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Search, Evaluate, and Read Evidence","\u002Fen\u002Facademic-writing\u002F02-reading-and-literature-matrix","en\u002Facademic-writing\u002F02-reading-and-literature-matrix",{"title":27,"path":28,"stem":29},"3. From Sources to Synthesis and Argument","\u002Fen\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs","en\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs",{"title":31,"path":32,"stem":33},"4. Literature Review and a Defensible Gap","\u002Fen\u002Facademic-writing\u002F04-writing-the-literature-review","en\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":35,"path":36,"stem":37},"5. Research Design, Evidence, and Core Sections","\u002Fen\u002Facademic-writing\u002F05-core-sections-and-evidence","en\u002Facademic-writing\u002F05-core-sections-and-evidence",{"title":39,"path":40,"stem":41},"6. Citation, Paraphrasing, Integrity, and AI","\u002Fen\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity","en\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity",{"title":43,"path":44,"stem":45},"7. Revision, Review, and Submission","\u002Fen\u002Facademic-writing\u002F07-revision-style-and-submission","en\u002Facademic-writing\u002F07-revision-style-and-submission",{"title":47,"path":48,"stem":49},"8. Research Workbook","\u002Fen\u002Facademic-writing\u002F08-literature-review-checklist-and-template","en\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":51,"path":52,"stem":53},"9. Research Workflow and Tools","\u002Fen\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management","en\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management",{"title":55,"path":56,"stem":57},"10. Worked Project — From Question to Defensible Conclusion","\u002Fen\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain","en\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain",{"title":59,"path":60,"stem":61,"children":62,"page":249},"Accounting","\u002Fen\u002Faccounting","en\u002Faccounting",[63,69,87,93,193],{"title":64,"path":65,"stem":66,"children":67},"Accounting — From Evidence to Decisions","\u002Fen\u002Faccounting\u002F00-index","en\u002Faccounting\u002F00-index",[68],{"title":64,"path":65,"stem":66},{"title":70,"path":71,"stem":72,"children":73},"Accounting Appendix","\u002Fen\u002Faccounting\u002Fappendix","en\u002Faccounting\u002Fappendix\u002Findex",[74,75,79,83],{"title":70,"path":71,"stem":72},{"title":76,"path":77,"stem":78},"Worked Examples and Error Diagnosis","\u002Fen\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls","en\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls",{"title":80,"path":81,"stem":82},"Accounting Glossary","\u002Fen\u002Faccounting\u002Fappendix\u002F26-glossary","en\u002Faccounting\u002Fappendix\u002F26-glossary",{"title":84,"path":85,"stem":86},"Reading and Evidence Map","\u002Fen\u002Faccounting\u002Fappendix\u002F27-reading-map","en\u002Faccounting\u002Fappendix\u002F27-reading-map",{"title":88,"path":89,"stem":90,"children":91},"Northstar Record-to-Decision Capstone","\u002Fen\u002Faccounting\u002Fcapstone","en\u002Faccounting\u002Fcapstone\u002Findex",[92],{"title":88,"path":89,"stem":90},{"title":94,"path":95,"stem":96,"children":97},"Financial Accounting","\u002Fen\u002Faccounting\u002Ffinancial-accounting","en\u002Faccounting\u002Ffinancial-accounting\u002Findex",[98,99,117,131,165,179],{"title":94,"path":95,"stem":96},{"title":100,"path":101,"stem":102,"children":103},"1. Foundations","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002Findex",[104,105,109,113],{"title":100,"path":101,"stem":102},{"title":106,"path":107,"stem":108},"Objectives and Qualitative Characteristics","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics",{"title":110,"path":111,"stem":112},"Equation and Elements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements",{"title":114,"path":115,"stem":116},"Accrual Basis, Estimates and Periods","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles",{"title":118,"path":119,"stem":120,"children":121},"2. Recording Transactions","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002Findex",[122,123,127],{"title":118,"path":119,"stem":120},{"title":124,"path":125,"stem":126},"Double-Entry and Debit\u002FCredit","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr",{"title":128,"path":129,"stem":130},"Accounting Cycle","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle",{"title":132,"path":133,"stem":134,"children":135},"3. Measurement and Adjustments","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002Findex",[136,137,141,145,149,153,157,161],{"title":132,"path":133,"stem":134},{"title":138,"path":139,"stem":140},"Revenue Recognition","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition",{"title":142,"path":143,"stem":144},"Inventory","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory",{"title":146,"path":147,"stem":148},"Receivables and Expected Credit Losses","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables",{"title":150,"path":151,"stem":152},"Property, Plant and Equipment","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe",{"title":154,"path":155,"stem":156},"Intangible Assets","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles",{"title":158,"path":159,"stem":160},"Leases","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases",{"title":162,"path":163,"stem":164},"Current and Deferred Income Tax","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax",{"title":166,"path":167,"stem":168,"children":169},"4. Reporting and Cash","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002Findex",[170,171,175],{"title":166,"path":167,"stem":168},{"title":172,"path":173,"stem":174},"Linked Financial Statements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements",{"title":176,"path":177,"stem":178},"Cash, Reconciliation and Internal Control","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control",{"title":180,"path":181,"stem":182,"children":183},"5. Analysis and Comparison","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002Findex",[184,185,189],{"title":180,"path":181,"stem":182},{"title":186,"path":187,"stem":188},"Ratio Analysis","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis",{"title":190,"path":191,"stem":192},"IFRS versus US GAAP","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap",{"title":194,"path":195,"stem":196,"children":197},"Management Accounting","\u002Fen\u002Faccounting\u002Fmanagement-accounting","en\u002Faccounting\u002Fmanagement-accounting\u002Findex",[198,199,217,235],{"title":194,"path":195,"stem":196},{"title":200,"path":201,"stem":202,"children":203},"1. Cost Foundations","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002Findex",[204,205,209,213],{"title":200,"path":201,"stem":202},{"title":206,"path":207,"stem":208},"Cost Concepts and Behaviour","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts",{"title":210,"path":211,"stem":212},"Costing Systems","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems",{"title":214,"path":215,"stem":216},"Variable and Absorption Costing","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption",{"title":218,"path":219,"stem":220,"children":221},"2. Planning and Control","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002Findex",[222,223,227,231],{"title":218,"path":219,"stem":220},{"title":224,"path":225,"stem":226},"Cost–Volume–Profit Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis",{"title":228,"path":229,"stem":230},"Budgeting and Variance Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances",{"title":232,"path":233,"stem":234},"Performance Measurement","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement",{"title":236,"path":237,"stem":238,"children":239},"3. Decisions and Investment","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002Findex",[240,241,245],{"title":236,"path":237,"stem":238},{"title":242,"path":243,"stem":244},"Short-Term Decisions","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions",{"title":246,"path":247,"stem":248},"Capital Budgeting","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting",false,{"title":251,"path":252,"stem":253,"children":254,"page":249},"Business Analytics","\u002Fen\u002Fbusiness-analytics","en\u002Fbusiness-analytics",[255,261,279,305,335,365,383,400],{"title":256,"path":257,"stem":258,"children":259},"Business