Sampling Designs and Data-Generation Processes

Introduction

Statistical quality management depends not only on how data are analysed, but also on how they are generated. A sophisticated estimator cannot correct a systematically biased sample, an incomplete sampling frame, or measurements that do not represent the quality characteristic of interest. Sampling design is therefore a methodological decision linking a target population, a data-collection process, an estimator, and the decisions that follow.

In total quality management (TQM), organizations frequently need evidence about defect rates, customer satisfaction, process capability, supplier performance, service delays, and complaint resolution. Inspecting every unit may be impossible, costly, or destructive. A properly designed sample can provide reliable information at a fraction of the cost. However, reliability requires more than selecting a convenient number of observations. The researcher must define the population, construct or evaluate a sampling frame, specify the selection mechanism, control nonresponse and measurement error, and preserve the possibility of valid statistical inference.

This chapter develops the principal probability-based sampling designs: simple random, systematic, stratified, cluster, and multistage sampling. It also examines data-generation processes, representativeness, randomization, selection bias, nonresponse, and measurement error. The emphasis is on design judgment: choosing a method that is statistically defensible and operationally feasible.

Learning objectives

By the end of this chapter, the reader should be able to:

1. Distinguish the target population, sampling frame, sample, parameter, and statistic.
2. Explain how a sampling design determines inclusion probabilities and inferential validity.
3. Design and evaluate simple random, systematic, stratified, cluster, and multistage samples.
4. Identify coverage error, selection bias, nonresponse bias, and measurement error.
5. Explain the role of randomization and assess representativeness without confusing it with demographic resemblance alone.
6. Select an appropriate design for quality-management and operational settings.
7. Evaluate the practical, ethical, and governance implications of a data-generation process.

1. The architecture of a sampling study

1.1 Population, frame, sample, and study variable

The target population is the complete set of units about which conclusions are intended. Units may be people, products, transactions, machines, suppliers, hospitals, or production shifts. The sampling unit is the unit selected at a particular stage; it need not be identical to the final element on which measurements are made.

The sampling frame is the operational list, database, map, register, or procedure from which units are selected. For example, a customer database may be a frame for customers, while a list of production lots may be a frame for lot-level inspection. A frame can be incomplete, duplicated, outdated, or contain units outside the target population.

The sample is the set of units actually selected. The study variable is the characteristic measured, such as waiting time or defect status. A population parameter describes the target population, whereas a sample statistic is computed from observed data.

For a finite population of size N with values y₁, y₂, …, y_N, the population mean is:

The sample mean for n observed units is:

Here, μ is a fixed but usually unknown parameter, ȳ is a statistic, N is population size, and n is sample size. The formula for ȳ is descriptive; whether it provides an unbiased or precise estimate of μ depends on the selection design and the data-quality process.

1.2 Probability sampling and inclusion probabilities

A probability sample uses a known, non-zero probability of selection for every target-population unit. Let π_i denote the probability that unit i is included. Designs with unequal probabilities can still be valid, provided the probabilities are known or estimable and incorporated into estimation.

A basic design-unbiased estimator of a population total is the Horvitz–Thompson estimator:

where s is the selected sample, y_i is the observed value for unit i, and π_i > 0 is its inclusion probability. For equal-probability sampling, π_i = n/N, so the estimator becomes (N/n)∑ᵢ∈s y_i. The estimator requires correct inclusion probabilities and assumes that measured values correspond to the intended units. It does not automatically correct nonresponse or measurement error.

A useful distinction is between sampling error and nonsampling error. Sampling error is the random difference between a sample result and the population value caused by observing only part of the population. Nonsampling error includes frame error, nonresponse, response bias, processing error, and measurement error. Increasing sample size generally reduces sampling error, but may not reduce systematic nonsampling error.

