In the rest of the text, SRS will be used to refer to SRS without replacement, unless stated otherwise. Usually, the SRS approach is conducted without replacement because it is more convenient and gives more precise results. An SRS with replacement means that there is a possibility that the sampled telephone entry may be selected twice or more.

SRS can be done with or without replacement. The 2,000 telephone entries corresponding to the 2,000 computer-generated random numbers would make up the sample. All numbers would have the same chance of being generated by the computer. If there were 10,000 entries in the telephone book and if the sample size was 2,000, then 2,000 numbers between 1 and 10,000 would need to be randomly generated by a computer. To draw a simple random sample from a telephone book, each entry would need to be numbered sequentially. To select a simple random sample, you need to list all of the units in the survey population. Consequently, each possible sample also has an equal chance of being selected.

In simple random sampling (SRS), each sampling unit of a population has an equal chance of being included in the sample. In the present section, each of these methods will be described briefly and illustrated with examples. Some operational constraints can also have an impact on that choice, such as characteristics of the survey frame. When choosing a probability sample design, the goal is to minimize the sampling error of the estimates for the most important survey variables, while simultaneously minimizing the time and cost of conducting the survey. There are several different ways in which a probability sample can be selected. However, because units from the population are randomly selected and each unit’s selection probability can be calculated, reliable estimates can be produced and statistical inferences can be made about the population. Probability sampling is more complex, more time-consuming and usually more costly than non-probability sampling. Probability sampling refers to the selection of a sample from a population, when this selection is based on the principle of randomization, that is, random selection or chance.

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