Sampling Without Replacement
In sampling without replacement, each sample unit of the population has only one chance to be selected in the sample. For example, if one draws a simple random sample such that no unit occurs more than one time in the sample, the sample is drawn without replacement. If a unit can occur one or more times in the sample, then the sample is drawn with replacement. The same concept applies to other types of sample designs. For example, in multi-stage sampling the first-stage sampling units (primary sampling units) can be drawn from strata without replacement or with replacement.
In the case of simple random sampling, the estimator of the population mean is