Applied Statistics & Data Analytics

Chapter 2
Data, Measurement, Sampling, and Quality

Doctorate in Business Administration
Applied Statistics & Data Analytics   •   Doctorate

2. Data, Measurement, Sampling, and Quality

Introduction: Why Data Quality Is a Research Problem

Applied statistics begins before statistical analysis. It begins with decisions about what will be observed, how observations will be represented, whose experiences will be included, and whether the resulting evidence is sufficiently trustworthy for the intended decision. A sophisticated model fitted to poorly defined, biased, or unreliable data can produce precise-looking but invalid conclusions. For doctoral researchers and senior managers, data quality is therefore not a technical afterthought; it is part of research design, organizational governance, and managerial judgment.

Business data are generated through many processes: customer transactions, employee surveys, accounting systems, operational sensors, social-media interactions, experiments, interviews, and administrative records. Each source reflects a particular purpose, population, measurement procedure, time period, and institutional context. Data must consequently be evaluated not only for statistical properties but also for provenance, meaning, relevance, and fitness for use.

This chapter develops an integrated framework for evaluating data, measurement, sampling, and quality. It explains data types and measurement scales; distinguishes reliability from validity; examines probability and non-probability sampling; introduces sample-size determination; and addresses selection bias, missing data, outliers, and data provenance. The chapter also considers ethical and technological issues, including automated data collection, algorithmic measurement, and the use of artificial intelligence in data preparation.

Learning Objectives

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

1. Distinguish major data types and measurement scales and select appropriate summaries and analytical methods.

2. Evaluate operational definitions using the concepts of reliability, validity, and measurement error.

3. Compare probability and non-probability sampling designs and assess their implications for inference.

4. Determine sample-size requirements using statistical, substantive, and operational considerations.

5. Diagnose selection bias, missing-data mechanisms, and influential outliers.

6. Document data provenance and judge whether a dataset is fit for a specific research or managerial purpose.

7. Design defensible data-quality procedures that address ethical, governance, technological, and organizational risks.

From Organizational Phenomena to Analyzable Data

A construct is an abstract concept of theoretical or managerial interest, such as organizational commitment, service quality, innovation capability, or perceived fairness. A variable is a measurable representation of a construct or characteristic. An observation is a value recorded for a particular unit, such as a customer, employee, firm, transaction, or country. The unit of analysis identifies the entity about which a conclusion is drawn. Confusing the unit of observation with the unit of analysis creates serious errors. For example, a study may record individual employees but make claims about organizations; such claims require an appropriate multilevel design and cannot be justified merely by aggregating individual records.

An operational definition specifies how a construct will be observed or measured. Consider employee engagement. It might be operationalized through a validated questionnaire, absenteeism records, voluntary turnover, participation in discretionary projects, or a combination of indicators. These operationalizations are not interchangeable. Each captures a different aspect of the construct and embeds assumptions about what engagement means.

Data may be classified according to several dimensions. Qualitative data consist of words, images, narratives, or symbolic material, although qualitative information can later be coded numerically. Quantitative data are represented numerically and are suitable for mathematical operations, subject to the meaning of their scale. Primary data are collected for the current investigation; secondary data were originally collected for another purpose, even if they are highly useful for the present study. Cross-sectional data describe units at one point or period, whereas longitudinal data follow units over time. Panel data repeatedly observe the same units; repeated cross-sectional data observe different samples from the same population at multiple times.

A second important distinction concerns discrete and continuous variables. Discrete variables take separate countable values, such as number of complaints. Continuous variables can, in principle, take values within an interval, such as delivery time or temperature. A variable recorded as a whole number may still represent an underlying continuous phenomenon if rounding has occurred. Binary variables have two categories, although the categories may be coded as zero and one without implying that the variable has the mathematical properties of a continuous measure.

Measurement Scales and the Meaning of Numbers

Measurement scales determine which transformations and comparisons are meaningful. Four conventional levels are especially useful.

Nominal measurement assigns observations to categories without an inherent order. Examples include industry sector, payment method, and country. Numbers used for nominal categories are labels, not quantities. A mean of payment-method codes has no substantive interpretation; frequencies, proportions, and the mode are appropriate summaries.

Ordinal measurement places categories in an order, but the distances between categories are not known to be equal. Examples include agreement categories, job grade, and service ratings such as poor, satisfactory, good, and excellent. Medians, percentiles, rank-based methods, and frequency distributions are generally defensible. Treating ordinal responses as interval-level scores may be acceptable in some survey applications when justified by the scale design and analytical purpose, but it is not automatically correct.

