Simple random sampling is a type of probability sampling where observations are randomly selected from a population with a known probability or sampling fraction. Typically, one begins with a list of N observations that are in the entire population from which one wants to extract a simple random sample (e.g., a list of registered voters); one can then generate k random case numbers (without replacement) in the range from 1 to N, and select the respective cases into the final sample (with a sampling fraction or known selection probability of k/N).

Refer to, for example, Kish (1965) for a detailed discussion of the advantages and characteristics of probability samples and EPSEM samples. In STATISTICA, you can create simple random probability (EPSEM) and stratified random samples using the Random Sampling options.