Evaluation, Usability and AccessibilityIntroductionA visualization is not successful merely because it is attractive, technically sophisticated, or based on accurate data. Its quality must be judged by whether intended users can understand it, interact with it, and use it to make appropriate decisions. Evaluation therefore forms a central part of the visualization lifecycle. It connects design intentions with observed user behaviour and provides evidence for iterative improvement. Evaluation in data visualization includes several related but distinct concerns. Effectiveness asks whether a visualization communicates the intended information accurately and supports the required analytical task. Usability asks whether users can accomplish their goals efficiently, effectively, and satisfactorily. Accessibility asks whether people with diverse sensory, cognitive, motor, linguistic, and technological abilities can perceive and operate the visualization. A visualization may perform well in one dimension and poorly in another: a chart can be analytically accurate but inaccessible to colour-blind users, or accessible in principle but too complex to use efficiently. At postgraduate level, visualization evaluation should be treated as a methodological problem rather than as a final inspection step. Researchers and practitioners must define evaluation goals, select suitable methods, operationalize quality criteria, collect valid evidence, interpret trade-offs, and translate findings into design decisions. Learning ObjectivesAfter completing this chapter, students should be able to: 1. Distinguish visualization effectiveness, usability, user experience, and accessibility. 2. Select and apply heuristic, empirical, and performance-based evaluation methods. 3. Design visualization user studies and identify threats to validity. 4. Calculate and interpret common usability metrics. 5. Apply accessibility principles and relevant standards to visual analytics systems. 6. Evaluate a visualization critically and propose evidence-based improvements. 7. Discuss ethical, organizational, and governance implications of evaluation. 1. Dimensions of Visualization Quality1.1 EffectivenessEffectiveness concerns the accuracy and appropriateness of the perceptual and cognitive mappings used by a visualization. A visualization is effective when users can correctly identify patterns, compare values, detect exceptions, and form suitable interpretations. Effectiveness depends on at least four factors: - Task fit: whether the representation supports the intended task, such as comparison, ranking, trend detection, distribution analysis, or correlation assessment.
- Perceptual accuracy: whether visual encodings allow users to estimate values and differences reliably.
- Cognitive fit: whether the display aligns with users’ knowledge, expectations, and reasoning strategies.
- Contextual adequacy: whether labels, annotations, units, provenance, and explanatory information are sufficient.
For example, a bar chart generally supports comparison more accurately than a pie chart because position along a common scale is easier to compare than angles or areas. However, a pie chart may be acceptable when showing a small number of clearly distinct parts of a whole and when exact comparison is not required. 1.2 UsabilityUsability is commonly understood through three dimensions: - Effectiveness: the extent to which users achieve specified goals accurately and completely.
- Efficiency: the resources, often time or effort, required to achieve those goals.
- Satisfaction: users’ perceived comfort, confidence, and acceptability.
These dimensions should be assessed for specified users, tasks, and contexts. A dashboard cannot be described as simply “usable” without identifying who uses it, for what purpose, and under what conditions. Usability also includes learnability, memorability, error tolerance, and support for recovery. A system used once by senior executives may require immediate comprehensibility, while a scientific analysis tool used daily by trained analysts may justify a steeper learning curve in exchange for greater analytical power. 1.3 User ExperienceUser experience extends beyond task completion. It includes trust, perceived credibility, emotional response, sense of control, and the quality of interaction over time. In high-stakes domains, trust must not be confused with visual polish. A clean interface may increase confidence without improving the accuracy of decisions. Evaluation should therefore measure actual performance as well as subjective impressions. 1.4 Accessibility and InclusionAccessibility concerns the removal of barriers that prevent people from perceiving information, operating controls, understanding content, or receiving equivalent outcomes. Inclusive design goes further by considering diversity from the beginning rather than retrofitting accommodations later. Relevant users may include people with: - colour-vision deficiency or low vision;
- blindness who rely on screen readers or tactile output;
- motor impairments affecting pointing, dragging, or precision selection;
- hearing impairments when visualization is accompanied by audio;
- cognitive or learning disabilities;
- temporary impairments, such as glare, injury, or noisy surroundings;
- limited bandwidth, old devices, or small screens.