2. Simple random sampling

2.1 Design and implementation

In simple random sampling without replacement (SRSWOR), every sample of n distinct units from N population units has the same probability of selection. Each unit consequently has inclusion probability:

A practical procedure is:

1. Define eligibility and the population time period.
2. Create a deduplicated frame and assign each unit a unique identifier.
3. Generate a random sample using a certified random-number generator.
4. Record the selected units and preserve the random seed or selection record.
5. Follow a predefined protocol for ineligible units, refusals, and substitutions.

Substituting a convenient unit for a selected unit changes the design and may introduce bias. If a selected unit is unavailable, the preferred response is a documented callback, a nonresponse adjustment, or a prespecified replacement rule that preserves known probabilities.

2.2 Estimation and precision

Under SRSWOR, the sample mean is unbiased for the population mean when every sample is equally likely. If s² is the sample variance, an estimated variance of the sample mean is:

The factor (1 − n/N) is the finite population correction (FPC). It is relevant when sampling without replacement and the sampling fraction n/N is not negligible. If the population is very large relative to the sample, the FPC is close to 1 and is often omitted.

For a two-sided approximate 95% confidence interval when a normal approximation is defensible:

The constant 1.96 applies to the standard normal approximation and should not be used automatically for very small samples or highly skewed data. For small samples with approximately normal measurements and unknown variance, a t critical value is generally more appropriate.

2.3 Strengths and limitations

SRS is conceptually simple, supports standard estimators, and avoids deliberate selection by investigators. Its limitations are practical: a complete frame is required, geographically dispersed units may be expensive to reach, and small but important subgroups may be missed by chance. SRS may also be inefficient when the population is heterogeneous and relevant auxiliary information is available.

Worked example: estimating a defect proportion

A plant has N = 10,000 sealed units. An SRS of n = 400 units finds x = 12 defective units. The estimated defect proportion is:

Thus, the estimated rate is 3%. Treating the observations as approximately independent for a planning calculation, the standard error is approximately:

A simple approximate 95% interval is 0.03 ± 1.96(0.00853), or approximately 1.3% to 4.7%. The interval is only a sampling-uncertainty statement. It does not account for missed units, misclassified defects, or a frame that excludes a production shift.

3. Systematic sampling

3.1 Design

Systematic sampling selects units at a regular interval from an ordered frame. If the intended sample size is n and the frame contains N units, the interval is often approximated by:

When k is an integer, select a random starting position r from 1 through k, then select positions r, r+k, r+2k, …. When N/n is not an integer, a linear or circular procedure should be specified carefully; rounding the interval without documenting its consequences can produce unequal inclusion probabilities.

The random start is essential. Selecting every tenth record beginning with the first record is not equivalent to probability-based systematic sampling. The order of the frame must also be examined. Ordering by geography, time, product type, or risk can improve precision if it creates implicit stratification, but periodic patterns can cause serious bias.

3.2 Example and periodicity risk

Suppose 1,200 transactions are arranged chronologically and a sample of 120 is required. The interval is k = 1,200/120 = 10. A random start of 7 selects transactions 7, 17, 27, and so on. If the process has a ten-transaction cycle—perhaps every tenth transaction is handled by a special machine—the sample may overrepresent one process condition. A random start does not eliminate periodicity; it only gives each allowable starting position a probability of selection. Investigators must inspect the ordering and, where necessary, randomize the frame order or use stratification.

3.3 Evaluation

Systematic sampling is efficient when a reliable ordered list exists and field staff need a simple rule. It can spread observations across the frame more evenly than SRS. It is inappropriate when the interval aligns with an unrecognized periodic process or when the frame is continuously changing without a clear sampling window.

4. Stratified sampling

4.1 Logic and allocation

In stratified sampling, the population is divided into non-overlapping, collectively exhaustive subpopulations called strata, and a sample is drawn separately within each stratum. Strata should be defined before selection and should be based on information relevant to the study variable or operational decision, such as plant, product family, customer segment, or supplier risk class.