Analytics — From Data to Defensible Action","\u002Fen\u002Fbusiness-analytics\u002F00-index","en\u002Fbusiness-analytics\u002F00-index",[260],{"title":256,"path":257,"stem":258},{"title":262,"path":263,"stem":264,"children":265},"0. Decision and Data Foundations","\u002Fen\u002Fbusiness-analytics\u002F00-intro","en\u002Fbusiness-analytics\u002F00-intro\u002Findex",[266,267,271,275],{"title":262,"path":263,"stem":264},{"title":268,"path":269,"stem":270},"Decision Framing","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing","en\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing",{"title":272,"path":273,"stem":274},"Data Contracts","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts","en\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts",{"title":276,"path":277,"stem":278},"Reproducible Analytics Workflow","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow","en\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow",{"title":280,"path":281,"stem":282,"children":283},"1. Descriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive","en\u002Fbusiness-analytics\u002F01-descriptive\u002Findex",[284,285,289,293,297,301],{"title":280,"path":281,"stem":282},{"title":286,"path":287,"stem":288},"Distributions and Exploratory Data Analysis","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda","en\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda",{"title":290,"path":291,"stem":292},"KPIs and Denominators","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators","en\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators",{"title":294,"path":295,"stem":296},"Segments, Cohorts and Funnels","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels","en\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels",{"title":298,"path":299,"stem":300},"Visual Evidence and Data Stories","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story","en\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story",{"title":302,"path":303,"stem":304},"Experiments and Causal Boundaries","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary","en\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary",{"title":306,"path":307,"stem":308,"children":309},"2. Predictive Analytics","\u002Fen\u002Fbusiness-analytics\u002F02-predictive","en\u002Fbusiness-analytics\u002F02-predictive\u002Findex",[310,311,315,319,323,327,331],{"title":306,"path":307,"stem":308},{"title":312,"path":313,"stem":314},"Validation, Baselines and Leakage","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage","en\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage",{"title":316,"path":317,"stem":318},"Regression and Forecasting","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting","en\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting",{"title":320,"path":321,"stem":322},"Classification and Calibration","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration","en\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration",{"title":324,"path":325,"stem":326},"Trees and Ensembles","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles","en\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles",{"title":328,"path":329,"stem":330},"Decision Metrics and Thresholds","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds","en\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds",{"title":332,"path":333,"stem":334},"Explainability, Monitoring and Drift","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift","en\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift",{"title":336,"path":337,"stem":338,"children":339},"3. Prescriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive","en\u002Fbusiness-analytics\u002F03-prescriptive\u002Findex",[340,341,345,349,353,357,361],{"title":336,"path":337,"stem":338},{"title":342,"path":343,"stem":344},"Decision-Making under Uncertainty","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty",{"title":346,"path":347,"stem":348},"Linear Optimisation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization",{"title":350,"path":351,"stem":352},"Inventory and Allocation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation",{"title":354,"path":355,"stem":356},"Queueing and Simulation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation",{"title":358,"path":359,"stem":360},"Pricing and Revenue Management","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation",{"title":362,"path":363,"stem":364},"Causal Targeting and Policy Learning","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting",{"title":366,"path":367,"stem":368,"children":369},"4. Deployment and Governance","\u002Fen\u002Fbusiness-analytics\u002F04-deployment","en\u002Fbusiness-analytics\u002F04-deployment\u002Findex",[370,371,375,379],{"title":366,"path":367,"stem":368},{"title":372,"path":373,"stem":374},"Data Products and Monitoring","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring","en\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring",{"title":376,"path":377,"stem":378},"Governance, Fairness and Privacy","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy","en\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy",{"title":380,"path":381,"stem":382},"Adoption and Business Value","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value","en\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value",{"title":384,"path":385,"stem":386,"children":387},"Appendix and Revision Tools","\u002Fen\u002Fbusiness-analytics\u002Fappendix","en\u002Fbusiness-analytics\u002Fappendix\u002Findex",[388,389,393,397],{"title":384,"path":385,"stem":386},{"title":390,"path":391,"stem":392},"Formula and Decision Map","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map","en\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map",{"title":394,"path":395,"stem":396},"Worked Examples and Pitfalls","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls","en\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls",{"title":84,"path":398,"stem":399},"\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map","en\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map",{"title":401,"path":402,"stem":403,"children":404},"Capstone — The Evening Delivery Promise","\u002Fen\u002Fbusiness-analytics\u002Fcapstone","en\u002Fbusiness-analytics\u002Fcapstone\u002Findex",[405],{"title":401,"path":402,"stem":403},{"title":407,"path":408,"stem":409,"children":410,"page":249},"Financial Economic Time Series","\u002Fen\u002Ffinancial-economic-time-series","en\u002Ffinancial-economic-time-series",[411,417,423,429,435,441,447,453,459,465,471],{"title":412,"path":413,"stem":414,"children":415},"Financial and Economic Time Series — Course Guide","\u002Fen\u002Ffinancial-economic-time-series\u002F00-intro","en\u002Ffinancial-economic-time-series\u002F00-intro\u002Findex",[416],{"title":412,"path":413,"stem":414},{"title":418,"path":419,"stem":420,"children":421},"Three Versions of Time Series","\u002Fen\u002Ffinancial-economic-time-series\u002F01-bridge","en\u002Ffinancial-economic-time-series\u002F01-bridge\u002Findex",[422],{"title":418,"path":419,"stem":420},{"title":424,"path":425,"stem":426,"children":427},"Data, Clocks, and Transformations","\u002Fen\u002Ffinancial-economic-time-series\u002F02-data-transformations","en\u002Ffinancial-economic-time-series\u002F02-data-transformations\u002Findex",[428],{"title":424,"path":425,"stem":426},{"title":430,"path":431,"stem":432,"children":433},"Predictive Regressions and Persistent Predictors","\u002Fen\u002Ffinancial-economic-time-series\u002F03-predictive-regressions","en\u002Ffinancial-economic-time-series\u002F03-predictive-regressions\u002Findex",[434],{"title":430,"path":431,"stem":432},{"title":436,"path":437,"stem":438,"children":439},"Volatility, Tails, and Financial Risk","\u002Fen\u002Ffinancial-economic-time-series\u002F04-volatility-risk","en\u002Ffinancial-economic-time-series\u002F04-volatility-risk\u002Findex",[440],{"title":436,"path":437,"stem":438},{"title":442,"path":443,"stem":444,"children":445},"Unit Roots, Cointegration, and Error Correction","\u002Fen\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration","en\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration\u002Findex",[446],{"title":442,"path":443,"stem":444},{"title":448,"path":449,"stem":450,"children":451},"VAR, Structural