Interval measurement has ordered values with equal intervals but no meaningful absolute zero. Temperature measured in Celsius and many psychometric scale scores are commonly treated as interval measures. Differences are interpretable, but ratios are not: 20 degrees Celsius is not twice as warm as 10 degrees Celsius.

Ratio measurement has equal intervals and a meaningful zero, allowing meaningful ratios. Revenue, production volume, elapsed time, and distance are examples. Addition, subtraction, multiplication, and division are meaningful when the measurement process supports them.

The scale classification is a guide, not a substitute for substantive reasoning. A financial ratio may be mathematically numeric but conceptually unstable if its denominator is near zero. A survey index may be constructed from ordinal items yet behave approximately as an interval measure when several well-designed items are combined. Researchers should state their assumptions and test whether conclusions are robust to alternative treatments.

Measurement error may be random or systematic. Random error produces inconsistent deviations and generally reduces precision. Systematic error shifts observations in a particular direction, as when respondents underreport undesirable behavior or a sensor is consistently miscalibrated. Classical measurement theory often represents an observed score as the sum of a true score and error, but the “true score” is theoretical and depends on the construct and measurement context. In applied research, the more useful question is whether the measurement supports the intended inference.

Reliability, Validity, and the Logic of Measurement Quality

Reliability concerns consistency. A reliable instrument produces relatively stable or internally coherent results under conditions in which the underlying construct has not changed. Test–retest reliability examines stability over time. Inter-rater reliability examines agreement among coders or assessors. Internal consistency examines whether items intended to measure the same construct are related. Cronbach’s alpha is widely reported, but it depends on assumptions such as tau-equivalence and can be inflated by adding redundant items. Omega coefficients may provide a more flexible estimate in some settings. Reliability is necessary for many forms of inference, but it is not sufficient: a consistently inaccurate measure can be highly reliable.

Validity concerns the defensibility of interpretations and uses of scores. Content validity asks whether the measure adequately represents the construct domain. Construct validity examines whether the measure behaves as theory predicts, including convergent and discriminant evidence. Criterion-related validity considers association with a relevant criterion, either concurrently or prospectively. Internal validity concerns whether a study supports a causal interpretation, whereas external validity concerns transferability or generalizability to other settings and populations. These forms of validity should not be treated as a single certificate attached permanently to an instrument; validity is an evidence-based argument for a particular interpretation, population, and use.

A useful framework is the total survey error perspective, which recognizes that error may arise from coverage, sampling, nonresponse, measurement, processing, and adjustment. A study can have a large sample and still be weak if the questionnaire induces socially desirable answers, the sampling frame excludes important groups, or data-processing rules alter responses. Similarly, validity threats in administrative data may arise because the recorded variable is a proxy for the managerial concept of interest.

Researchers should pilot instruments and procedures before full deployment. Cognitive interviewing can reveal how respondents interpret questions. A pilot can identify ambiguous wording, excessive burden, response-order effects, missing response options, and failures in digital interfaces. Translation and back-translation may be necessary in multinational research, although literal translation alone does not ensure conceptual equivalence.

Sampling as a Basis for Inference

The target population is the complete set of units about which the researcher wishes to draw conclusions. The sampling frame is the operational list or mechanism from which the sample is selected. The frame may omit eligible units, include ineligible units, or contain duplicates. The sample is the subset actually observed. A parameter describes the target population; a statistic describes the sample and is used to estimate the parameter.

Probability sampling gives each eligible unit a known, non-zero probability of selection. In simple random sampling, units are selected from a complete frame using a random mechanism. Stratified sampling divides the population into relevant strata and samples within each stratum. Stratification can improve precision and ensure representation of important subgroups, particularly when strata differ substantially. Cluster sampling selects groups such as branches, schools, or regions and then observes units within selected clusters. It may reduce cost but usually increases sampling variance because units within a cluster tend to resemble one another. Multistage sampling combines these procedures, for example selecting regions, then firms, then employees.

Systematic sampling selects every kth unit after a random start. It is efficient but can be biased if the frame has periodic ordering that coincides with the sampling interval. Disproportionate designs intentionally oversample small or strategically important groups; analysis then requires appropriate weights if population-representative estimates are desired.