If stratum h contains N_h units and n_h are sampled, its sampling fraction is n_h/N_h. The overall estimator of the population mean is:

Here, H is the number of strata, ȳ_h is the sample mean in stratum h, and W_h is the stratum's population weight. The weights must reflect the population, not the number sampled, unless allocation happens to be proportional.

Under independent SRSWOR within strata, an estimated variance is:

where s_h² is the sample variance in stratum h. The formula assumes correct stratum sizes, independent sampling within strata, and valid measurements.

4.2 Allocation strategies

Proportional allocation sets n_h = n(N_h/N). It is straightforward and maintains similar sampling fractions across strata. Disproportionate allocation deliberately samples some strata more heavily, for example small high-risk suppliers or rare complaint categories. Weighted estimation is then essential.

If stratum costs and variability differ, a classical minimum-variance allocation under a fixed budget is approximately proportional to N_h S_h/√c_h, where S_h is the stratum standard deviation and c_h is per-unit sampling cost. This allocation assumes reliable planning values and a variance objective; it may be modified to guarantee minimum sample sizes for reporting or regulatory purposes.

4.3 Why stratification can improve quality evidence

Stratification is especially valuable when strata are internally homogeneous but differ from one another. It ensures representation of important groups and permits separate operational conclusions. However, poorly defined or overlapping strata create classification ambiguity. Post hoc grouping after observing outcomes can also create misleading inferences unless clearly treated as exploratory analysis.

5. Cluster sampling

5.1 Concept

Cluster sampling selects groups, or clusters, rather than individual elements. Examples include selecting hospitals and surveying patients within them, selecting production lines and inspecting items on those lines, or selecting geographic routes and interviewing households. In one-stage cluster sampling, all elements in selected clusters are measured. In two-stage cluster sampling, a sample of elements is selected within each chosen cluster.

Clusters are often chosen for logistical convenience, but elements within a cluster tend to resemble one another. This positive intracluster correlation reduces the effective amount of independent information. A common planning approximation is the design effect:

where m is the average number of sampled elements per cluster and ρ is the intracluster correlation coefficient (ICC). The expression assumes approximately equal cluster sizes and a common ICC. If ρ = 0, clustering has no variance penalty under this approximation; as ρ increases, sampling more elements within the same cluster yields diminishing information.

An approximate effective sample size is:

For example, if m = 10 and ρ = 0.20, then DEFF ≈ 1 + 9(0.20) = 2.8. A sample of 280 clustered observations may contain information comparable, for variance purposes, to roughly 100 independent observations. The calculation is an approximation and does not replace a design-based variance estimator.

5.2 Cluster versus stratified sampling

The distinction is central. In stratified sampling, units are sampled from every stratum, and strata are ideally internally homogeneous. In cluster sampling, only some clusters are sampled, and clusters ideally resemble miniature versions of the population. Stratification often increases precision; clustering often reduces cost but increases variance.

6. Multistage and complex designs

Multistage sampling selects units through successive stages. A national service-quality study might select regions, then facilities within regions, then departments, then transactions. At each stage, the selection probability must be defined. If the stages are conditionally independent according to the design, the final inclusion probability for an element is the product of its stage-specific probabilities:

where L is the number of stages and π_iℓ is the conditional probability of selecting the unit's stage-ℓ component, given selection at earlier stages. In practice, unequal cluster sizes, sampling with probability proportional to size, nonresponse, and subsampling require careful weighting.

A common design is probability-proportional-to-size (PPS) sampling, in which larger clusters have greater selection probability. PPS can produce approximately equal element probabilities when a fixed number of elements is subsequently selected within each selected cluster. The size measure must be current, relevant, and not itself systematically biased.

Complex designs require variance methods that account for strata, clusters, and weights. Treating all observations as independent can substantially understate standard errors and produce overconfident decisions. Survey-weighted estimators, Taylor linearization, replication methods, or suitable model-based methods may be used depending on the design and software.

