
Methods of producing random samples
- Tables of random numbers
- Mathematical algorithms for pseudorandom number generators
- Physical randomisation devices such as coins, playing cards or sophisticated devices such as ERNIE
An example application
The CEO of a company which provides call centres is considering the introduction of new software that she hopes that will reduce average call handling times. She designs an experiment to find out the reduction in mean call handling time associated with the new software. At one of her call centres a sample of 50 call agents will use the new software and the remaining 150 staff will use the existing software. She knows that if she simply asks the centre manager to choose the staff to operate the new software he will likely choose the most intelligent and cooperative agents. The results of the trial will thus be subject to substantial bias in favour of the new software. To avoid this problem she allocates the agents randomly by putting the names of the agents in a column in a spreadsheet. She then creates a second column consisting of random numbers from the spreadsheet's random number generator. By sorting using the second column as the sort key she puts the staff names in random order and selects the first 50 names. These will be the staff using the new software.See also
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