Random Sampling

A sample is random when a chance mechanism selects the units. In a simple random sample of size $n$, every sample of that size is equally likely: number the population, generate random numbers, take the matching units, skipping repeats (without replacement) or allowing them (with replacement). Stratified sampling splits the population into homogeneous strata and runs an SRS within each, guaranteeing representation and steadying the estimate. Cluster sampling randomly selects whole groups, ideally each a miniature of the population, and measures everyone inside. Systematic sampling takes a random start and a fixed interval.

The traps are all substitutions. Haphazard stands in for random: whoever walks by, whoever replies first, whatever looks typical, none of which is a chance mechanism. Cluster gets called stratified because both involve groups, though one samples within every group and the other takes all of some groups. A systematic sample gets called an SRS though most samples are impossible under it. And when a sampling plan has a flaw, the reflex is to enlarge it, as if more of the same selection could repair how the selecting is done.