Sampling Methods and Bias

The four designs AP asks about

• Simple random sample (SRS) — every group of size $n$ equally likely.
• Stratified — split into homogeneous strata, take an SRS within each. Reduces variability when strata differ.
• Cluster — split into clusters, randomly choose whole clusters. Cheaper, usually more variable.
• Systematic — pick every $k$-th unit after a random start.

Convenience and voluntary response are not random designs; both are biased by construction.

Bias is not fixed by a bigger sample

Undercoverage, non-response and question wording all push the estimate in a systematic direction. Increasing $n$ shrinks random variability, not systematic error — a large biased sample is simply a precise wrong answer.