Accessibility is not a niche requirement. It improves clarity for many users, including those viewing dashboards on mobile devices, in poor lighting, or under time pressure. 2. A Framework for EvaluationA rigorous evaluation begins by specifying five elements: 1. Stakeholders: Who will use, interpret, maintain, or be affected by the visualization? 2. Tasks: What decisions or analytical activities must be supported? 3. Claims: What should users be able to conclude from the display? 4. Context: Where, when, and with what technology will use occur? 5. Success criteria: What evidence will demonstrate acceptable performance? A useful evaluation plan combines three levels: 2.1 Representation LevelThis level examines the mapping from data to visual form. Questions include: - Is the chosen chart appropriate for the data type and task?
- Are quantitative differences represented by position, length, angle, area, colour, or another channel?
- Are scales, baselines, transformations, and aggregation methods justified?
- Is uncertainty represented rather than concealed?
2.2 Interaction LevelThis level examines navigation, filtering, selection, zooming, brushing, linking, and annotation. Important questions include whether controls are discoverable, reversible, consistent, and understandable. Interaction should reduce cognitive workload rather than merely add functionality. 2.3 Decision and Organizational LevelAt this level, evaluation considers whether visualization use improves decisions, coordination, or operational outcomes. A dashboard may perform well in a laboratory task but fail in practice because data are delayed, organizational incentives are misaligned, or users do not trust the data source. 3. Heuristic Evaluation and Expert Review3.1 Purpose and ProcedureHeuristic evaluation is a structured inspection performed by one or more evaluators using recognized principles. It is relatively inexpensive and can identify problems before recruiting users. A typical procedure is: 1. Define the user groups, tasks, and evaluation scope. 2. Select or adapt a set of heuristics. 3. Ask evaluators to inspect the visualization independently. 4. Record evidence, location, affected users, and severity. 5. Reconcile findings and prioritize corrective actions. Important heuristics for visualization include: - Visibility of system status: filters, loading states, current selections, and data freshness are visible.
- Match with the real world: terminology, units, and ordering reflect users’ mental models.
- Consistency and standards: similar controls and encodings behave consistently.
- Recognition rather than recall: legends, labels, and instructions are available when needed.
- User control and freedom: users can undo filters, reset views, and recover from errors.
- Error prevention: dangerous interpretations and invalid actions are constrained.
- Minimalism: irrelevant decoration and excessive controls do not compete with the analytical task.
- Help and explanation: complex transformations, uncertainty, and definitions are documented.
3.2 Severity AssessmentSeverity should not be based solely on an evaluator’s personal preference. A practical rating considers: - frequency: how often the problem occurs;
- impact: how strongly it affects task performance or interpretation;
- persistence: whether users can recover easily;
- scope: how many users or tasks are affected.
A missing axis unit in a safety dashboard may be critical even if it appears only once, whereas a minor alignment inconsistency may be low severity despite being visible throughout the interface. 3.3 Strengths and LimitationsExpert review is fast, useful early, and effective at detecting known interaction and communication problems. However, experts may disagree, overlook domain-specific practices, or predict problems that real users do not experience. It should therefore complement, not replace, empirical testing. 4. Empirical User Studies4.1 Formative and Summative EvaluationFormative evaluation occurs during design and aims to discover problems and guide improvement. Small, carefully selected sessions can be highly valuable because they reveal misunderstandings, vocabulary problems, and unexpected strategies. Summative evaluation assesses a relatively mature design against predefined requirements. It often uses larger samples, controlled tasks, comparative designs, or formal success criteria. 4.2 Study DesignsA within-subjects design exposes each participant to multiple visualization conditions. It controls for individual differences but may suffer from learning, fatigue, and order effects. Counterbalancing the order of conditions can reduce these effects. A between-subjects design assigns participants to different conditions. It avoids carryover effects but generally requires more participants and careful matching or randomization. A benchmark task study gives participants standardized questions, such as identifying the highest category or detecting an outlier. It supports quantitative comparison but may simplify real-world analysis. A field study observes use in the natural organizational environment. It provides ecological validity but makes causal interpretation more difficult because many variables cannot be controlled. A think-aloud study asks users to verbalize their reasoning. It helps reveal interpretations and misunderstandings, but verbalization can alter behaviour and may be difficult during complex or time-sensitive tasks. 4.3 Sampling and ValidityParticipants should represent important user characteristics, including domain expertise, visualization literacy, assistive-technology use, and relevant accessibility needs. Convenience samples of university students may be acceptable for early interface inspection but cannot automatically support claims about professional populations. Four forms of validity are especially important: - Construct validity: do the measures represent the intended concept, such as comprehension or trust?
