S2 4.1, S2 4.2 - Samples and sampling distributions
A sample gives one set of observations; another sample could give a different result. S2 4.1 explains who or what is being sampled and the tradeoffs between a census and a sample survey. S2 4.2 turns a numerical sample summary into a random variable with its own sampling distribution.
Population census sample and sampling unit
Can asking 200 people tell you what 2000 people think? Before considering the number asked, identify the group the conclusion is meant to describe and how its members could enter the survey.
Suppose a college wants to estimate the mean journey time of its 2000 enrolled students. The population is all 2000 enrolled students, even if only 200 answer. Those 200 respondents form a sample. Each student is a sampling unit: the individual member selected for observation.
Population and sample
A population is the complete collection of units under investigation. A census attempts to obtain information from every member of that population. A sample is a subset selected from it; a sampling unit is an individual unit that can be selected.
The unit depends on the question. For a survey of household energy bills, it may be a household rather than a person. Asking every member of ten selected households is still a sample of the town's households; it is not a town census.
A census describes the intended coverage. If some people fail to respond, calling it a census does not magically supply their missing observations. Likewise, a large sample of volunteers need not represent the population well.
Key idea
Define the population from the question you want to answer, then identify what is actually selected. The units observed and the population described must fit together.
Use this distinction in a different setting.
Sampling frames and survey tradeoffs
A selection method needs a practical way to identify the population's members. The list used for that purpose is the sampling frame, and it can differ from the population you intended to study.
Sampling frame
A sampling frame is a list or other record of the sampling units from which a sample can be selected. For a student survey it might be the enrolment register; for a survey of homes it might be an address list.
A college register that omits recent entrants gives those entrants no chance of selection. Duplicate records may give some students extra chances. Selecting randomly from a defective frame does not fix these coverage problems. Even a good frame cannot prevent errors from non-response, misleading questions or inaccurate measurement.
A census can describe small subgroups in detail and, if every unit is measured correctly, removes the uncertainty caused by observing only a sample. It usually costs more and takes longer; a slow census may describe conditions that have changed before results are available. It can still suffer from non-response and recording errors.
A sample survey is usually cheaper and faster, allowing more care per observation. It also leaves sampling variability: a different selected sample may give a different estimate. A small or badly selected sample may miss important groups.
For destructive testing, a sample is often essential. Testing every light bulb until it fails would leave none to sell. For a small group's emergency contact details, a census may be worthwhile because a missing individual's details matter directly.
Watch out
“Census” does not mean “free from every error”. Complete observation removes sampling uncertainty, but measurement, coverage and response errors can remain.
Choose a design for the purpose, rather than assuming that more observations solve every problem.
Continue this lesson.
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