Identification, and Local Projections","\u002Fen\u002Ffinancial-economic-time-series\u002F06-var-identification","en\u002Ffinancial-economic-time-series\u002F06-var-identification\u002Findex",[452],{"title":448,"path":449,"stem":450},{"title":454,"path":455,"stem":456,"children":457},"State Space, Mixed Frequency, and Nowcasting","\u002Fen\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting","en\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting\u002Findex",[458],{"title":454,"path":455,"stem":456},{"title":460,"path":461,"stem":462,"children":463},"Forecast Evaluation for Decisions","\u002Fen\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation","en\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation\u002Findex",[464],{"title":460,"path":461,"stem":462},{"title":466,"path":467,"stem":468,"children":469},"Integrated R Laboratory","\u002Fen\u002Ffinancial-economic-time-series\u002F09-r-laboratory","en\u002Ffinancial-economic-time-series\u002F09-r-laboratory\u002Findex",[470],{"title":466,"path":467,"stem":468},{"title":472,"path":473,"stem":474,"children":475},"Capstones, Data, and Reading Ladder","\u002Fen\u002Ffinancial-economic-time-series\u002F10-capstone-readings","en\u002Ffinancial-economic-time-series\u002F10-capstone-readings\u002Findex",[476],{"title":472,"path":473,"stem":474},{"title":478,"path":479,"stem":480,"children":481,"page":249},"Intro To Economics","\u002Fen\u002Fintro-to-economics","en\u002Fintro-to-economics",[482,486,490,494,498,502,506,510,514,518,522,526,530],{"title":483,"path":484,"stem":485},"Introduction to Economics — Decisions, Markets, and the Macroeconomy","\u002Fen\u002Fintro-to-economics\u002F00-intro","en\u002Fintro-to-economics\u002F00-intro",{"title":487,"path":488,"stem":489},"Chapter 1 — Choice, Opportunity Cost, and Trade","\u002Fen\u002Fintro-to-economics\u002F01-foundations","en\u002Fintro-to-economics\u002F01-foundations",{"title":491,"path":492,"stem":493},"Chapter 2 — Demand, Supply, Equilibrium, and Welfare","\u002Fen\u002Fintro-to-economics\u002F02-demand-and-supply","en\u002Fintro-to-economics\u002F02-demand-and-supply",{"title":495,"path":496,"stem":497},"Chapter 3 — Elasticity, Revenue, and Tax Incidence","\u002Fen\u002Fintro-to-economics\u002F03-elasticity","en\u002Fintro-to-economics\u002F03-elasticity",{"title":499,"path":500,"stem":501},"Chapter 4 — Firms, Market Power, and Market Failure","\u002Fen\u002Fintro-to-economics\u002F04-market-structures","en\u002Fintro-to-economics\u002F04-market-structures",{"title":503,"path":504,"stem":505},"Chapter 5 — GDP, Income, Wealth, and Welfare","\u002Fen\u002Fintro-to-economics\u002F05-gdp-and-wealth","en\u002Fintro-to-economics\u002F05-gdp-and-wealth",{"title":507,"path":508,"stem":509},"Chapter 6 — Inflation, Purchasing Power, and Labour Markets","\u002Fen\u002Fintro-to-economics\u002F06-inflation-and-unemployment","en\u002Fintro-to-economics\u002F06-inflation-and-unemployment",{"title":511,"path":512,"stem":513},"Chapter 7 — Productivity, Technology, and Economic Growth","\u002Fen\u002Fintro-to-economics\u002F07-economic-growth","en\u002Fintro-to-economics\u002F07-economic-growth",{"title":515,"path":516,"stem":517},"Chapter 8 — Money, Credit, and Banking","\u002Fen\u002Fintro-to-economics\u002F08-money-and-banking","en\u002Fintro-to-economics\u002F08-money-and-banking",{"title":519,"path":520,"stem":521},"Chapter 9 — Business Cycles, AD–AS, and Monetary Policy","\u002Fen\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as","en\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as",{"title":523,"path":524,"stem":525},"Chapter 10 — Fiscal Policy, Distribution, and Public Debt","\u002Fen\u002Fintro-to-economics\u002F10-fiscal-policy","en\u002Fintro-to-economics\u002F10-fiscal-policy",{"title":527,"path":528,"stem":529},"Chapter 11 — Trade, Capital Flows, and Exchange Rates","\u002Fen\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates","en\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates",{"title":531,"path":532,"stem":533},"Chapter 12 — Integrated Economic Analysis Studio","\u002Fen\u002Fintro-to-economics\u002F12-review-and-case-studies","en\u002Fintro-to-economics\u002F12-review-and-case-studies",{"title":535,"path":536,"stem":537,"children":538,"page":249},"Microeconometrics","\u002Fen\u002Fmicroeconometrics","en\u002Fmicroeconometrics",[539,557,563,581,603,629,651,673,691,709],{"title":540,"path":541,"stem":542,"children":543},"0. Causal Questions and Designs","\u002Fen\u002Fmicroeconometrics\u002F00-foundations","en\u002Fmicroeconometrics\u002F00-foundations\u002Findex",[544,545,549,553],{"title":540,"path":541,"stem":542},{"title":546,"path":547,"stem":548},"Causal Questions and Estimands","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands","en\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands",{"title":550,"path":551,"stem":552},"Potential Outcomes and Experiments","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments","en\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments",{"title":554,"path":555,"stem":556},"Causal Diagrams and Controls","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls","en\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls",{"title":558,"path":559,"stem":560,"children":561},"Microeconometrics — Designing Credible Counterfactuals","\u002Fen\u002Fmicroeconometrics\u002F00-index","en\u002Fmicroeconometrics\u002F00-index",[562],{"title":558,"path":559,"stem":560},{"title":564,"path":565,"stem":566,"children":567},"1. Regression and Inference","\u002Fen\u002Fmicroeconometrics\u002F01-regression","en\u002Fmicroeconometrics\u002F01-regression\u002Findex",[568,569,573,577],{"title":564,"path":565,"stem":566},{"title":570,"path":571,"stem":572},"OLS as a Projection","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection","en\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection",{"title":574,"path":575,"stem":576},"FWL, Selection and Controls","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls","en\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls",{"title":578,"path":579,"stem":580},"Inference and Clustering","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering","en\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering",{"title":582,"path":583,"stem":584,"children":585},"2. Instruments and Panel Data","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002Findex",[586,587,591,595,599],{"title":582,"path":583,"stem":584},{"title":588,"path":589,"stem":590},"Instrumental Variables","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification",{"title":592,"path":593,"stem":594},"Weak Instruments and LATE","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late",{"title":596,"path":597,"stem":598},"Panel Fixed Effects","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects",{"title":600,"path":601,"stem":602},"Dynamic Panels and Limits","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel",{"title":604,"path":605,"stem":606,"children":607},"3. Policy Evaluation Designs","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs","en\u002Fmicroeconometrics\u002F03-policy-designs\u002Findex",[608,609,613,617,621,625],{"title":604,"path":605,"stem":606},{"title":610,"path":611,"stem":612},"Difference-in-Differences","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core",{"title":614,"path":615,"stem":616},"Staggered DID and Event Studies","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies",{"title":618,"path":619,"stem":620},"Regression Discontinuity","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd",{"title":622,"path":623,"stem":624},"Matching, Weighting and Overlap","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting",{"title":626,"path":627,"stem":628},"Synthetic Control","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control",{"title":630,"path":631,"stem":632,"children":633},"Module 4 — Choice and Limited Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002Findex",[634,635,639,643,647],{"title":630,"path":631,"stem":632},{"title":636,"path":637,"stem":638},"Binary Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice",{"title":640,"path":641,"stem":642},"Multinomial and