7. The data-generation process: beyond selection

A sampling design is only one component of a data-generation process. A useful process model is:

Target population → frame → selection → contact/response → measurement → processing → analysis → decision

An error at any link can affect the final conclusion.

7.1 Coverage and frame error

Undercoverage occurs when eligible units are absent from the frame. Overcoverage occurs when ineligible or duplicate units are included. A frame may also contain incorrect contact information or stale status codes. Frame evaluation should document the source, reference date, update frequency, duplicate controls, eligibility rules, and reconciliation with independent counts.

A complete frame is not always necessary for probability inference, but its deficiencies must be understood and addressed. For example, a customer survey based only on registered online users excludes customers who purchase through other channels. The resulting inference should be limited or supplemented with another frame.

7.2 Selection bias

Selection bias occurs when inclusion is related to the outcome or its determinants in a way not adequately controlled by the design or adjustment. Convenience samples, voluntary online polls, interviewer discretion, and replacing nonrespondents with easily reached units are common sources.

Random selection protects against deliberate selection preferences and, under repeated sampling, supports unbiasedness. It does not guarantee that every realized sample resembles the population on every variable. Nor does randomization repair a deficient frame or biased measurement instrument.

7.3 Nonresponse

Nonresponse may occur because a unit cannot be contacted, refuses, is unavailable, or provides an unusable response. Unit nonresponse means no usable information is obtained; item nonresponse means some questions or measurements are missing.

A response rate is informative but not a complete bias diagnostic. A high response rate can still be biased if nonrespondents differ systematically; a lower rate may be acceptable if nonresponse is weakly related to the outcome after adjustment. Good practice includes multiple contact attempts, varied contact modes, neutral communications, short instruments, incentives where appropriate, refusal classification, and comparison of respondents with frame variables.

Nonresponse weighting may adjust estimates when response propensities can be modelled using relevant auxiliary variables. Imputation can address item missingness under explicit assumptions, such as missing at random conditional on observed variables. Neither adjustment is a universal cure: unmeasured differences can remain.

7.4 Measurement error

Measurement error is the difference between the recorded value and the construct or true value intended. It can arise from ambiguous definitions, faulty instruments, recall limitations, interviewer effects, social desirability, leading questions, or inconsistent inspection criteria.

For a measured value Y* and intended value Y, measurement error is often represented as:

where E is measurement error. If E has mean zero and is independent of Y, repeated measurements may average out random error. If error is systematic—for example, a gauge consistently reads 0.4 units high—averaging does not remove bias. In quality control, gauge repeatability and reproducibility studies, calibration, blinded assessment, operational definitions, and assessor training are important controls.

7.5 Processing and linkage error

Data can be altered through coding, transcription, deduplication, record linkage, unit conversion, or software processing. A documented data dictionary, validation rules, audit trails, version control, and independent checks reduce these risks. Automated systems should not be assumed accurate merely because they process data rapidly.

8. Representativeness, randomization, and causal interpretation

Representativeness has at least two meanings. Design representativeness concerns whether the selection mechanism gives target units appropriate inclusion probabilities. Compositional similarity concerns whether observed sample characteristics resemble known population margins. A sample can be compositionally similar by chance yet arise from a biased mechanism; conversely, a valid random sample may differ from population margins in a particular realization.

Post-stratification or calibration can align sample estimates with trusted population totals. Such adjustment can improve precision and reduce bias under suitable assumptions, but it does not create information about units absent from the frame or correct invalid measurements.

Randomization in sampling should be distinguished from randomization in experiments. Sampling randomization supports generalization from a sample to a population. Treatment randomization supports causal comparisons between interventions. A probability sample alone does not establish that one process improvement caused an observed change; causal claims require an appropriate intervention design or credible causal methodology.