Non-probability methods include convenience, purposive, quota, respondent-driven, and snowball sampling. They may be appropriate for exploratory research, hard-to-reach populations, qualitative inquiry, or situations lacking a usable frame. Their limitation is not simply that they are “small.” The central problem is that selection probabilities are unknown, making sampling-error estimation and design-based generalization difficult. Large online panels can still yield biased estimates if participation is related to the outcome or if coverage is incomplete.

Sampling error is the random discrepancy between a sample estimate and the population parameter that arises because only part of the population is observed. Nonsampling errors include coverage error, nonresponse, measurement error, processing error, and specification error. Increasing sample size reduces some random sampling error but does not automatically correct systematic errors.

Sample Size: Statistical Power and Practical Judgment

Sample size should be determined before data collection whenever possible. For estimating a population proportion under simple random sampling, a commonly used approximate formula is:

n = z²p(1 − p) / e²,

where z is the critical value for the desired confidence level, p is the anticipated proportion, and e is the tolerated margin of error. When p is unknown, 0.5 produces the largest required sample under this formula. For a finite population, a finite-population correction may reduce the required size when the sample is a substantial fraction of the population.

For hypothesis testing and regression, sample size depends on the expected effect size, variability, significance level, desired power, number of predictors, dependence among observations, and design features such as clustering. A statistically significant result is not necessarily practically important, and a small but meaningful effect may require a large sample. Power analysis should therefore be linked to substantive consequences, not used mechanically.

Attrition, nonresponse, subgroup analysis, and missing data must be considered. If a longitudinal study expects 20 percent attrition, the recruitment target must exceed the final analyzable sample. Cluster designs require a design effect, often approximated as 1 + (m − 1)ρ, where m is the average cluster size and ρ is the intraclass correlation. The effective sample size may be much smaller than the nominal number of observations.

Doctoral research should distinguish precision-based sample-size justification from convenience-based claims. When probability sampling is absent, a formula for a random sample’s margin of error does not magically establish representativeness. In such cases, researchers should emphasize the sampling mechanism, target population, inclusion criteria, expected heterogeneity, and sensitivity analyses.

Selection Bias, Missing Data, and Outliers

Selection bias occurs when inclusion in the observed dataset is related to characteristics that affect the outcome or the relationship being studied. It can arise through exclusion from the frame, refusal to participate, attrition, self-selection into treatment, or platform-specific participation. For example, a customer-satisfaction survey sent only by email excludes customers with no recorded email address and may overrepresent highly engaged customers.

A useful diagnostic is to compare respondents and nonrespondents on available characteristics, examine participation patterns across subgroups, and model response propensity where appropriate. Weighting, calibration, follow-up contacts, and sensitivity analysis may reduce or reveal bias, but no adjustment can recover information that was never measured without assumptions. Researchers should report the likely direction and implications of selection bias rather than merely stating a response rate.

Missing data are commonly classified as missing completely at random (MCAR), missing at random (MAR), or missing not at random (MNAR). MCAR means missingness is unrelated to observed and unobserved values. MAR means missingness can be explained by observed information conditional on the variables included in the model. MNAR means missingness depends on unobserved values even after conditioning on observed data. These are assumptions about a missingness mechanism, not properties that can usually be proven from the observed dataset alone.

Listwise deletion is simple but can reduce power and introduce bias. Single imputation, such as replacing values with a mean, understates uncertainty and distorts relationships. Multiple imputation creates several plausible completed datasets, analyzes each, and combines results while reflecting imputation uncertainty. In longitudinal or causal studies, model-based approaches and sensitivity analyses may be more appropriate. The method must be aligned with the data-generating process and the estimand.

Outliers are observations that differ markedly from the general pattern. A univariate outlier is unusual on one variable; a multivariate outlier is unusual in a combination of variables; an influential observation changes model estimates substantially. Outliers may be data-entry errors, valid extreme cases, members of a different population, or evidence of a nonlinear or heterogeneous process. Blind deletion is inappropriate. Researchers should verify the record, assess substantive plausibility, compare robust and conventional analyses, and document any exclusion rule established before examining results.

Data Provenance and Fitness for Use

Data provenance is the documented history of data: where they originated, how they were collected, transformed, merged, stored, and accessed. A provenance record should identify the source organization, collection dates, population and frame, definitions, instruments, coding schemes, versions, transformations, linkage keys, quality checks, and responsible personnel. A data dictionary should define variables, units, permitted values, missing-value codes, and derivation rules.