Ordered Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice",{"title":644,"path":645,"stem":646},"Count Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes",{"title":648,"path":649,"stem":650},"Censoring, Truncation and Selection","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection",{"title":652,"path":653,"stem":654,"children":655},"Module 5 — Modern Causal Analysis","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal","en\u002Fmicroeconometrics\u002F05-modern-causal\u002Findex",[656,657,661,665,669],{"title":652,"path":653,"stem":654},{"title":658,"path":659,"stem":660},"Double Machine Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml",{"title":662,"path":663,"stem":664},"Heterogeneity and Policy Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy",{"title":666,"path":667,"stem":668},"Sensitivity and Partial Identification","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id",{"title":670,"path":671,"stem":672},"External Validity and Transport","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity",{"title":674,"path":675,"stem":676,"children":677},"Module 6 — From Data to Auditable Evidence","\u002Fen\u002Fmicroeconometrics\u002F06-workflow","en\u002Fmicroeconometrics\u002F06-workflow\u002Findex",[678,679,683,687],{"title":674,"path":675,"stem":676},{"title":680,"path":681,"stem":682},"Data Provenance","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance","en\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance",{"title":684,"path":685,"stem":686},"Reproducibility and Reporting","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting","en\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting",{"title":688,"path":689,"stem":690},"Paper and Evidence Audit","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit","en\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit",{"title":692,"path":693,"stem":694,"children":695},"Appendix — Revision and Evidence Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix","en\u002Fmicroeconometrics\u002Fappendix\u002Findex",[696,697,701,705],{"title":692,"path":693,"stem":694},{"title":698,"path":699,"stem":700},"Formula and Design Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map","en\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map",{"title":702,"path":703,"stem":704},"Ten Worked Microeconometric Pitfalls","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls","en\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls",{"title":706,"path":707,"stem":708},"Reading and Software Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map","en\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map",{"title":710,"path":711,"stem":712,"children":713},"Capstone — Should Northbridge Expand Pathways?","\u002Fen\u002Fmicroeconometrics\u002Fcapstone","en\u002Fmicroeconometrics\u002Fcapstone\u002Findex",[714],{"title":710,"path":711,"stem":712},{"title":716,"path":717,"stem":718,"children":719,"page":249},"Microeconomics","\u002Fen\u002Fmicroeconomics","en\u002Fmicroeconomics",[720,726,732,738,744,750,756,762,768,774,780,786,792],{"title":721,"path":722,"stem":723,"children":724},"Advanced Microeconomics — Course Guide","\u002Fen\u002Fmicroeconomics\u002F00-intro","en\u002Fmicroeconomics\u002F00-intro\u002Findex",[725],{"title":721,"path":722,"stem":723},{"title":727,"path":728,"stem":729,"children":730},"Module 1 — Choice, Duality, and Revealed Preference","\u002Fen\u002Fmicroeconomics\u002F01-fundations","en\u002Fmicroeconomics\u002F01-fundations\u002Findex",[731],{"title":727,"path":728,"stem":729},{"title":733,"path":734,"stem":735,"children":736},"Module 2 — Comparative Statics and Welfare Measurement","\u002Fen\u002Fmicroeconomics\u002F02-comparative-statics","en\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[737],{"title":733,"path":734,"stem":735},{"title":739,"path":740,"stem":741,"children":742},"Module 3 — Choice under Risk and Insurance","\u002Fen\u002Fmicroeconomics\u002F03-uncertainty","en\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[743],{"title":739,"path":740,"stem":741},{"title":745,"path":746,"stem":747,"children":748},"Module 4 — General Equilibrium and Welfare","\u002Fen\u002Fmicroeconomics\u002F04-general-equilibrium","en\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[749],{"title":745,"path":746,"stem":747},{"title":751,"path":752,"stem":753,"children":754},"Module 5 — Static, Dynamic, and Repeated Games","\u002Fen\u002Fmicroeconomics\u002F05-game-theory","en\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[755],{"title":751,"path":752,"stem":753},{"title":757,"path":758,"stem":759,"children":760},"Module 6 — Oligopoly, Entry, and Algorithmic Pricing","\u002Fen\u002Fmicroeconomics\u002F06-oligopoly","en\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[761],{"title":757,"path":758,"stem":759},{"title":763,"path":764,"stem":765,"children":766},"Module 7 — Information Economics and Contracts","\u002Fen\u002Fmicroeconomics\u002F07-information-economics","en\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[767],{"title":763,"path":764,"stem":765},{"title":769,"path":770,"stem":771,"children":772},"Module 8 — Mechanism Design and Auctions","\u002Fen\u002Fmicroeconomics\u002F08-mechanism-design","en\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[773],{"title":769,"path":770,"stem":771},{"title":775,"path":776,"stem":777,"children":778},"Module 9 — Behavioural and Experimental Microeconomics","\u002Fen\u002Fmicroeconomics\u002F09-behavioural-economics","en\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[779],{"title":775,"path":776,"stem":777},{"title":781,"path":782,"stem":783,"children":784},"Module 10 — Externalities, Public Goods, and Collective Action","\u002Fen\u002Fmicroeconomics\u002F10-externalities-public-goods","en\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[785],{"title":781,"path":782,"stem":783},{"title":787,"path":788,"stem":789,"children":790},"Module 11 — Matching and Market Design","\u002Fen\u002Fmicroeconomics\u002F11-market-design","en\u002Fmicroeconomics\u002F11-market-design\u002Findex",[791],{"title":787,"path":788,"stem":789},{"title":793,"path":794,"stem":795,"children":796},"Module 12 — Integrated Microeconomic Design Studio","\u002Fen\u002Fmicroeconomics\u002F12-review","en\u002Fmicroeconomics\u002F12-review\u002Findex",[797],{"title":793,"path":794,"stem":795},{"title":799,"path":800,"stem":801,"children":802},"Playground","\u002Fen\u002Fplayground","en\u002Fplayground\u002Findex",[803,804,808,812,816,820],{"title":799,"path":800,"stem":801},{"title":805,"path":806,"stem":807},"Typst Plugin Playground","\u002Fen\u002Fplayground\u002F01-typstex","en\u002Fplayground\u002F01-typstex",{"title":809,"path":810,"stem":811},"Citation Plugin Test","\u002Fen\u002Fplayground\u002F02-citation","en\u002Fplayground\u002F02-citation",{"title":813,"path":814,"stem":815},"Pyodide Playground","\u002Fen\u002Fplayground\u002F03-pyodide","en\u002Fplayground\u002F03-pyodide",{"title":817,"path":818,"stem":819},"WebR Playground","\u002Fen\u002Fplayground\u002F04-webr","en\u002Fplayground\u002F04-webr",{"title":821,"path":822,"stem":823},"Chart.js 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文献综述的构建与写作","\u002Fzh\u002Facademic-writing\u002F04-writing-the-literature-review","zh\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":1056,"path":1057,"stem":1058},"8. 文献综述清单与模板","\u002Fzh\u002Facademic-writing\u002F08-literature-review-checklist-and-template","zh\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":1060,"path":1061,"stem":1062},"10. 