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There are dozens of methods of selecting members, using a variety of mathematical techniques, but the key is that each subject has a random, calculable chance of being selected. There is no human intervention involved in the selection.
Simple (random) Sampling The sample is selected entirely at random
Stratified The population is first divided in to exclusive subgroups based on some predetermined criteria (e.g. location), then samples are selected at random
Proportionate Stratified As above, but a smaller group that would otherwise not provide statistically valid results may be oversampled then the results weighted to correct for this...
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