Fitness for use is purpose-dependent. A dataset may be adequate for monitoring broad trends but unsuitable for estimating causal effects. Six dimensions are particularly useful: accuracy, completeness, consistency, timeliness, uniqueness, and validity. Additional dimensions include accessibility, interpretability, security, and representativeness. Data quality is therefore not an intrinsic label. It is a relationship between data characteristics and a proposed decision or inference.

A practical data-quality workflow begins by specifying the intended use and estimand. The researcher then audits the source and frame, inspects structure and distributions, checks duplicates and referential integrity, verifies units and coding, examines missingness and outliers, compares records with external benchmarks where possible, and preserves a reproducible audit trail. Transformations should be scripted rather than performed invisibly in spreadsheets. Version control and immutable raw-data storage help distinguish original observations from processed analytical files.

Illustrative Case: Evaluating a Customer Retention Dataset

Background

A fictional subscription-based software company, Northstar Systems, wants to identify factors associated with customer cancellation. The analytics team receives a dataset containing 48,000 customer records, monthly invoices, product-usage logs, support tickets, contract information, and a binary cancellation indicator.

Situation and Problem

An initial dashboard reports that customers using the mobile application are 30 percent less likely to cancel. Senior managers propose shifting development resources toward mobile features. A doctoral researcher is asked to evaluate whether the dataset supports this conclusion.

Analysis

The researcher first defines the population and estimand. The intended population is all active business customers during the study period, while the dataset includes only customers with at least one successful invoice and a valid email address. Customers who never completed payment and accounts managed through resellers are absent from the frame. This creates possible coverage and selection problems.

The unit of analysis is the customer-month, but the initial regression treats all 48,000 records as independent customers. A check reveals repeated observations for many customers, requiring a longitudinal or clustered approach. Mobile-app use is measured from logged sessions. Customers with limited technical integration may have unrecorded usage, and the logging system changed halfway through the period. Thus, apparent non-use may partly represent measurement error.

Cancellation is also not uniformly defined. Monthly customers are coded as cancelled after one missed renewal, while annual customers are coded only after contract expiration. The outcome therefore combines different exposure periods and business rules. The researcher constructs a consistent time-to-event definition and documents the change.

Missingness is concentrated among small firms and reseller accounts. Rather than imputing all missing usage as zero, the researcher distinguishes genuine zero use from unavailable logging data. Extreme usage values are checked against raw logs; several are duplicated event records and are corrected, while a small number represent legitimate high-volume clients.

Approach and Solution

The team creates a provenance register, separates raw and processed data, reconciles customer identifiers across billing and product systems, and performs a sensitivity analysis using alternative definitions of mobile use and cancellation. It models cancellation with clustered standard errors and controls for contract type, tenure, firm size, support burden, and acquisition channel. Because the dataset is observational, the analysis is framed as association rather than proof that mobile use causes retention.

Outcome

The mobile-use association becomes smaller after accounting for contract type and customer tenure. It remains positive but is not sufficient to justify a major causal investment by itself. The analysis instead suggests that mobile use is partly a marker of customer maturity and product integration. Management commissions a targeted experiment involving selected mobile enhancements and pre-specifies retention outcomes.

Learning Points

The case illustrates that data quality involves definitions, coverage, dependence, missingness, measurement systems, and provenance. The apparent analytical result was not necessarily false, but its managerial interpretation was too strong. Quality assessment changed the decision from an unsupported resource shift to a testable intervention.

Ethical, Governance, and Technological Considerations

Data collection and analysis must respect informed consent, privacy, confidentiality, contractual restrictions, and applicable data-protection law. De-identification reduces risk but does not guarantee anonymity, especially when records can be linked with external sources. Researchers should collect only data necessary for the stated purpose, restrict access, protect credentials, define retention periods, and assess whether secondary use is ethically and legally permissible.

Fairness is a data-quality issue as well as an ethical issue. If historical decisions reflect discrimination or if some groups are systematically underrepresented, predictive models may reproduce inequity. A model can be statistically accurate overall while performing poorly for a protected or vulnerable subgroup. Audits should examine coverage, error rates, missingness, and outcomes across relevant groups.