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x_i\u002Fn",[1828,1885,1888,1951],{"className":1886,"ariaHidden":1849},[1887],"katex-html",[1828,1889,1892,1897,1939,1944,1948],{"className":1890},[1891],"base",[1828,1893],{"className":1894,"style":1896},[1895],"strut","height:0.5678em;",[1828,1898,1902],{"className":1899},[1900,1901],"mord","accent",[1828,1903,1906],{"className":1904},[1905],"vlist-t",[1828,1907,1910],{"className":1908},[1909],"vlist-r",[1828,1911,1914,1926],{"className":1912,"style":1896},[1913],"vlist",[1828,1915,1917,1922],{"style":1916},"top:-3em;",[1828,1918],{"className":1919,"style":1921},[1920],"pstrut","height:3em;",[1828,1923,1853],{"className":1924},[1900,1925],"mathnormal",[1828,1927,1928,1931],{"style":1916},[1828,1929],{"className":1930,"style":1921},[1920],[1828,1932,1936],{"className":1933,"style":1935},[1934],"accent-body","left:-0.2222em;",[1828,1937,1857],{"className":1938},[1900],[1828,1940],{"className":1941,"style":1943},[1942],"mspace","margin-right:0.2778em;",[1828,1945,1860],{"className":1946},[1947],"mrel",[1828,1949],{"className":1950,"style":1943},[1942],[1828,1952,1954,1958,1965,1969,2021,2024],{"className":1953},[1891],[1828,1955],{"className":1956,"style":1957},[1895],"height:1em;vertical-align:-0.25em;",[1828,1959,1863],{"className":1960,"style":1964},[1961,1962,1963],"mop","op-symbol","small-op","position:relative;top:0em;",[1828,1966],{"className":1967,"style":1968},[1942],"margin-right:0.1667em;",[1828,1970,1972,1975],{"className":1971},[1900],[1828,1973,1853],{"className":1974},[1900,1925],[1828,1976,1979],{"className":1977},[1978],"msupsub",[1828,1980,1983,2012],{"className":1981},[1905,1982],"vlist-t2",[1828,1984,1986,2007],{"className":1985},[1909],[1828,1987,1990],{"className":1988,"style":1989},[1913],"height:0.3117em;",[1828,1991,1993,1997],{"style":1992},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1828,1994],{"className":1995,"style":1996},[1920],"height:2.7em;",[1828,1998,2004],{"className":1999},[2000,2001,2002,2003],"sizing","reset-size6","size3","mtight",[1828,2005,1871],{"className":2006},[1900,1925,2003],[1828,2008,2011],{"className":2009},[2010],"vlist-s","​",[1828,2013,2015],{"className":2014},[1909],[1828,2016,2019],{"className":2017,"style":2018},[1913],"height:0.15em;",[1828,2020],{},[1828,2022,1875],{"className":2023},[1900],[1828,2025,1878],{"className":2026},[1900,1925],"; median for the middle observation",[1822,2029,2030],{},"skew, weights, repeated units, missingness",[1804,2032,2033,2036,2150],{},[1822,2034,2035],{},"What share experienced an event?",[1822,2037,2038],{},[1828,2039,2041,2070],{"className":2040},[1831],[1828,2042,2044],{"className":2043},[1835],[1837,2045,2046],{"xmlns":1839},[1841,2047,2048,2067],{},[1844,2049,2050,2058,2060,2063,2065],{},[1847,2051,2052,2055],{"accent":1849},[1851,2053,2054],{},"p",[1855,2056,2057],{},"^",[1855,2059,1860],{},[1851,2061,2062],{},"y",[1851,2064,1875],{"mathvariant":1874},[1851,2066,1878],{},[1880,2068,2069],{"encoding":1882},"\\hat p=y\u002Fn",[1828,2071,2073,2134],{"className":2072,"ariaHidden":1849},[1887],[1828,2074,2076,2080,2125,2128,2131],{"className":2075},[1891],[1828,2077],{"className":2078,"style":2079},[1895],"height:0.8889em;vertical-align:-0.1944em;",[1828,2081,2083],{"className":2082},[1900,1901],[1828,2084,2086,2116],{"className":2085},[1905,1982],[1828,2087,2089,2113],{"className":2088},[1909],[1828,2090,2093,2101],{"className":2091,"style":2092},[1913],"height:0.6944em;",[1828,2094,2095,2098],{"style":1916},[1828,2096],{"className":2097,"style":1921},[1920],[1828,2099,2054],{"className":2100},[1900,1925],[1828,2102,2103,2106],{"style":1916},[1828,2104],{"className":2105,"style":1921},[1920],[1828,2107,2110],{"className":2108,"style":2109},[1934],"left:-0.1667em;",[1828,2111,2057],{"className":2112},[1900],[1828,2114,2011],{"className":2115},[2010],[1828,2117,2119],{"className":2118},[1909],[1828,2120,2123],{"className":2121,"style":2122},[1913],"height:0.1944em;",[1828,2124],{},[1828,2126],{"className":2127,"style":1943},[1942],[1828,2129,1860],{"className":2130},[1947],[1828,2132],{"className":2133,"style":1943},[1942],[1828,2135,2137,2140,2144,2147],{"className":2136},[1891],[1828,2138],{"className":2139,"style":1957},[1895],[1828,2141,2062],{"className":2142,"style":2143},[1900,1925],"margin-right:0.0359em;",[1828,2145,1875],{"className":2146},[1900],[1828,2148,1878],{"className":2149},[1900,1925],[1822,2151,2152],{},"eligible denominator, complete follow-up, duplicate rows",[1804,2154,2155,2158,2483],{},[1822,2156,2157],{},"How uncertain is a simple rate?",[1822,2159,2160],{},[1828,2161,2163,2229],{"className":2162},[1831],[1828,2164,2166],{"className":2165},[1835],[1837,2167,2168],{"xmlns":1839},[1841,2169,2170,2226],{},[1844,2171,2172,2175,2178,2182,2188,2191,2194],{},[1851,2173,2174],{},"S",[1851,2176,2177],{},"E",[1855,2179,2181],{"stretchy":2180},"false","(",[1847,2183,2184,2186],{"accent":1849},[1851,2185,2054],{},[1855,2187,2057],{},[1855,2189,2190],{"stretchy":2180},")",[1855,2192,2193],{},"≈",[2195,2196,2197],"msqrt",{},[1844,2198,2199,2205,2207,2211,2214,2220,2222,2224],{},[1847,2200,2201,2203],{"accent":1849},[1851,2202,2054],{},[1855,2204,2057],{},[1855,2206,2181],{"stretchy":2180},[2208,2209,2210],"mn",{},"1",[1855,2212,2213],{},"−",[1847,2215,2216,2218],{"accent":1849},[1851,2217,2054],{},[1855,2219,2057],{},[1855,2221,2190],{"stretchy":2180},[1851,2223,1875],{"mathvariant":1874},[1851,2225,1878],{},[1880,2227,2228],{"encoding":1882},"SE(\\hat p)\\approx\\sqrt{\\hat p(1-\\hat p)\u002Fn}",[1828,2230,2232,2304],{"className":2231,"ariaHidden":1849},[1887],[1828,2233,2235,2238,2242,2245,2249,2291,2295,2298,2301],{"className":2234},[1891],[1828,2236],{"className":2237,"style":1957},[1895],[1828,2239,2174],{"className":2240,"style":2241},[1900,1925],"margin-right:0.0576em;",[1828,2243,2177],{"className":2244,"style":2241},[1900,1925],[1828,2246,2181],{"className":2247},[2248],"mopen",[1828,2250,2252],{"className":2251},[1900,1901],[1828,2253,2255,2283],{"className":2254},[1905,1982],[1828,2256,2258,2280],{"className":2257},[1909],[1828,2259,2261,2269],{"className":2260,"style":2092},[1913],[1828,2262,2263,2266],{"style":1916},[1828,2264],{"className":2265,"style":1921},[1920],[1828,2267,2054],{"className":2268},[1900,1925],[1828,2270,2271,2274],{"style":1916},[1828,2272],{"className":2273,"style":1921},[1920],[1828,2275,2277],{"className":2276,"style":2109},[1934],[1828,2278,2057],{"className":2279},[1900],[1828,2281,2011],{"className":2282},[2010],[1828,2284,2286],{"className":2285},[1909],[1828,2287,2289],{"className":2288,"style":2122},[1913],[1828,2290],{},[1828,2292,2190],{"className":2293},[2294],"mclose",[1828,2296],{"className":2297,"style":1943},[1942],[1828,2299,2193],{"className":2300},[1947],[1828,2302],{"className":2303,"style":1943},[1942],[1828,2305,2307,2311],{"className":2306},[1891],[1828,2308],{"className":2309,"style":2310},[1895],"height:1.24em;vertical-align:-0.305em;",[1828,2312,2315],{"className":2313},[1900,2314],"sqrt",[1828,2316,2318,2474],{"className":2317},[1905,1982],[1828,2319,2321,2471],{"className":2320},[1909],[1828,2322,2325,2448],{"className":2323,"style":2324},[1913],"height:0.935em;",[1828,2326,2330,2334],{"className":2327,"style":2329},[2328],"svg-align","top:-3.2em;",[1828,2331],{"className":2332,"style":2333},[1920],"height:3.2em;",[1828,2335,2338,2380,2383,2386,2390,2394,2397,2439,2442,2445],{"className":2336,"style":2337},[1900],"padding-left:1em;",[1828,2339,2341],{"className":2340},[1900,1901],[1828,2342,2344,2372],{"className":2343},[1905,1982],[1828,2345,2347,2369],{"className":2346},[1909],[1828,2348,2350,2358],{"className":2349,"style":2092},[1913],[1828,2351,2352,2355],{"style":1916},[1828,2353],{"className":2354,"style":1921},[1920],[1828,2356,2054],{"className":2357},[1900,1925],[1828,2359,2360,2363],{"style":1916},[1828,2361],{"className":2362,"style":1921},[1920],[1828,2364,2366],{"className":2365,"style":2109},[1934],[1828,2367,2057],{"className":2368},[1900],[1828,2370,2011],{"className":2371},[2010],[1828,2373,2375],{"className":2374},[1909],[1828,2376,2378],{"className":2377,"style":2122},[1913],[1828,2379],{},[1828,2381,2181],{"className":2382},[2248],[1828,2384,2210],{"className":2385},[1900],[1828,2387],{"className":2388,"style":2389},[1942],"margin-right:0.2222em;",[1828,2391,2213],{"className":2392},[2393],"mbin",[1828,2395],{"className":2396,"style":2389},[1942],[1828,2398,2400],{"className":2399},[1900,1901],[1828,2401,2403,2431],{"className":2402},[1905,1982],[1828,2404,2406,2428],{"className":2405},[1909],[1828,2407,2409,2417],{"className":2408,"style":2092},[1913],[1828,2410,2411,2414],{"style":1916},[1828,2412],{"className":2413,"style":1921},[1920],[1828,2415,2054],{"className":2416},[1900,1925],[1828,2418,2419,2422],{"style":1916},[1828,2420],{"className":2421,"style":1921},[1920],[1828,2423,2425],{"className":2424,"style":2109},[1934],[1828,2426,2057],{"className":2427},[1900],[1828,2429,2011],{"className":2430},[2010],[1828,2432,2434],{"className":2433},[1909],[1828,2435,2437],{"className":2436,"style":2122},[1913],[1828,2438],{},[1828,2440,2190],{"className":2441},[2294],[1828,2443,1875],{"className":2444},[1900],[1828,2446,1878],{"className":2447},[1900,1925],[1828,2449,2451,2454],{"style":2450},"top:-2.895em;",[1828,2452],{"className":2453,"style":2333},[1920],[1828,2455,2459],{"className":2456,"style":2458},[2457],"hide-tail","min-width:1.02em;height:1.28em;",[2460,2461,2467],"svg",{"xmlns":2462,"width":2463,"height":2464,"viewBox":2465,"preserveAspectRatio":2466},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.28em","0 