STAT1008 Chap.1 Populations, Samples and Data Collection
Populations, Samples and Data Collection
Populations, Samples and Data Collection sets up the vocabulary every later answer depends on. A population is the full group a conclusion is about; a sample is the part actually measured; a parameter describes the population and a statistic estimates it from the sample.
The chapter compares simple random, stratified, systematic and cluster designs with convenience, judgement, quota and snowball samples, classifies variables as nominal, ordinal, discrete or continuous, and separates sampling error from coverage, non-response and measurement error. Workshop and tutorial questions in this topic usually open a longer problem, so precise vocabulary earns early marks.
A typical item describes a real survey, asks you to name its population, frame and design, and then asks which errors could bias the result and how a better design would reduce them.
What this chapter covers
- 01
The statistical workflow from problem to decision
- 02
Population, sample, parameter and statistic
- 03
Exploratory analysis versus statistical inference
- 04
Sampling frames and coverage
- 05
Random and non-random sampling designs
- 06
Categorical and numerical variable types
- 07
Sampling and non-sampling error
Worked example · free
Name the parts of a survey design
- 1Population: all 6,000 registered borrowers. Frame: the membership database. Sample: the 50 people selected.
- 1Parameter: the mean number of loans last term for all 6,000 borrowers, usually unknown.
- 1Statistic: the mean number of loans for the 50 sampled borrowers, used to estimate that parameter.
- 1Loans last term is numerical discrete, because it is a count of whole loans.
- 1Preferred format is categorical nominal, because print, e-book and audio are labels with no natural order.
Key terms
- Sampling frame
- A sampling frame is the list, map or register used to represent the population when a sample is drawn.
- Parameter
- A parameter is a numerical characteristic of a population, usually unknown and estimated from sample data.
- Stratified sampling
- Stratified sampling divides the frame into subgroups called strata and draws a simple random sample within each one.
- Non-response error
- Non-response error arises when selected units provide no data, either for the whole survey or for particular items.
- Measurement error
- Measurement error is a difference between the value recorded in a survey and the respondent’s true value.
- Systematic sampling
- Systematic sampling selects every k-th unit from an ordered frame after a random start within the first k units.
Populations, Samples and Data Collection FAQ
What is the difference between a parameter and a statistic?
A parameter describes the whole population and is usually unknown, such as the true mean income of all adults. A statistic is calculated from the sample you collected, such as the mean income of 200 surveyed people, and serves as its estimate.
When is cluster sampling a weaker choice than simple random sampling?
Cluster sampling saves cost by measuring every unit inside a few randomly chosen groups. If units inside each cluster resemble one another, the sample carries less information than a simple random sample of the same size, so estimates are less precise.
Does a bigger sample remove survey bias?
No. A larger sample shrinks sampling error, the chance variation between samples. Coverage gaps in the frame, refusals and leading questions are non-sampling errors, and they remain however many responses are collected.
What is a sampling frame and why does it matter?
A sampling frame is the list or register from which a sample is actually drawn. If the frame leaves out part of the population, such as renters missing from a rates register, those people can never be selected, and the estimate can be biased however carefully the sample is drawn.
Is a postcode a numerical variable?
No. A postcode is made of digits, but the digits act as a label for a place, and arithmetic on them is meaningless. It is a categorical nominal variable, like a student ID number or a business registration number.
Exam move
Make a one-page table of the four random designs and four non-random designs, with one line each for how units are chosen, the main advantage and the main weakness. Practise naming population, frame, sample, parameter and statistic for invented scenarios until the five labels come out in a single sentence.
For variable classification, drill numeric-looking codes such as postcodes, ID numbers and rating codes, since these are the items most often misclassified. Finally, rehearse the difference between sampling error and bias with one example of each from a survey you know.
When you practise design questions, use a three-step answer: name the design, state its main weakness in the context given, then propose a better design and say what it fixes. This pattern matches the workshop solutions and turns an open question into a checklist you can complete under time pressure.
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