Populations, Samples, and Observational Units

Quick check

A hospital studies all emergency visits but observes 500 records. Which statement correctly separates the target population from the sample?

1. AThe target population is every row in the available database, and the sample is whichever subset remains after cleaning, even if the database omits entire target groups.

   Available records define an operational frame, not automatically the population the decision concerns.

2. BThe target population is the full group about which the analyst wants to draw a conclusion, while the sample is the smaller observed group.

   The distinction fixes both the group actually measured and the larger group the conclusion is intended to describe.

3. CThe target population and sample become identical once the sample exceeds half of the listed records, regardless of who was excluded from the list.

   Sampling fraction does not erase the distinction or repair frame undercoverage.

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Quick check

A study analyzes patients, and each patient has three visit rows. What is the distinction between an observational unit and a measured variable?

1. AA case or observational unit is the entity from which measurements are collected, and a variable is a characteristic that can vary across cases.

   Measurements belong to entities, so identifying the entity first prevents fields or repeated rows from being counted as new cases.

2. BAn observational unit is one cell in a table, while a variable is the row containing all recorded cells.

   The definitions are reversed: the unit is the measured entity and variables are its characteristics.

3. CEach repeated visit row is a new independent patient, even when several rows belong to the same person.

   Repeated visits share one patient, so extra rows cannot create new independent patients.

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Quick check

Why can a statistic computed from the 500 observed visits differ from the corresponding population parameter?

1. AA sample fact is automatically a population fact whenever the sample contains more than one thousand units.

   Sample size reduces random variation but does not eliminate it or guarantee representation.

2. BNothing learned from a sample can describe a population under any design, because only a census permits inference.

   Probability sampling and justified models can connect sample evidence to a population with stated uncertainty.

3. CFacts about a sample are not necessarily facts about the population because samples vary.

   A different sample can yield a different summary, which is why observed results need an inferential link to the population.

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Quick check

A survey draws 100,000 addresses from a frame that excludes temporary housing. What problem remains despite the sample size?

1. AA larger sample from an incomplete frame removes coverage bias because the standard error decreases.

   Precision within the covered frame does not give omitted target members a chance of selection.

2. BIncreasing the size of a sample from a systematically incomplete frame does not remove coverage bias.

   Undercoverage is systematic: repeatedly sampling omitted groups at probability zero cannot make them represented.

3. CCoverage bias disappears once most listed units respond, even if an entire region is absent from the list and the sample remains very large.

   High response inside a defective frame cannot represent target groups missing from that frame.

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Quick check

A device records each of 40 patients once per minute for an hour, the readings are positively correlated, and the target is patient-to-patient variation. Why are 2,400 rows not automatically 2,400 independent units?

1. ATreat all minute-level readings as independent because their timestamps differ.

   Different timestamps do not remove the shared patient effects or serial dependence among readings.

2. BUse 2,400 as the independent sample size because every stored row contains a distinct measurement.

   Distinct values or rows are not distinct independently sampled entities.

3. CWhen several records come from the same person or cluster, the record count is not automatically the number of independent observational units.

   Records inside a person or cluster share information, so row count can overstate the effective number of independent units.

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Quick check

A large weekday sample estimates visits precisely, but its frame omits nights and the target covers all emergency visits. How should the conclusion's scope be stated?

1. AThe scope of a conclusion should be narrowed when the observed sample does not represent parts of the intended population.

   Matching scope to coverage avoids claiming representation for target members who could not enter the observed sample.

2. BThe conclusion should retain its original population scope even when some target groups had no chance to enter the frame.

   Scope must reflect actual coverage and selection.

3. CThe conclusion should be narrowed to the observed records only, even after a defensible representative design.

   A justified design can support inference beyond observed cases, with uncertainty.

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