0 400000 1296","xMinYMin slice",[2468,2469],"path",{"d":2470},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[1828,2472,2011],{"className":2473},[2010],[1828,2475,2477],{"className":2476},[1909],[1828,2478,2481],{"className":2479,"style":2480},[1913],"height:0.305em;",[1828,2482],{},[1822,2484,2485],{},"independence and adequate counts; use better interval methods near 0 or 1",[1804,2487,2488,2491,2689],{},[1822,2489,2490],{},"How did a KPI change?",[1822,2492,2493],{},[1828,2494,2496,2535],{"className":2495},[1831],[1828,2497,2499],{"className":2498},[1835],[1837,2500,2501],{"xmlns":1839},[1841,2502,2503,2532],{},[1844,2504,2505,2507,2513,2515,2522,2524,2526],{},[1855,2506,2181],{"stretchy":2180},[1865,2508,2509,2511],{},[1851,2510,1853],{},[2208,2512,2210],{},[1855,2514,2213],{},[1865,2516,2517,2519],{},[1851,2518,1853],{},[2208,2520,2521],{},"0",[1855,2523,2190],{"stretchy":2180},[1851,2525,1875],{"mathvariant":1874},[1865,2527,2528,2530],{},[1851,2529,1853],{},[2208,2531,2521],{},[1880,2533,2534],{"encoding":1882},"(x_1-x_0)\u002Fx_0",[1828,2536,2538,2597],{"className":2537,"ariaHidden":1849},[1887],[1828,2539,2541,2544,2547,2588,2591,2594],{"className":2540},[1891],[1828,2542],{"className":2543,"style":1957},[1895],[1828,2545,2181],{"className":2546},[2248],[1828,2548,2550,2553],{"className":2549},[1900],[1828,2551,1853],{"className":2552},[1900,1925],[1828,2554,2556],{"className":2555},[1978],[1828,2557,2559,2580],{"className":2558},[1905,1982],[1828,2560,2562,2577],{"className":2561},[1909],[1828,2563,2566],{"className":2564,"style":2565},[1913],"height:0.3011em;",[1828,2567,2568,2571],{"style":1992},[1828,2569],{"className":2570,"style":1996},[1920],[1828,2572,2574],{"className":2573},[2000,2001,2002,2003],[1828,2575,2210],{"className":2576},[1900,2003],[1828,2578,2011],{"className":2579},[2010],[1828,2581,2583],{"className":2582},[1909],[1828,2584,2586],{"className":2585,"style":2018},[1913],[1828,2587],{},[1828,2589],{"className":2590,"style":2389},[1942],[1828,2592,2213],{"className":2593},[2393],[1828,2595],{"className":2596,"style":2389},[1942],[1828,2598,2600,2603,2643,2646,2649],{"className":2599},[1891],[1828,2601],{"className":2602,"style":1957},[1895],[1828,2604,2606,2609],{"className":2605},[1900],[1828,2607,1853],{"className":2608},[1900,1925],[1828,2610,2612],{"className":2611},[1978],[1828,2613,2615,2635],{"className":2614},[1905,1982],[1828,2616,2618,2632],{"className":2617},[1909],[1828,2619,2621],{"className":2620,"style":2565},[1913],[1828,2622,2623,2626],{"style":1992},[1828,2624],{"className":2625,"style":1996},[1920],[1828,2627,2629],{"className":2628},[2000,2001,2002,2003],[1828,2630,2521],{"className":2631},[1900,2003],[1828,2633,2011],{"className":2634},[2010],[1828,2636,2638],{"className":2637},[1909],[1828,2639,2641],{"className":2640,"style":2018},[1913],[1828,2642],{},[1828,2644,2190],{"className":2645},[2294],[1828,2647,1875],{"className":2648},[1900],[1828,2650,2652,2655],{"className":2651},[1900],[1828,2653,1853],{"className":2654},[1900,1925],[1828,2656,2658],{"className":2657},[1978],[1828,2659,2661,2681],{"className":2660},[1905,1982],[1828,2662,2664,2678],{"className":2663},[1909],[1828,2665,2667],{"className":2666,"style":2565},[1913],[1828,2668,2669,2672],{"style":1992},[1828,2670],{"className":2671,"style":1996},[1920],[1828,2673,2675],{"className":2674},[2000,2001,2002,2003],[1828,2676,2521],{"className":2677},[1900,2003],[1828,2679,2011],{"className":2680},[2010],[1828,2682,2684],{"className":2683},[1909],[1828,2685,2687],{"className":2686,"style":2018},[1913],[1828,2688],{},[1822,2690,2691],{},"same definition, period and currency; distinguish percent from percentage points",[1804,2693,2694,2697,2841],{},[1822,2695,2696],{},"Which stage loses volume?",[1822,2698,2699,2700],{},"funnel conversion ",[1828,2701,2703,2737],{"className":2702},[1831],[1828,2704,2706],{"className":2705},[1835],[1837,2707,2708],{"xmlns":1839},[1841,2709,2710,2734],{},[1844,2711,2712,2726,2728],{},[1865,2713,2714,2716],{},[1851,2715,1878],{},[1844,2717,2718,2721,2724],{},[1851,2719,2720],{},"k",[1855,2722,2723],{},"+",[2208,2725,2210],{},[1851,2727,1875],{"mathvariant":1874},[1865,2729,2730,2732],{},[1851,2731,1878],{},[1851,2733,2720],{},[1880,2735,2736],{"encoding":1882},"n_{k+1}\u002Fn_k",[1828,2738,2740],{"className":2739,"ariaHidden":1849},[1887],[1828,2741,2743,2746,2798,2801],{"className":2742},[1891],[1828,2744],{"className":2745,"style":1957},[1895],[1828,2747,2749,2752],{"className":2748},[1900],[1828,2750,1878],{"className":2751},[1900,1925],[1828,2753,2755],{"className":2754},[1978],[1828,2756,2758,2789],{"className":2757},[1905,1982],[1828,2759,2761,2786],{"className":2760},[1909],[1828,2762,2765],{"className":2763,"style":2764},[1913],"height:0.3361em;",[1828,2766,2767,2770],{"style":1992},[1828,2768],{"className":2769,"style":1996},[1920],[1828,2771,2773],{"className":2772},[2000,2001,2002,2003],[1828,2774,2776,2780,2783],{"className":2775},[1900,2003],[1828,2777,2720],{"className":2778,"style":2779},[1900,1925,2003],"margin-right:0.0315em;",[1828,2781,2723],{"className":2782},[2393,2003],[1828,2784,2210],{"className":2785},[1900,2003],[1828,2787,2011],{"className":2788},[2010],[1828,2790,2792],{"className":2791},[1909],[1828,2793,2796],{"className":2794,"style":2795},[1913],"height:0.2083em;",[1828,2797],{},[1828,2799,1875],{"className":2800},[1900],[1828,2802,2804,2807],{"className":2803},[1900],[1828,2805,1878],{"className":2806},[1900,1925],[1828,2808,2810],{"className":2809},[1978],[1828,2811,2813,2833],{"className":2812},[1905,1982],[1828,2814,2816,2830],{"className":2815},[1909],[1828,2817,2819],{"className":2818,"style":2764},[1913],[1828,2820,2821,2824],{"style":1992},[1828,2822],{"className":2823,"style":1996},[1920],[1828,2825,2827],{"className":2826},[2000,2001,2002,2003],[1828,2828,2720],{"className":2829,"style":2779},[1900,1925,2003],[1828,2831,2011],{"className":2832},[2010],[1828,2834,2836],{"className":2835},[1909],[1828,2837,2839],{"className":2838,"style":2018},[1913],[1828,2840],{},[1822,2842,2843],{},"ordered eligibility and consistent cohort",[2054,2845,2846,2847,2851,2852,2855],{},"Example: a late rate moving from 8% to 6% falls by ",[2848,2849,2850],"strong",{},"2 percentage points",", or ",[2848,2853,2854],{},"25% relative",". State which one.",[1793,2857,2859],{"id":2858},"predict-an-unknown-outcome","Predict an unknown outcome",[1798,2861,2862,2873],{},[1801,2863,2864],{},[1804,2865,2866,2868,2870],{},[1807,2867,1809],{},[1807,2869,1812],{},[1807,2871,2872],{},"Decision interpretation",[1817,2874,2875,2886,3255,3510,3521],{},[1804,2876,2877,2880,2883],{},[1822,2878,2879],{},"How large is numeric error?",[1822,2881,2882],{},"$MAE=n^{-1}\\sum",[1822,2884,2885],{},"y_i-\\hat y_i",[1804,2887,2888,2891,3252],{},[1822,2889,2890],{},"Are large errors especially costly?",[1822,2892,2893],{},[1828,2894,2896,2964],{"className":2895},[1831],[1828,2897,2899],{"className":2898},[1835],[1837,2900,2901],{"xmlns":1839},[1841,2902,2903,2961],{},[1844,2904,2905,2908,2911,2913,2915,2917],{},[1851,2906,2907],{},"R",[1851,2909,2910],{},"M",[1851,2912,2174],{},[1851,2914,2177],{},[1855,2916,1860],{},[2195,2918,2919],{},[1844,2920,2921,2932,2934,2936,2942,2944,2954],{},[2922,2923,2924,2926],"msup",{},[1851,2925,1878],{},[1844,2927,2928,2930],{},[1855,2929,2213],{},[2208,2931,2210],{},[1855,2933,1863],{},[1855,2935,2181],{"stretchy":2180},[1865,2937,2938,2940],{},[1851,2939,2062],{},[1851,2941,1871],{},[1855,2943,2213],{},[1865,2945,2946,2952],{},[1847,2947,2948,2950],{"accent":1849},[1851,2949,2062],{},[1855,2951,2057],{},[1851,2953,1871],{},[2922,2955,2956,2958],{},[1855,2957,2190],{"stretchy":2180},[2208,2959,2960],{},"2",[1880,2962,2963],{"encoding":1882},"RMSE=\\sqrt{n^{-1}\\sum(y_i-\\hat