- Internal validity: can observed differences reasonably be attributed to the visualization rather than confounding variables?
- External validity: are findings transferable to other users, tasks, or settings?
- Ecological validity: does the study resemble actual use conditions?
5. Task Performance and Usability Metrics5.1 Task SuccessTask success may be recorded as binary completion, partial completion, or a graded score. A binary success rate is: \[ S = \frac{C}{N} \times 100 \] where \(C\) is the number of successfully completed tasks and \(N\) is the total number attempted. This measure is appropriate when success criteria are clearly defined, but it can conceal important differences in partial understanding or error severity. 5.2 Time on TaskTime on task is usually measured from the point at which the task is presented until the participant gives a final answer or completes the required action. It should be reported with a measure of variation, such as the median and interquartile range, especially when completion times are skewed. Comparisons should use equivalent instructions, data complexity, and stopping rules. 5.3 Error RateErrors may include incorrect answers, invalid interactions, misinterpretations, or failure to notice relevant information. An error rate can be calculated as: \[ E = \frac{I}{A} \] where \(I\) is the number of incorrect or otherwise defined error events and \(A\) is the number of opportunities for error. The denominator must be specified because “error rate” is ambiguous without defining the unit of analysis. 5.4 EfficiencyWhen both accuracy and time matter, one may report successful tasks per unit time: \[ \text{Efficiency} = \frac{C}{T} \] where \(C\) is the number of successful tasks and \(T\) is total task time. This metric is meaningful only when tasks are comparable and when increasing speed does not produce unacceptable loss of accuracy. 5.5 Subjective MeasuresQuestionnaires can measure perceived ease, confidence, workload, and satisfaction. The System Usability Scale (SUS) is a widely used ten-item instrument producing a score from 0 to 100 after a specified scoring procedure. SUS is useful for benchmarking perceived usability, but it does not diagnose particular design problems and should not be treated as a direct percentage of task success. Other instruments may measure workload, trust, or user experience. Researchers must use validated instruments where possible, report administration procedures, and avoid interpreting subjective confidence as evidence of correctness. 5.6 Statistical InterpretationDescriptive statistics should be accompanied by uncertainty and effect-size information where appropriate. Statistical significance alone does not establish practical importance. A small improvement in time may be statistically reliable but operationally irrelevant; conversely, a moderate improvement may matter greatly in a safety-critical workflow even with a small sample. Researchers should predefine primary outcomes, document exclusions, and avoid testing many outcomes selectively. For small or non-normal samples, medians, rank-based methods, bootstrapped intervals, or carefully justified models may be preferable to unexamined assumptions of normality. 6. Evaluating Accessibility6.1 Perceivable InformationInformation should not depend on a single sensory channel. Colour should not be the only indicator of category, status, or severity. Use redundant encodings such as labels, patterns, position, shape, or line style. Text and graphical elements require sufficient contrast against their background, while meaningful differences should remain visible in grayscale and under common forms of colour-vision deficiency. Charts should provide meaningful alternative text or a textual summary. A useful description states the chart type, variables, principal pattern, notable exceptions, and relevant uncertainty. Simply writing “sales chart” is not an equivalent alternative. 6.2 Operable InteractionInteractive visualizations should support keyboard operation where feasible. Focus indicators must be visible, controls should have logical order, and actions requiring precise dragging should have alternatives. Time limits, animation, and rapidly changing displays should be controllable or pausable when they interfere with comprehension. 6.3 Understandable ContentUse plain, consistent terminology; explain abbreviations; provide units and definitions; and make filtering consequences clear. Do not silently change scales, aggregation levels, or data time periods. Error messages should identify the problem and explain how to recover. 6.4 Robust TechnologyA visualization should work with different browsers, screen readers, input devices, zoom levels, and display sizes where the target environment requires it. Semantic structure, accessible names, and programmatically determinable states are important for assistive technologies. The Web Content Accessibility Guidelines (WCAG) organize accessibility around the principles perceivable, operable, understandable, and robust. Conformance levels and success criteria should be considered during requirements analysis, not only during final testing. Accessibility standards provide a baseline; they do not guarantee that a visualization is understandable or useful for every person. 6.5 Accessibility Evaluation MethodsA strong accessibility evaluation combines: - automated checking for detectable structural and contrast problems;
- manual keyboard and focus testing;
- screen-reader testing with representative technologies;
- zoom, reflow, and responsive-layout testing;
- review by users with disabilities;
- task-based assessment of equivalent outcomes.