9. Choosing a design: an integrated framework

Design selection should begin with the decision, not with a preferred technique. The following questions are useful:

A quality-management team should prepare a design protocol before observing outcomes. It should specify the estimand, population, frame, selection method, randomization procedure, sample size, replacement and nonresponse rules, measurement protocol, weighting, variance estimation, and reporting limitations.

10. Sample-size reasoning

Sample size is driven by desired precision, variability, confidence level, cost, and design. For estimating a large-population proportion with anticipated proportion p, margin of error e, and normal critical value z, a common planning formula is:

The formula assumes a probability sample with an approximately independent estimator, a sufficiently large sample for the approximation, and a specified absolute margin of error. If p is unknown, p = 0.5 gives the largest binomial variance and therefore a conservative calculation.

For a finite population, one commonly applies:

where N is the population size. For clustered designs, the independent-observation requirement should be inflated approximately by the design effect: n_clustered ≈ n_independent × DEFF. Anticipated nonresponse also requires adjustment. If the expected response rate is r, the number initially contacted may be approximated by n_contact = n_complete/r, provided the response-rate assumption is meaningful.

These formulas are planning tools, not substitutes for a complete design. Precision for subgroup estimates, unequal weights, skewed outcomes, finite populations, and regulatory requirements may dominate the calculation.

11. Illustrative case: supplier defect surveillance

Background

A manufacturer purchases components from 240 suppliers. Supplier size varies considerably, and historical evidence suggests that small high-risk suppliers have more quality incidents. The organization wants an annual estimate of the overall incoming defect rate and separate evidence for high-risk suppliers.

Problem

The purchasing department proposes surveying the 30 suppliers with the largest purchase volume and inspecting ten recent shipments from each. This plan is operationally simple but excludes small suppliers and may overrepresent suppliers with good automated records. In addition, shipments from the same supplier may be correlated.

Analysis

The target population is all eligible component shipments received during the defined fiscal year. The frame is the enterprise receiving database, reconciled with accounts payable and warehouse records. Suppliers are classified into three prespecified risk strata—low, medium, and high—using information available before sampling. Within each stratum, suppliers are selected using PPS so that larger suppliers have greater probability of selection. A fixed number of shipments is then selected randomly within each selected supplier.

This is a multistage stratified cluster design. The supplier is a first-stage cluster; shipment is the final element. Because shipments from a supplier may share manufacturing conditions, the analysis must account for clustering. High-risk suppliers are oversampled to support a useful stratum-specific estimate, while weights restore the overall population representation.

Approach and controls

The protocol includes:

• a frozen frame date and duplicate reconciliation;
• random seeds and an auditable selection log;
• prespecified rules for cancelled or ineligible shipments;
• at least two contact attempts for missing records;
• a calibrated inspection method with blinded defect classification where feasible;
• recording of supplier, plant, product family, and shipment date as auxiliary variables;
• design weights incorporating supplier and shipment selection probabilities;
• variance estimation using supplier as a cluster;
• separate reporting of overall, stratum-specific, and supplier-level findings.

Outcome

The resulting estimates are more defensible than the proposed largest-supplier census because the design covers all risk strata and explicitly represents the shipment population. The organization also learns whether risk is concentrated within suppliers, between suppliers, or across product families. If nonresponse is concentrated among high-risk suppliers, the report presents sensitivity analyses rather than hiding the issue behind a single overall rate.

Learning points

The case illustrates that sampling design is a decision architecture. Oversampling is not automatically bias; it becomes bias when unequal probabilities are ignored. Clustered observations are not equivalent to independent observations. Finally, measurement, frame, and response controls are as important as the random selection itself.

12. Ethical, governance, and contemporary issues

Sampling plans should minimize unnecessary burden, protect confidentiality, and define who may access identifiable records. Quality data can affect supplier contracts, employee evaluation, customer treatment, or regulatory reporting; therefore, data governance should specify purpose limitation, retention, access controls, and correction procedures. Sensitive populations require additional safeguards and, where applicable, institutional or regulatory review.