Digital platforms and artificial-intelligence tools can automate validation, anomaly detection, entity resolution, coding, and imputation. They can also introduce opaque transformations, hallucinated values, feedback loops, and automation bias. AI-generated classifications should be treated as provisional measurements requiring human review, documented prompts or model versions, and appropriate validation. Automated anomaly detection should flag records for investigation rather than delete them without substantive examination.

Emerging practice is moving toward machine-readable metadata, data catalogs, lineage graphs, privacy-preserving record linkage, synthetic data for controlled development, and reproducible analytical pipelines. These technologies improve governance only when organizational responsibilities are clear. A lineage graph cannot compensate for an undefined construct, and synthetic data cannot automatically preserve the validity of rare subgroups or causal relationships.

Common Errors and Best Practices

Frequent mistakes include treating coded categories as quantitative measurements, assuming reliability proves validity, using a large convenience sample as evidence of representativeness, applying random-sampling margins of error to non-probability samples, deleting missing cases without examining mechanisms, removing outliers solely because they weaken a result, and reporting a predictive association as a causal effect.

Good practice is to:

  • define the population, unit of analysis, construct, and estimand before collecting or analyzing data;
  • document the frame, selection mechanism, inclusion criteria, and expected sources of bias;
  • use measurement instruments with evidence appropriate to the intended population and context;
  • justify sample size using effect size, precision, power, design effect, attrition, and substantive importance;
  • distinguish genuine zeros, not-applicable values, unknown values, and system failures;
  • investigate unusual observations before deciding how to handle them;
  • preserve raw data, record every transformation, and use reproducible scripts;
  • report limitations and sensitivity analyses transparently; and
  • match the strength of managerial recommendations to the strength of the evidence.

Chapter Summary

Data quality begins with conceptual clarity. Researchers must distinguish constructs, variables, observations, units of analysis, populations, and frames. Data types and measurement scales determine which summaries and transformations are meaningful. Reliability concerns consistency, whereas validity concerns the defensibility of interpretations and uses; neither should be assessed in isolation from context.

Sampling design determines the basis for generalization. Probability sampling permits design-based inference when implemented properly, while non-probability sampling may be useful but requires cautious claims. Sample size depends on precision, power, effect size, design structure, attrition, and practical purpose. Selection bias, missing data, and outliers must be diagnosed as features of the data-generating process rather than treated as routine cleaning problems.

Provenance records the history of data and supports reproducibility, accountability, and governance. Fitness for use is purpose-dependent: a dataset suitable for description may be unsuitable for causal inference. Ethical and technological safeguards are essential as organizations increasingly combine administrative systems, digital traces, automation, and AI. The central professional principle is simple: the credibility of an analytical conclusion cannot exceed the quality and appropriateness of the evidence on which it rests.

Key Terms

Construct: An abstract concept that a study seeks to represent or explain.

Operational definition: A specification of how a construct or variable is observed and measured.

Unit of analysis: The entity about which a research conclusion is made.

Target population: The complete set of units to which the researcher intends to generalize.

Sampling frame: The operational list or mechanism from which a sample is selected.

Parameter: A numerical characteristic of a population.

Statistic: A numerical characteristic calculated from a sample.

Nominal scale: A categorical scale with no inherent order.

Ordinal scale: A ranked scale whose category intervals are not assumed equal.

Interval scale: A scale with equal intervals but no meaningful absolute zero.

Ratio scale: A scale with equal intervals and a meaningful zero.

Reliability: The consistency or stability of a measurement procedure.

Validity: The strength of evidence supporting an interpretation or use of a measure.

Sampling error: Random discrepancy caused by observing a sample rather than the whole population.

Selection bias: Systematic distortion caused by the process determining which units are observed.

Missing-data mechanism: The process that determines why values are absent, such as MCAR, MAR, or MNAR.

Outlier: An observation unusually distant from the pattern of other observations.

Influential observation: An observation whose inclusion materially changes an analytical result.

Data provenance: The documented origin, history, transformation, and custody of data.

Fitness for use: The suitability of data for a specified analytical or managerial purpose.

Review Questions

Short Answer Questions

1. How do the unit of observation and the unit of analysis differ?

2. Why is a meaningful zero important in distinguishing ratio from interval measurement?

3. What is the difference between reliability and validity?

4. Why can increasing sample size fail to correct selection bias?

5. What information should a data-provenance record contain?

Long Answer Questions

1. Explain the four measurement scales and discuss how scale properties influence statistical summaries and analytical choices.

