Which of the following types of sampling is likely to have maximum bias?

Concept: sampling techniques fall into two families. In probability sampling a randomisation rule decides who enters the sample, so every unit of the population carries a known, non-zero chance of selection and no person's preference can steer the outcome. In non-probability sampling entry is decided instead by judgement, convenience or the social contacts of the people involved, so selection chances are neither known nor controlled.

Sampling bias is a systematic — not chance — divergence between the sample and the population it is meant to represent. The randomisation rule is precisely the device that holds such systematic divergence in check, so bias is at its largest where no randomisation rule operates at all.

Application: classify each offered technique by how a unit gets into the sample.

Three of the four techniques embed a randomisation rule; snowball sampling does not. Its members are, by construction, people connected to the few starting contacts, so individuals who are well connected or similar to those contacts get over-represented while isolated members of the population may have no route into the sample at all. That distortion is systematic rather than random, which is why snowball sampling is the technique likely to carry maximum bias.

Cross-check:

• More data does not cure it. Under simple, stratified or cluster random sampling, raising the sample size shrinks the gap between sample and population, because that gap is chance error. Under snowball sampling more referrals only extend the same networks, so the distortion survives any sample size.

• Do not confuse imprecision with bias. Cluster random sampling is less precise than simple random sampling at the same sample size, because units inside a cluster resemble one another; that inflates the standard error, but the estimator itself stays unbiased.

• Stratification pushes the other way. Splitting the population into strata before drawing lets the design fix each stratum's share of the sample in advance — equal to its share of the population under proportionate allocation, or deliberately unequal under disproportionate allocation — so subgroup representation is decided by an explicit plan instead of being left uncontrolled, as it is under referral-driven recruitment.

Answer: Snowball sampling.