Automated tools are valuable but limited. They cannot reliably determine whether a chart’s description communicates its analytical message or whether an interaction model is cognitively understandable. 7. A Worked Evaluation ExampleConsider an institutional dashboard showing postgraduate student progression. The dashboard contains a stacked bar chart by department, a line chart of completion rates over time, filters for cohort and demographic group, and a colour-coded warning indicator. The evaluation team defines three tasks: 1. Identify the department with the lowest completion rate in the latest year. 2. Compare completion rates for two cohorts. 3. Determine whether any department exceeds a predefined concern threshold. Twenty participants complete the tasks using the existing dashboard. Across 60 task attempts, 51 are completed correctly. The task-success rate is therefore: \[ S = \frac{51}{60} \times 100 = 85\% \] The study also records 12 interpretation errors. If there are 60 task opportunities, the error rate is: \[ E = \frac{12}{60} = 0.20 = 20\% \] Heuristic review identifies three problems: the warning indicator relies only on red and green, the selected cohort is not sufficiently visible, and the threshold definition is hidden in a tooltip that is unavailable to keyboard users. Interviews reveal that several participants interpret the stacked bars as showing trends rather than composition. The team makes four changes: - adds labels and a non-colour warning symbol;
- provides a persistent filter summary and reset control;
- displays the threshold definition beside the chart;
- replaces the stacked bars with grouped bars for the comparison task.
A second study uses equivalent but different data. Success rises to 56 of 60 attempts, or 93.3%, and interpretation errors fall to 5 of 60, or 8.3%. These results suggest improvement, but they do not prove that every change caused the improvement. Practice, differences in data difficulty, and participant composition must be considered. The correct conclusion is that the revised design provides evidence of better performance under the tested conditions and merits further validation. 8. Illustrative Case Study: Emergency Department Operations DashboardBackgroundThis fictional case concerns an emergency department that uses a dashboard to monitor waiting time, bed occupancy, staffing, and patient flow. The dashboard is viewed by clinicians, administrators, and shift coordinators, often under time pressure. ProblemAlthough the dashboard contains extensive information, staff report inconsistent interpretations. Some users miss a capacity warning because it is displayed only through colour. Others cannot determine whether a sudden change reflects current conditions or delayed data. The organization initially assumes that adding more charts will solve the problem. AnalysisA multidisciplinary evaluation team conducts heuristic review, observation, interviews, and task testing. The team identifies a mismatch between user tasks and dashboard structure. Administrators need weekly trend and resource summaries; shift coordinators need immediate exceptions and operational actions; clinicians need patient-flow context. These groups are forced to use the same dense screen. Testing shows that users can locate values but struggle to answer action-oriented questions such as, “Which unit requires intervention now, and why?” The dashboard also lacks a visible data-refresh timestamp and provides no accessible alternative to the colour-coded status system. Approach and SolutionThe team redesigns the dashboard around decision tasks rather than data categories. The opening view contains a concise status summary, timestamp, and prioritized exceptions. Detailed trend views remain available through navigation. Warnings use colour plus symbols and text. Keyboard-accessible controls, persistent filter states, and explanatory definitions are added. A textual summary is generated for screen-reader users and for incident reports. Evaluation uses simulated shift scenarios and a limited field pilot. Measures include correct identification of the highest-priority issue, time to first appropriate action, explanation accuracy, and perceived workload. The team also monitors whether staff continue to use informal spreadsheets, since workarounds may indicate unresolved usability problems. OutcomeThe pilot shows fewer missed warnings and faster identification of the relevant unit. However, users request clearer uncertainty information because some indicators are based on delayed feeds. The team therefore adds data freshness and confidence annotations rather than presenting all values as equally current and certain. Learning Points1. Evaluation must begin with decisions and tasks, not chart selection. 2. Different user groups may require different views of the same data. 3. Accessibility features can improve use under stress and poor viewing conditions. 4. Trust depends on provenance, freshness, definitions, and honest uncertainty communication. 