2. Compare simple random, stratified, cluster, and multistage sampling, including their implications for cost, precision, and inference.

3. Discuss how sample size should be justified in a doctoral business study involving statistical power, attrition, clustering, and practical significance.

4. Explain MCAR, MAR, and MNAR missingness and evaluate the strengths and weaknesses of common responses to missing data.

5. Develop an integrated framework for assessing whether a secondary dataset is fit for a managerial decision.

Analytical / Application Questions

1. A firm surveys only customers who contacted its support center and concludes that its entire customer base is dissatisfied. Identify the likely sources of bias and propose a more defensible design.

2. A regression result changes substantially when five extreme observations are removed. Explain the diagnostic steps you would take before deciding whether to retain, transform, or exclude them.

3. A researcher has a customer-month dataset but analyzes it as if each row were an independent customer. Explain the threats to inference and recommend an appropriate analytical strategy.

22. Multiple Choice Questions with Answers

Question 1

A researcher records employees’ job grades as Junior, Intermediate, Senior, and Executive. Which measurement scale is most appropriate?

A. Nominal

B. Ordinal

C. Interval

D. Ratio

Correct Answer: B. Ordinal

Question 2

Which statement best distinguishes reliability from validity?

A. Reliability concerns sample size, while validity concerns population size.

B. Reliability concerns consistency, while validity concerns the defensibility of interpretation and use.

C. Reliability applies only to qualitative data, while validity applies only to quantitative data.

D. Reliability proves that a measure captures the intended construct.

Correct Answer: B. Reliability concerns consistency, while validity concerns the defensibility of interpretation and use.

Question 3

A company samples firms separately within each industry sector to ensure that small sectors are represented. Which design is being used?

A. Cluster sampling

B. Convenience sampling

C. Stratified sampling

D. Systematic sampling

Correct Answer: C. Stratified sampling

Question 4

A large online survey has a very high response count, but participation is voluntary and concentrated among highly engaged customers. What is the main concern?

A. The sample necessarily has excessive statistical power.

B. The data cannot contain missing values.

C. The large size eliminates coverage and selection bias.

D. The estimates may be biased because participation is related to customer engagement.

Correct Answer: D. The estimates may be biased because participation is related to customer engagement.

Question 5

In a cluster sample, individuals within the same branch tend to be similar. What is the likely consequence?

A. The effective sample size may be smaller than the nominal sample size.

B. The sample automatically becomes a simple random sample.

C. Sampling variance must be zero.

D. The measurement scale changes from ordinal to ratio.

Correct Answer: A. The effective sample size may be smaller than the nominal sample size.

Question 6

Which action is most defensible when an extreme observation is discovered in a dataset?

A. Delete it immediately because it may distort the mean.

B. Replace it with the median without documentation.

C. Verify its source and assess its substantive plausibility before deciding how to handle it.

D. Retain it automatically because all observations are equally valid.

Correct Answer: C. Verify its source and assess its substantive plausibility before deciding how to handle it.

Question 7

A survey question is answered less often by respondents with high income, even after observed demographic variables are considered. Which missing-data mechanism may be plausible?

A. Missing completely at random

B. Missing at random only by definition

C. Missing not at random

D. No missing-data mechanism is involved

Correct Answer: C. Missing not at random

Question 8

Which statement about data provenance is most accurate?

A. It records the origin, transformations, and custody of data.

B. It is limited to the date on which a spreadsheet was created.

C. It replaces the need for a data dictionary.

D. It guarantees that a dataset is valid for every purpose.

Correct Answer: A. It records the origin, transformations, and custody of data.

Question 9

Why is applying a conventional random-sample margin-of-error formula to a convenience sample problematic?

A. Convenience samples are always too small for analysis.

B. The formula assumes a known probability-based selection process that may not exist.

C. Margins of error apply only to qualitative research.

D. The formula can be used only when the population is infinite.

Correct Answer: B. The formula assumes a known probability-based selection process that may not exist.

Question 10

A customer-use variable is missing because the logging system failed, but analysts code all such cases as zero use. What is the most serious risk?

A. The variable becomes nominal rather than quantitative.

B. The procedure may confuse unavailable information with genuine non-use and bias the results.

C. The dataset will necessarily become larger.

D. Coding missing values as zero always improves validity.

Correct Answer: B. The procedure may confuse unavailable information with genuine non-use and bias the results.

Applied Statistics & Data Analytics
Chapter 2 of 15