Define the target population before expanding a survey

Define the ecological target

A target population is the set of units about which a study intends to infer. The sampling frame is the operational list or spatial representation from which units can actually be selected. They can differ because of access restrictions, omitted habitats, outdated maps or ambiguous eligibility. A precise estimate for the frame need not represent the target.

Specify the observation model

Probability sampling gives units known nonzero selection probabilities under a defined design. Random selection within accessible sites can protect against convenience choices there, but cannot give omitted sites a chance to enter the sample. Increasing the number of accessible observations may reduce sampling variability while leaving noncoverage bias intact.

Work through the sampling logic

The original finite population has 100 equal sites. Accessible sites have one supplied mean count; omitted sites have a different stipulated mean. Because both are known in this invented audit, the target total can be computed and compared with naive expansion. In an actual inaccessible region, its mean would not be available merely because a formula asks for it.

Challenge the inference

Frame error, nonresponse and imperfect detection are distinct. Frame error excludes eligible units before selection; nonresponse prevents obtaining a selected unit’s measurement; detection can miss organisms within a surveyed unit. They require different design or analysis responses. Replacing every inaccessible random site with a convenient nearby site can change inclusion probabilities and must not be treated as harmless.

Design a defensible survey

A defensible protocol records the target definition, eligibility rules, frame version, selection mechanism and dispositions for missing sites. If part of the target remains unsupported, narrow the inference explicitly or evaluate a stated sensitivity range. Never invent observations for inaccessible sites or enter unsafe habitats to satisfy a sampling quota.

Worked original packet

With 60 accessible sites averaging 4 individuals and 40 omitted sites averaging the stipulated 10, the true synthetic total is 640. Expanding the accessible mean to all 100 gives 400, a shortfall of 240. More exact measurements at those same accessible sites do not remove this coverage error.

Investigation

Compare accessible shares 40 and 80 at mean 4. Reconstruct the target and naive totals, then identify which omitted-site information is supplied only by the fictional packet.

Changed-case transfer

If 80 sites are accessible with mean 6 and omitted sites have mean 10, calculate the target total and naive expansion. What cannot be inferred when the omitted mean is unknown?

Feedback

Target 80×6+20×10=680; naive 600; error−80. Without the omitted mean or defensible auxiliary information, the exact target total is not identified by accessible measurements.

Sources and evidence boundary

Original instructional prose, values and exercises. Context checked 30 October 2026: primary agency source. All observations are synthetic. No organism collection, trapping, tagging, release or unsafe-site access is requested; a real study requires qualified design, permission and supervision. Public feedback is practice, not independently verified mastery.