Digital platforms and AI can improve frame maintenance, contact scheduling, anomaly detection, and adaptive allocation. They can also amplify historical exclusions. A machine-learning model trained on past response patterns may systematically deprioritize hard-to-reach groups. Automated selection should therefore preserve auditable inclusion probabilities, permit human review, monitor subgroup coverage, and document model versions. Predictive convenience is not a substitute for probability sampling when population inference is required.

Adaptive and responsive designs can alter sample allocation during fieldwork using observed response or quality signals. Such designs may be efficient, but the adaptation rules must be specified, recorded, and incorporated into inclusion probabilities and variance estimation. Otherwise, the final estimates may be difficult to interpret.

Challenges and limitations

No sampling design dominates in every setting. SRS may be expensive; systematic sampling may fail under periodicity; stratification depends on accurate auxiliary information; cluster sampling sacrifices precision for logistics; and multistage designs require sophisticated weighting and variance estimation. Probability sampling also cannot guarantee accurate conclusions when the construct is poorly defined or measurements are unreliable.

A further limitation is that sampling error is often easier to quantify than nonsampling error. Organizations may report a narrow confidence interval while overlooking severe undercoverage or systematic misclassification. Professional reporting should therefore distinguish statistical precision from overall data quality and should disclose design effects, response rates, frame limitations, weighting, and sensitivity analyses.

Best-practice checklist

1. Define the estimand, target population, unit, and reference period.
2. Audit the frame for coverage, duplication, eligibility, and timeliness.
3. Use random selection and preserve an auditable selection record.
4. Stratify when important subgroups require guaranteed representation.
5. Use clusters for logistical efficiency only after assessing intracluster similarity.
6. Document all inclusion probabilities and weights.
7. Establish nonresponse and replacement rules before fieldwork.
8. Validate instruments, inspectors, coding, and data transfers.
9. Use design-appropriate variance estimation.
10. Report limitations and distinguish sampling uncertainty from other errors.

Chapter Summary

Sampling design determines how observations enter a study and therefore how confidently statistics can describe a target population. Simple random sampling gives equal selection probabilities and straightforward inference. Systematic sampling is efficient when a frame is well ordered and free of damaging periodicity. Stratified sampling ensures subgroup coverage and can improve precision, especially when strata are internally homogeneous. Cluster and multistage sampling reduce field cost but introduce dependence and require design-aware variance estimation.

A valid data-generation process extends beyond random selection. Frame coverage, nonresponse, measurement, processing, and confidentiality all influence the credibility of quality evidence. Randomization protects against deliberate selection preferences but does not repair a deficient frame or biased measurement. Representativeness should be assessed through the design, auxiliary information, response patterns, and sensitivity analysis rather than demographic resemblance alone. In TQM, defensible sampling is a governance capability: it connects operational decisions to evidence whose limitations are understood and openly reported.

Key Terms

Target population: The complete set of units about which conclusions are intended.

Sampling frame: The operational list or procedure from which units are selected.

Sampling unit: The unit selected at a particular stage of sampling.

Element: The unit on which the final measurement is made.

Parameter: A numerical characteristic of a population.

Statistic: A numerical quantity calculated from sample data.

Inclusion probability: The probability that a specified population unit enters the sample.

Simple random sampling: Selection in which every sample of a specified size has equal probability.

Systematic sampling: Selection of units at a regular interval after a random start.

Stratified sampling: Sampling separately within defined, non-overlapping population groups.

Cluster sampling: Sampling groups of elements rather than only individual elements.

Multistage sampling: Sampling through two or more successive selection stages.

Finite population correction: The variance adjustment for sampling without replacement from a finite population.

Design effect: The ratio of variance under a complex design to variance under a comparable independent design.

Coverage error: Error caused by mismatch between the target population and sampling frame.

Nonresponse bias: Bias arising when responding and nonresponding units differ in relevant ways.

