Which one of the following is a non-probability sampling?

Concept — Sampling designs fall into two families according to how a unit's chance of entering the sample is fixed. In a probability design every unit of the sampling frame has a known, non-zero chance of selection and that chance is set by a randomising device, so sampling error can be estimated. In a non-probability design the investigator's own judgement, convenience or quota decides who is included, so no unit's inclusion probability is known or computable.

Application — Among the four designs offered, purposive sampling (also called judgemental sampling) admits a unit because the investigator judges it relevant to the study's aim, for example surveying only principals of accredited colleges when studying accreditation practice. Because inclusion follows the investigator's criteria and not a randomising device, no unit's inclusion probability is known or computable, which places purposive sampling in the non-probability family.

Cross-check — how the other three designs fix the inclusion probability:

• Simple random: units are drawn from the whole frame by lot or by a random-number table, so for a sample of size n every one of the N units carries the same known inclusion probability n/N.

• Systematic: a random start is chosen inside the first k units of an ordered frame and every k-th unit is taken thereafter, so every unit carries the known inclusion probability 1/k.

• Stratified: the frame is split into homogeneous strata and a random draw is made inside each stratum, so the inclusion probability is known stratum by stratum.

All three of these rest on a randomising device and therefore belong to the probability family, so purposive sampling is the non-probability sampling in this set.