5. Field outcomes and workarounds may reveal problems that laboratory tests miss. 9. Challenges, Ethics, and GovernanceEvaluation can unintentionally reproduce exclusion. Recruiting only highly educated, technically confident participants may make a design appear more usable than it is. Participants with disabilities should be compensated fairly and should not be treated merely as compliance testers. Data collected during usability studies may include sensitive behaviour, health information, or employment-related judgments; consent, minimization, secure storage, and controlled access are essential. Visualization evaluation also raises questions of fairness. A system may achieve high average accuracy while systematically disadvantaging a particular group. Results should therefore be examined by relevant user characteristics when sample size and privacy allow. Accessibility and fairness should be treated as quality requirements, not optional enhancements. Organizations must govern versioning, data provenance, metric definitions, and changes made in response to evaluation. A dashboard that changes its calculation without recording the change can undermine longitudinal comparisons. In regulated or safety-critical contexts, evaluation evidence, approval responsibilities, and audit trails should be documented. 10. Technology, AI, and Contemporary DevelopmentsModern visualization systems increasingly use AI to recommend charts, summarize trends, detect anomalies, generate natural-language explanations, or adapt interfaces to users. These capabilities can reduce effort, but they introduce risks. An automatically generated chart may choose an inappropriate aggregation, omit uncertainty, or imply causation. A language model may produce a fluent but incorrect summary. AI-assisted visualizations should therefore provide provenance, disclose transformations, expose assumptions, and allow human inspection. Evaluation should test not only whether users complete tasks, but whether automation changes their error patterns, overconfidence, and ability to detect incorrect outputs. Human oversight is especially important in medical, financial, public-sector, and safety-related applications. Other contemporary developments include remote usability testing, interaction logging, eye tracking, multimodal interfaces, responsive visualization, and sonification. These methods can provide useful evidence, but instrumentation must not replace direct engagement with users. Eye movement, clickstream, or biometric data are proxies; they require careful interpretation and raise additional privacy concerns. 11. Best-Practice Evaluation ProcessA practical iterative process is: 1. Define users, decisions, tasks, risks, and accessibility requirements. 2. Inspect the design using heuristics and standards. 3. Test early prototypes with representative users. 4. Combine performance, error, satisfaction, and qualitative evidence. 5. Analyze findings by task and user group, not only by overall average. 6. Prioritize issues according to impact, frequency, risk, and repair cost. 7. Implement changes while preserving a record of design rationale. 8. Retest with equivalent tasks and document remaining limitations. 9. Validate in realistic operational settings. 10. Monitor the deployed visualization for drift, workarounds, and emerging needs. The objective is not to eliminate every possible problem. It is to identify and reduce risks that matter for the intended decisions while maintaining transparency about residual limitations. Chapter SummaryVisualization evaluation determines whether a display supports accurate interpretation, efficient interaction, inclusive access, and appropriate decisions. Effectiveness concerns task and perceptual fit; usability concerns effectiveness, efficiency, and satisfaction; accessibility concerns equivalent access for people with diverse abilities and technologies. Heuristic evaluation offers rapid expert inspection, while user studies provide behavioural evidence. Formative studies guide design improvement, and summative studies assess mature systems against requirements. Important measures include task success, time, errors, efficiency, workload, satisfaction, and confidence. Metrics must be operationally defined and interpreted with attention to validity, practical significance, and uncertainty. Accessibility requires perceivable, operable, understandable, and robust content. Automated tools are useful but cannot replace manual testing and participation by users with disabilities. Ethical evaluation requires representative recruitment, privacy protection, fairness analysis, and responsible governance. AI-assisted visualization demands additional scrutiny of provenance, uncertainty, automation bias, and human oversight. The strongest practice is iterative: define tasks, inspect, test, redesign, retest, and monitor in the field. Key TermsHeuristic evaluation: Expert inspection of a system against recognized usability principles. Effectiveness: Accuracy and appropriateness with which a visualization supports intended tasks. Usability: The effectiveness, efficiency, and satisfaction of specified users in a specified context. Accessibility: The extent to which people with diverse abilities can perceive, operate, understand, and use a system. Formative evaluation: Evaluation conducted to discover problems and improve a design during development. Summative evaluation: Evaluation used to judge a mature design against defined requirements. Task success: The extent