Measurement error: Difference between a recorded value and the intended construct or true value.

Weight: A factor used to reflect unequal selection or response probabilities.

Representativeness: The extent to which the design and data support valid population inference.

Randomization: Use of a chance mechanism to determine selection or allocation.

Review Questions

Short Answer Questions

1. Distinguish a target population from a sampling frame.
2. Why is a random start necessary in systematic sampling?
3. State one major difference between stratified and cluster sampling.
4. What does the finite population correction represent?
5. Why can increasing sample size fail to correct measurement bias?

Long Answer Questions

1. Explain the design, assumptions, strengths, and limitations of simple random sampling.
2. Compare proportional and disproportionate allocation in stratified sampling, including the role of weights.
3. Explain how intracluster correlation affects the efficiency of cluster samples.
4. Describe a complete data-generation process for a customer-satisfaction study and identify potential errors at each stage.
5. Discuss why randomization supports population inference but does not by itself establish causal effects.

Analytical / Application Questions

1. A hospital wants to estimate patient waiting time across emergency, outpatient, and diagnostic departments. Propose a sampling design, justify the allocation, and specify how you would address clustering and nonresponse.
2. A factory samples every 20th item from a production line, but the line changes tooling every 20 items. Diagnose the problem and propose a revised design.
3. A supplier survey oversamples high-risk suppliers and reports an unweighted overall defect rate. Explain the inferential problem and describe the information needed to produce a defensible weighted estimate.

Multiple Choice Questions with Answers

Question 1

Which feature defines a simple random sample without replacement?

A. Every population unit is selected with certainty

B. Every sample of the specified size has equal probability of selection

C. Units are selected at fixed time intervals without a random start

D. Only the largest clusters are selected

Correct Answer: B. Every sample of the specified size has equal probability of selection

Question 2

A frame contains 1,000 units and a systematic sample of 100 is required. What is the nominal sampling interval?

A. 5

B. 10

C. 50

D. 100

Correct Answer: B. 10

Question 3

Which design is most appropriate when small, high-risk subgroups must be guaranteed representation?

A. Stratified sampling

B. Unrestricted convenience sampling

C. One-stage cluster sampling only

D. Voluntary response sampling

Correct Answer: A. Stratified sampling

Question 4

If the average cluster size is 8 and the intracluster correlation coefficient is 0.25, the approximate design effect is:

A. 1.25

B. 2.00

C. 2.75

D. 8.25

Correct Answer: C. 2.75

Question 5

In stratified estimation, why are population stratum weights used?

A. To remove all measurement error

B. To reflect each stratum’s share of the target population

C. To make every stratum sample size equal

D. To eliminate the need for a sampling frame

Correct Answer: B. To reflect each stratum’s share of the target population

Question 6

Which problem occurs when eligible units are missing from the sampling frame?

A. Undercoverage

B. Intracluster correlation

C. Finite population correction

D. Randomization

Correct Answer: A. Undercoverage

Question 7

For a measured value represented by Y* = Y + E, what does E denote?

A. The population size

B. The sampling fraction

C. Measurement error

D. The design weight

Correct Answer: C. Measurement error

Question 8

A survey samples only volunteers who choose to respond to an online invitation. The principal concern is:

A. Voluntary-response selection bias

B. Finite population correction

C. Perfect representativeness

D. Guaranteed equal inclusion probabilities

Correct Answer: A. Voluntary-response selection bias

Question 9

In a multistage design, when applicable, the final inclusion probability is obtained by:

A. Adding all stage probabilities

B. Multiplying the conditional probabilities across stages

C. Using only the probability at the final stage

D. Ignoring cluster selection probabilities

Correct Answer: B. Multiplying the conditional probabilities across stages

Question 10

If an independent-observation requirement is 200 and the estimated design effect is 2.5, the approximate clustered sample size needed is:

A. 80

B. 200

C. 400

D. 500

Correct Answer: D. 500