Which of the following sampling methods in research are non-probability based?…

CONCEPT: In research methodology, sampling methods split into two families. In probability sampling, every unit of the population has a known, non-zero chance of selection, usually via a random mechanism, so results can be generalised with a calculable margin of error. In non-probability sampling, units are selected using the researcher's judgement, convenience, or a chain of referrals, so selection probability is unknown and results cannot be generalised with the same statistical confidence.

APPLICATION: Classify each of the five methods against this test.

1. Random sampling selects units purely by chance with equal/known probability – it is the defining case of probability sampling.

2. Cluster sampling randomly selects whole clusters (groups) from the population before sampling within them – the cluster-selection step is itself random, so it is probability-based.

3. Judgement (purposive) sampling relies on the researcher's own judgement to hand-pick units believed to be representative – no random mechanism is involved, so it is non-probability.

4. Snowball sampling starts from a few known subjects who then refer further subjects – selection depends entirely on existing contacts, not chance, so it is non-probability.

5. Dimensional sampling extends quota sampling by picking units to fill combinations of several relevant characteristics (dimensions) – the researcher deliberately fills each cell rather than drawing units at random, so it is non-probability.

So the non-probability methods among the five are judgement sampling, snowball sampling, and dimensional sampling.

CROSS-CHECK: Random sampling and cluster sampling both retain a random-selection step, so ruling them out (and keeping only judgement, snowball and dimensional sampling) is consistent with the probability-vs-non-probability test above.