to which users complete a specified task correctly. Time on task: The elapsed time required to complete a defined task. Error rate: The proportion of defined error events relative to opportunities for error. Efficiency: A relationship between successful performance and resources such as time. Ecological validity: The degree to which study conditions resemble real-world use. Construct validity: The degree to which a measure represents the intended concept. Cognitive workload: The mental effort required to perform a task. Redundant encoding: Representing information through more than one visual or sensory channel. Alternative text: A textual representation of meaningful visual content. WCAG: Web Content Accessibility Guidelines for accessible web content and applications. Data provenance: Information about the origin, transformation, and freshness of data. Counterbalancing: Varying condition order to reduce learning and order effects. Inclusive design: Designing for diverse users from the beginning of the process. Automation bias: The tendency to over-trust or over-rely on automated recommendations. Review QuestionsShort Answer Questions1. Distinguish visualization effectiveness from usability. 2. What is the purpose of heuristic evaluation? 3. Why should colour not be the only encoding for an important status? 4. Define formative evaluation and state when it is most useful. 5. What are the four organizing principles of WCAG? Long Answer Questions1. Explain how a postgraduate researcher could design a rigorous visualization user study, including sampling, task design, measures, and threats to validity. 2. Compare heuristic evaluation, benchmark task studies, field studies, and think-aloud studies. Discuss the strengths and limitations of each. 3. Explain how accessibility should be evaluated in an interactive visualization, covering automated, manual, and user-based methods. 4. Discuss the role of task success, time, errors, efficiency, and subjective measures in assessing visualization usability. 5. Analyze the ethical and governance issues involved in evaluating an AI-assisted visualization system. Analytical / Application Questions1. A dashboard has a 90% task-success rate but users frequently misinterpret uncertainty indicators. Should it be considered usable? Justify your answer and propose an evaluation plan. 2. Design an evaluation study for a public-health dashboard used by analysts, policymakers, and members of the public. Specify tasks, participants, metrics, accessibility tests, and decision criteria. 3. A visualization uses red and green alone to indicate risk and requires drag-and-drop filtering. Identify the likely accessibility barriers and propose a revised interaction and encoding strategy. Multiple Choice Questions with AnswersQuestion 1Which evaluation dimension primarily concerns whether users can complete intended tasks accurately and efficiently? A. Usability B. Data provenance C. Colour harmony D. Rendering performance Correct Answer: A. Usability Question 2What is the main purpose of formative evaluation? A. To certify regulatory compliance only B. To discover problems and guide design improvement C. To replace all user testing D. To measure server capacity Correct Answer: B. To discover problems and guide design improvement Question 3A study records 45 successful tasks out of 50 attempts. What is the task-success rate? A. 5% B. 45% C. 90% D. 95% Correct Answer: C. 90% Question 4Which design most directly reduces dependence on colour alone? A. Using a larger title B. Adding symbols and text labels C. Removing the legend D. Reducing chart dimensions Correct Answer: B. Adding symbols and text labels Question 5Which issue is most characteristic of a within-subjects study? A. It cannot measure task time B. It requires no participants C. Learning and order effects may occur D. It prevents comparison between conditions Correct Answer: C. Learning and order effects may occur Question 6What does ecological validity refer to? A. Whether study conditions resemble real-world use B. Whether a chart uses ecological data C. Whether participants are experts D. Whether a result is statistically significant Correct Answer: A. Whether study conditions resemble real-world use Question 7Which WCAG principle concerns keyboard operation and interaction controls? A. Perceivable B. Operable C. Understandable D. Robust Correct Answer: B. Operable Question 8Why is an automated accessibility checker insufficient by itself? A. It cannot detect any contrast problems B. It cannot determine whether analytical meaning is understandable C. It always requires a laboratory D. It measures only task completion time Correct Answer: B. It cannot determine whether analytical meaning is understandable Question 9If 12 errors occur across 60 defined task opportunities, what is the error rate? A. 5% B. 12% C. 20% D. 72% Correct Answer: C. 20% Question 10What is a major risk of AI-generated visualization summaries? A. They always require printed charts B. They may produce fluent but incorrect interpretations C. They eliminate the need for data provenance D. They cannot display quantitative data Correct Answer: B. They may produce fluent but incorrect interpretations
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