y_i)^2}",[1828,2965,2967,2997],{"className":2966,"ariaHidden":1849},[1887],[1828,2968,2970,2974,2978,2982,2985,2988,2991,2994],{"className":2969},[1891],[1828,2971],{"className":2972,"style":2973},[1895],"height:0.6833em;",[1828,2975,2907],{"className":2976,"style":2977},[1900,1925],"margin-right:0.0077em;",[1828,2979,2910],{"className":2980,"style":2981},[1900,1925],"margin-right:0.109em;",[1828,2983,2174],{"className":2984,"style":2241},[1900,1925],[1828,2986,2177],{"className":2987,"style":2241},[1900,1925],[1828,2989],{"className":2990,"style":1943},[1942],[1828,2992,1860],{"className":2993},[1947],[1828,2995],{"className":2996,"style":1943},[1942],[1828,2998,3000,3003],{"className":2999},[1891],[1828,3001],{"className":3002,"style":2310},[1895],[1828,3004,3006],{"className":3005},[1900,2314],[1828,3007,3009,3244],{"className":3008},[1905,1982],[1828,3010,3012,3241],{"className":3011},[1909],[1828,3013,3015,3229],{"className":3014,"style":2324},[1913],[1828,3016,3018,3021],{"className":3017,"style":2329},[2328],[1828,3019],{"className":3020,"style":2333},[1920],[1828,3022,3024,3061,3064,3067,3070,3111,3114,3117,3120,3200],{"className":3023,"style":2337},[1900],[1828,3025,3027,3030],{"className":3026},[1900],[1828,3028,1878],{"className":3029},[1900,1925],[1828,3031,3033],{"className":3032},[1978],[1828,3034,3036],{"className":3035},[1905],[1828,3037,3039],{"className":3038},[1909],[1828,3040,3043],{"className":3041,"style":3042},[1913],"height:0.7401em;",[1828,3044,3046,3049],{"style":3045},"top:-2.989em;margin-right:0.05em;",[1828,3047],{"className":3048,"style":1996},[1920],[1828,3050,3052],{"className":3051},[2000,2001,2002,2003],[1828,3053,3055,3058],{"className":3054},[1900,2003],[1828,3056,2213],{"className":3057},[1900,2003],[1828,3059,2210],{"className":3060},[1900,2003],[1828,3062],{"className":3063,"style":1968},[1942],[1828,3065,1863],{"className":3066,"style":1964},[1961,1962,1963],[1828,3068,2181],{"className":3069},[2248],[1828,3071,3073,3076],{"className":3072},[1900],[1828,3074,2062],{"className":3075,"style":2143},[1900,1925],[1828,3077,3079],{"className":3078},[1978],[1828,3080,3082,3103],{"className":3081},[1905,1982],[1828,3083,3085,3100],{"className":3084},[1909],[1828,3086,3088],{"className":3087,"style":1989},[1913],[1828,3089,3091,3094],{"style":3090},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1828,3092],{"className":3093,"style":1996},[1920],[1828,3095,3097],{"className":3096},[2000,2001,2002,2003],[1828,3098,1871],{"className":3099},[1900,1925,2003],[1828,3101,2011],{"className":3102},[2010],[1828,3104,3106],{"className":3105},[1909],[1828,3107,3109],{"className":3108,"style":2018},[1913],[1828,3110],{},[1828,3112],{"className":3113,"style":2389},[1942],[1828,3115,2213],{"className":3116},[2393],[1828,3118],{"className":3119,"style":2389},[1942],[1828,3121,3123,3166],{"className":3122},[1900],[1828,3124,3126],{"className":3125},[1900,1901],[1828,3127,3129,3158],{"className":3128},[1905,1982],[1828,3130,3132,3155],{"className":3131},[1909],[1828,3133,3135,3143],{"className":3134,"style":2092},[1913],[1828,3136,3137,3140],{"style":1916},[1828,3138],{"className":3139,"style":1921},[1920],[1828,3141,2062],{"className":3142,"style":2143},[1900,1925],[1828,3144,3145,3148],{"style":1916},[1828,3146],{"className":3147,"style":1921},[1920],[1828,3149,3152],{"className":3150,"style":3151},[1934],"left:-0.1944em;",[1828,3153,2057],{"className":3154},[1900],[1828,3156,2011],{"className":3157},[2010],[1828,3159,3161],{"className":3160},[1909],[1828,3162,3164],{"className":3163,"style":2122},[1913],[1828,3165],{},[1828,3167,3169],{"className":3168},[1978],[1828,3170,3172,3192],{"className":3171},[1905,1982],[1828,3173,3175,3189],{"className":3174},[1909],[1828,3176,3178],{"className":3177,"style":1989},[1913],[1828,3179,3180,3183],{"style":3090},[1828,3181],{"className":3182,"style":1996},[1920],[1828,3184,3186],{"className":3185},[2000,2001,2002,2003],[1828,3187,1871],{"className":3188},[1900,1925,2003],[1828,3190,2011],{"className":3191},[2010],[1828,3193,3195],{"className":3194},[1909],[1828,3196,3198],{"className":3197,"style":2018},[1913],[1828,3199],{},[1828,3201,3203,3206],{"className":3202},[2294],[1828,3204,2190],{"className":3205},[2294],[1828,3207,3209],{"className":3208},[1978],[1828,3210,3212],{"className":3211},[1905],[1828,3213,3215],{"className":3214},[1909],[1828,3216,3218],{"className":3217,"style":3042},[1913],[1828,3219,3220,3223],{"style":3045},[1828,3221],{"className":3222,"style":1996},[1920],[1828,3224,3226],{"className":3225},[2000,2001,2002,2003],[1828,3227,2960],{"className":3228},[1900,2003],[1828,3230,3231,3234],{"style":2450},[1828,3232],{"className":3233,"style":2333},[1920],[1828,3235,3237],{"className":3236,"style":2458},[2457],[2460,3238,3239],{"xmlns":2462,"width":2463,"height":2464,"viewBox":2465,"preserveAspectRatio":2466},[2468,3240],{"d":2470},[1828,3242,2011],{"className":3243},[2010],[1828,3245,3247],{"className":3246},[1909],[1828,3248,3250],{"className":3249,"style":2480},[1913],[1828,3251],{},[1822,3253,3254],{},"large misses receive quadratic weight",[1804,3256,3257,3260,3507],{},[1822,3258,3259],{},"Are probabilities accurate?",[1822,3261,3262,3263],{},"Brier ",[1828,3264,3266,3314],{"className":3265},[1831],[1828,3267,3269],{"className":3268},[1835],[1837,3270,3271],{"xmlns":1839},[1841,3272,3273,3311],{},[1844,3274,3275,3277,3287,3289,3291,3297,3299,3305],{},[1855,3276,1860],{},[2922,3278,3279,3281],{},[1851,3280,1878],{},[1844,3282,3283,3285],{},[1855,3284,2213],{},[2208,3286,2210],{},[1855,3288,1863],{},[1855,3290,2181],{"stretchy":2180},[1865,3292,3293,3295],{},[1851,3294,2062],{},[1851,3296,1871],{},[1855,3298,2213],{},[1865,3300,3301,3303],{},[1851,3302,2054],{},[1851,3304,1871],{},[2922,3306,3307,3309],{},[1855,3308,2190],{"stretchy":2180},[2208,3310,2960],{},[1880,3312,3313],{"encoding":1882},"=n^{-1}\\sum(y_i-p_i)^2",[1828,3315,3317,3330,3432],{"className":3316,"ariaHidden":1849},[1887],[1828,3318,3320,3324,3327],{"className":3319},[1891],[1828,3321],{"className":3322,"style":3323},[1895],"height:0.3669em;",[1828,3325,1860],{"className":3326},[1947],[1828,3328],{"className":3329,"style":1943},[1942],[1828,3331,3333,3337,3374,3377,3380,3383,3423,3426,3429],{"className":3332},[1891],[1828,3334],{"className":3335,"style":3336},[1895],"height:1.0641em;vertical-align:-0.25em;",[1828,3338,3340,3343],{"className":3339},[1900],[1828,3341,1878],{"className":3342},[1900,1925],[1828,3344,3346],{"className":3345},[1978],[1828,3347,3349],{"className":3348},[1905],[1828,3350,3352],{"className":3351},[1909],[1828,3353,3356],{"className":3354,"style":3355},[1913],"height:0.8141em;",[1828,3357,3359,3362],{"style":3358},"top:-3.063em;margin-right:0.05em;",[1828,3360],{"className":3361,"style":1996},[1920],[1828,3363,3365],{"className":3364},[2000,2001,2002,2003],[1828,3366,3368,3371],{"className":3367},[1900,2003],[1828,3369,2213],{"className":3370},[1900,2003],[1828,3372,2210],{"className":3373},[1900,2003],[1828,3375],{"className":3376,"style":1968},[1942],[1828,3378,1863],{"className":3379,"style":1964},[1961,1962,1963],[1828,3381,2181],{"className":3382},[2248],[1828,3384,3386,3389],{"className":3385},[1900],[1828,3387,2062],{"className":3388,"style":2143},[1900,1925],[1828,3390,3392],{"className":3391},[1978],[1828,3393,3395,3415],{"className":3394},[1905,1982],[1828,3396,3398,3412],{"className":3397},[1909],[1828,3399,3401],{"className":3400,"style":1989},[1913],[1828,3402,3403,3406],{"style":3090},[1828,3404],{"className":3405,"style":1996},[1920],[1828,3407,3409],{"className":3408},[2000,2001,2002,2003],[1828,3410,1871],{"className":3411},[1900,1925,2003],[1828,3413,2011],{"className":3414},[2010],[1828,3416,3418],{"className":3417},[1909],[1828,3419,3421],{"className":3420,"style":2018},[1913],[1828,3422],{},[1828,3424],{"className":3425,"style":2389},[1942],[1828,3427,2213],{"className":3428},[2393],[1828,3430],{"className":3431,"style":2389},[1942],[1828,3433,3435,3438,3478],{"className":3434},[1891],[1828,3436],{"className":3437,"style":3336},[1895],[1828,3439,3441,3444],{"className":3440},[1900],[1828,3442,2054],{"className":3443},[1900,1925],[1828,3445,3447],{"className":3446},[1978],[1828,3448,3450,3470],{"className":3449},[1905,1982],[1828,3451,3453,3467],{"className":3452},[1909],[1828,3454,3456],{"className":3455,"style":1989},[1913],[1828,3457,3458,3461],{"style":1992},[1828,3459],{"className":3460,"style":1996},[1920],[1828,3462,3464],{"className":3463},[2000,2001,2002,2003],[1828,3465,1871],{"className":3466},[1900,1925,2003],[1828,3468,2011],{"className":3469},[2010],[1828,3471,3473],{"className":3472},[1909],[1828,3474,3476],{"className":3475,"style":2018},[1913],[1828,3477],{},[1828,3479,3481,3484],{"className":3480},[2294],[1828,3482,2190],{"className":3483},[2294],[1828,3485,3487],{"className":3486},[1978],[1828,3488,3490],{"className":3489},[1905],[1828,3491,3493],{"className":3492},[1909],[1828,3494,3496],{"className":3495,"style":3355},[1913],[1828,3497,3498,3501],{"style":3358},[1828,3499],{"className":3500,"style":1996},[1920],[1828,3502,3504],{"className":3503},[2000,2001,2002,2003],[1828,3505,2960],{"className":3506},[1900,2003],[1822,3508,3509],{},"calibration