CDT502 Chap.4 Sampling and Credible Inference
Sampling and Credible Inference
This chapter follows the route from population and parameter through sampling rule, sample and statistic. It distinguishes random sampling error from systematic coverage, nonresponse and measurement bias, then compares simple random, stratified, cluster, systematic and convenience designs. Sampling distributions and standard errors explain precision without allowing a large sample to excuse a flawed frame.
Start with the decision population rather than the file already available. Name the people, transactions, places and time period to which the action applies. Then describe the sampling frame and identify eligible units with no route into it. A random selection from an incomplete frame can be executed perfectly and still fail to represent the omitted units. The design determines what the sample can carry.
Simple random sampling offers a transparent probability basis when a frame exists. Stratification protects coverage of decision-relevant groups and can improve precision. Cluster sampling reduces collection cost but often yields less independent information because units within a selected group resemble one another. Systematic sampling is operationally simple but can align with periodic order in the list.
Non-probability designs may support exploration, access or hypothesis development, yet their population reach must stay limited. Separate random variation from systematic error. Another probability sample would yield a different statistic, creating a sampling distribution that can be summarised by a standard error. Larger samples reduce this component at a square-root rate.
Coverage, nonresponse and measurement mechanisms require redesign, adjustment or a narrower claim rather than more observations from the same process. When reporting an interval, state the procedure, assumptions and target. A narrow range does not certify valid measurement or representative selection. Close with a scope sentence that names exclusions and the operational period.
Making boundaries visible gives the decision owner a way to judge whether the evidence travels to the intended setting.
What this chapter covers
- 01
Population, parameter, sample and statistic
- 02
Probability sampling designs
- 03
Coverage and nonresponse
- 04
Sampling error versus bias
- 05
Sampling distributions
- 06
Standard error and confidence
Worked example · free
See how sample size changes random uncertainty
- 3Compute sqrt[0.60(0.40)/100].
- 2Compute the value when the sample size is four hundred.
- 2Explain what the comparison does not repair.
Key terms
- Coverage Error
- Mismatch created when the sampling frame omits eligible units or includes ineligible ones.
- Nonresponse Error
- Distortion that can arise when selected units do not provide usable data and response relates to the outcome.
- Stratified Sampling
- A design that samples within defined population groups to protect coverage or improve precision.
Sampling and Credible Inference FAQ
Why does a large sample not guarantee representativeness?
Sample size controls random precision after a selection process is established. If parts of the target population have zero inclusion probability or response depends on the outcome, more observations from the same mechanism repeat the distortion more precisely. Audit the frame and response path before celebrating a narrow interval.
When should I use stratified sampling?
Use stratification when known population groups matter to the decision or have different outcome patterns. Divide the frame into mutually exclusive strata and sample within each. Preserve selection probabilities and apply weights when allocation differs from population shares, especially if subgroup precision is intentionally protected.
What does a confidence interval mean?
It comes from a procedure that would cover the fixed population parameter at the stated long-run rate across repeated samples under the same design and assumptions. For one realised sample, describe the interval as values compatible with the evidence and assumptions rather than assigning a probability to the fixed parameter.
Exam move
Take every population claim and write six labels beneath it: target population, frame, unit, inclusion rule, nonresponse path and measurement rule. Then separate what larger sample size can improve from what only redesign can repair. Practise the square-root rule until sample-size comparisons can be predicted without arithmetic.
Compare two feasible designs for the same decision and identify which groups each protects, what each costs and how weighting would enter. For every survey claim, distinguish selected units from responding units and calculate the response rate before interpreting an outcome rate.
Draw repeated-sample sketches that keep the parameter fixed while statistics vary, then explain a confidence procedure without assigning randomness to the parameter after sampling. Review one large convenience dataset and write why its precision cannot repair coverage. Finish each problem with a scope sentence naming the units or periods that remain outside the evidence.
Working through Sampling and Credible Inference in CDT502? Sia is AskSia’s AI Statistics tutor — ask any CDT502 Sampling and Credible Inference question and get a clear, step-by-step explanation grounded in how CDT502 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