and discrimination together",[1804,3511,3512,3515,3518],{},[1822,3513,3514],{},"Does ranking separate events?",[1822,3516,3517],{},"AUROC or precision–recall curve",[1822,3519,3520],{},"ranking over thresholds, not policy value",[1804,3522,3523,3526,3529],{},[1822,3524,3525],{},"Is a chosen action threshold worthwhile?",[1822,3527,3528],{},"act if expected incremental benefit exceeds cost",[1822,3530,3531,3532,3535],{},"requires calibrated risk ",[2848,3533,3534],{},"and"," credible intervention effect",[2054,3537,3538],{},"Always compare with a feasible baseline on data later than training. A lower test error is evidence about the defined population and period, not a permanent property.",[1793,3540,3542],{"id":3541},"choose-an-action","Choose an action",[1798,3544,3545,3558],{},[1801,3546,3547],{},[1804,3548,3549,3552,3555],{},[1807,3550,3551],{},"Decision",[1807,3553,3554],{},"Core object",[1807,3556,3557],{},"Main assumption",[1817,3559,3560,3749,4079,4271,4552,4620],{},[1804,3561,3562,3565,3746],{},[1822,3563,3564],{},"uncertain alternatives",[1822,3566,3567],{},[1828,3568,3570,3625],{"className":3569},[1831],[1828,3571,3573],{"className":3572},[1835],[1837,3574,3575],{"xmlns":1839},[1841,3576,3577,3622],{},[1844,3578,3579,3581,3584,3586,3589,3591,3593,3600,3603,3605,3607,3609,3611,3613,3615,3618,3620],{},[1851,3580,2177],{},[1851,3582,3583],{},"V",[1855,3585,2181],{"stretchy":2180},[1851,3587,3588],{},"a",[1855,3590,2190],{"stretchy":2180},[1855,3592,1860],{},[1865,3594,3595,3597],{},[1855,3596,1863],{},[1851,3598,3599],{},"s",[1851,3601,3602],{},"P",[1855,3604,2181],{"stretchy":2180},[1851,3606,3599],{},[1855,3608,2190],{"stretchy":2180},[1851,3610,3583],{},[1855,3612,2181],{"stretchy":2180},[1851,3614,3588],{},[1855,3616,3617],{"separator":1849},",",[1851,3619,3599],{},[1855,3621,2190],{"stretchy":2180},[1880,3623,3624],{"encoding":1882},"EV(a)=\\sum_s P(s)V(a,s)",[1828,3626,3628,3658],{"className":3627,"ariaHidden":1849},[1887],[1828,3629,3631,3634,3637,3640,3643,3646,3649,3652,3655],{"className":3630},[1891],[1828,3632],{"className":3633,"style":1957},[1895],[1828,3635,2177],{"className":3636,"style":2241},[1900,1925],[1828,3638,3583],{"className":3639,"style":2389},[1900,1925],[1828,3641,2181],{"className":3642},[2248],[1828,3644,3588],{"className":3645},[1900,1925],[1828,3647,2190],{"className":3648},[2294],[1828,3650],{"className":3651,"style":1943},[1942],[1828,3653,1860],{"className":3654},[1947],[1828,3656],{"className":3657,"style":1943},[1942],[1828,3659,3661,3665,3708,3711,3715,3718,3721,3724,3727,3730,3733,3737,3740,3743],{"className":3660},[1891],[1828,3662],{"className":3663,"style":3664},[1895],"height:1.0497em;vertical-align:-0.2997em;",[1828,3666,3668,3671],{"className":3667},[1961],[1828,3669,1863],{"className":3670,"style":1964},[1961,1962,1963],[1828,3672,3674],{"className":3673},[1978],[1828,3675,3677,3699],{"className":3676},[1905,1982],[1828,3678,3680,3696],{"className":3679},[1909],[1828,3681,3684],{"className":3682,"style":3683},[1913],"height:0.0017em;",[1828,3685,3687,3690],{"style":3686},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1828,3688],{"className":3689,"style":1996},[1920],[1828,3691,3693],{"className":3692},[2000,2001,2002,2003],[1828,3694,3599],{"className":3695},[1900,1925,2003],[1828,3697,2011],{"className":3698},[2010],[1828,3700,3702],{"className":3701},[1909],[1828,3703,3706],{"className":3704,"style":3705},[1913],"height:0.2997em;",[1828,3707],{},[1828,3709],{"className":3710,"style":1968},[1942],[1828,3712,3602],{"className":3713,"style":3714},[1900,1925],"margin-right:0.1389em;",[1828,3716,2181],{"className":3717},[2248],[1828,3719,3599],{"className":3720},[1900,1925],[1828,3722,2190],{"className":3723},[2294],[1828,3725,3583],{"className":3726,"style":2389},[1900,1925],[1828,3728,2181],{"className":3729},[2248],[1828,3731,3588],{"className":3732},[1900,1925],[1828,3734,3617],{"className":3735},[3736],"mpunct",[1828,3738],{"className":3739,"style":1968},[1942],[1828,3741,3599],{"className":3742},[1900,1925],[1828,3744,2190],{"className":3745},[2294],[1822,3747,3748],{},"probabilities and consequences are adequate",[1804,3750,3751,3754,4076],{},[1822,3752,3753],{},"value of perfect 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counterfactual trends",[1804,5485,5486,5489,5492],{},[1822,5487,5488],{},"regression discontinuity",[1822,5490,5491],{},"outcome jump at assignment cutoff",[1822,5493,5494],{},"manipulation and extrapolation away from cutoff",[1804,5496,5497,5500,5503],{},[1822,5498,5499],{},"adjusted observation",[1822,5501,5502],{},"conditional treated–comparison contrast",[1822,5504,5505],{},"unmeasured confounding and weak overlap",[2054,5507,5508,5509,5537,5538,5619],{},"Prediction asks about ",[1828,5510,5512,5525],{"className":5511},[1831],[1828,5513,5515],{"className":5514},[1835],[1837,5516,5517],{"xmlns":1839},[1841,5518,5519,5523],{},[1844,5520,5521],{},[1851,5522,4965],{},[1880,5524,4965],{"encoding":1882},[1828,5526,5528],{"className":5527,"ariaHidden":1849},[1887],[1828,5529,5531,5534],{"className":5530},[1891],[1828,5532],{"className":5533,"style":2973},[1895],[1828,5535,4965],{"className":5536,"style":2389},[1900,1925],"; causal analysis asks about 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A high predicted risk can coexist with zero treatment effect.",[1793,5621,5623],{"id":5622},"operate-the-system","Operate the system",[1798,5625,5626,5639],{},[1801,5627,5628],{},[1804,5629,5630,5633,5636],{},[1807,5631,5632],{},"Layer",[1807,5634,5635],{},"Numerator or signal",[1807,5637,5638],{},"Denominator or reference",[1817,5640,5641,5652,5663,5674,5685],{},[1804,5642,5643,5646,5649],{},[1822,5644,5645],{},"coverage",[1822,5647,5648],{},"eligible cases scored on time",[1822,5650,5651],{},"all eligible cases",[1804,5653,5654,5657,5660],{},[1822,5655,5656],{},"adoption",[1822,5658,5659],{},"executed recommendations",[1822,5661,5662],{},"delivered or viewed recommendations—state which",[1804,5664,5665,5668,5671],{},[1822,5666,5667],{},"calibration",[1822,5669,5670],{},"observed event rate in a score band",[1822,5672,5673],{},"mature, labelled decisions in that band",[1804,5675,5676,5679,5682],{},[1822,5677,5678],{},"subgroup error",[1822,5680,5681],{},"relevant errors for a defined group",[1822,5683,5684],{},"actual negatives, positives or predictions according to metric",[1804,5686,5687,5690,5693],{},[1822,5688,5689],{},"incremental value",[1822,5691,5692],{},"outcome difference caused by policy",[1822,5694,5695],{},"credible counterfactual, not historical total",[2054,5697,5698],{},"A metric without its denominator, comparison and response rule is not operationally complete.",[2054,5700,5701],{},[3588,5702,5704],{"href":5703},".\u002F25-worked-examples-pitfalls","Next: Worked Examples and Pitfalls",{"title":10,"searchDepth":5706,"depth":5706,"links":5707},2,[5708,5709,5710,5711,5712],{"id":1795,"depth":5706,"text":1796},{"id":2858,"depth":5706,"text":2859},{"id":3541,"depth":5706,"text":3542},{"id":4920,"depth":5706,"text":4921},{"id":5622,"depth":5706,"text":5623},"A compact map from business questions to quantities, assumptions and actions","md",{},true,{"title":390,"description":5713},"tFPD24MmjJBDTuiFx8XBcLM9ncmEsEEJ2Rk2lQSt_wM",[5720,5722],{"title":384,"path":385,"stem":386,"description":5721,"children":-1},"Formula routes, compact worked pitfalls and a dated evidence map",{"title":394,"path":395,"stem":396,"description":5723,"children":-1},"Short cases that expose common analytic errors before they reach a decision",1785754722949]