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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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可视化","\u002Fzh\u002Fplayground\u002F05-chartjs","zh\u002Fplayground\u002F05-chartjs",{"title":1634,"path":1635,"stem":1636,"children":1637},"概率论与数理统计","\u002Fzh\u002Fprob-and-stats","zh\u002Fprob-and-stats\u002Findex",[1638,1639,1645,1680,1727],{"title":1634,"path":1635,"stem":1636},{"title":1640,"path":1641,"stem":1642,"children":1643},"第零章：概率统计的对象与学习方法","\u002Fzh\u002Fprob-and-stats\u002F00-intro","zh\u002Fprob-and-stats\u002F00-intro\u002Findex",[1644],{"title":1640,"path":1641,"stem":1642},{"title":1646,"path":1647,"stem":1648,"children":1649,"page":249},"01 Probability","\u002Fzh\u002Fprob-and-stats\u002F01-probability","zh\u002Fprob-and-stats\u002F01-probability",[1650,1656,1662,1668,1674],{"title":1651,"path":1652,"stem":1653,"children":1654},"第一章：概率论基础","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F01-prob-theory","zh\u002Fprob-and-stats\u002F01-probability\u002F01-prob-theory\u002Findex",[1655],{"title":1651,"path":1652,"stem":1653},{"title":1657,"path":1658,"stem":1659,"children":1660},"第二章：随机变量与分布","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F02-random-variables","zh\u002Fprob-and-stats\u002F01-probability\u002F02-random-variables\u002Findex",[1661],{"title":1657,"path":1658,"stem":1659},{"title":1663,"path":1664,"stem":1665,"children":1666},"第三章：期望、方差与条件矩","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F03-moment","zh\u002Fprob-and-stats\u002F01-probability\u002F03-moment\u002Findex",[1667],{"title":1663,"path":1664,"stem":1665},{"title":1669,"path":1670,"stem":1671,"children":1672},"第四章：常见分布族与建模机制","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F04-families","zh\u002Fprob-and-stats\u002F01-probability\u002F04-families\u002Findex",[1673],{"title":1669,"path":1670,"stem":1671},{"title":1675,"path":1676,"stem":1677,"children":1678},"第五章：收敛与渐近理论","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F05-asymptotics","zh\u002Fprob-and-stats\u002F01-probability\u002F05-asymptotics\u002Findex",[1679],{"title":1675,"path":1676,"stem":1677},{"title":1681,"path":1682,"stem":1683,"children":1684,"page":249},"02 Statistics","\u002Fzh\u002Fprob-and-stats\u002F02-statistics","zh\u002Fprob-and-stats\u002F02-statistics",[1685,1691,1697,1703,1709,1715,1721],{"title":1686,"path":1687,"stem":1688,"children":1689},"第六章：抽样分布","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F01-sampling","zh\u002Fprob-and-stats\u002F02-statistics\u002F01-sampling\u002Findex",[1690],{"title":1686,"path":1687,"stem":1688},{"title":1692,"path":1693,"stem":1694,"children":1695},"第七章：区间估计","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F02-interval-estimation","zh\u002Fprob-and-stats\u002F02-statistics\u002F02-interval-estimation\u002Findex",[1696],{"title":1692,"path":1693,"stem":1694},{"title":1698,"path":1699,"stem":1700,"children":1701},"第八章：点估计理论","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F03-point-estimation","zh\u002Fprob-and-stats\u002F02-statistics\u002F03-point-estimation\u002Findex",[1702],{"title":1698,"path":1699,"stem":1700},{"title":1704,"path":1705,"stem":1706,"children":1707},"第九章：点估计方法","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F04-pe-method","zh\u002Fprob-and-stats\u002F02-statistics\u002F04-pe-method\u002Findex",[1708],{"title":1704,"path":1705,"stem":1706},{"title":1710,"path":1711,"stem":1712,"children":1713},"第十章：假设检验原理","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F05-hypothesis","zh\u002Fprob-and-stats\u002F02-statistics\u002F05-hypothesis\u002Findex",[1714],{"title":1710,"path":1711,"stem":1712},{"title":1716,"path":1717,"stem":1718,"children":1719},"第十一章：常用检验方法与选择","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F06-hypothesis-method","zh\u002Fprob-and-stats\u002F02-statistics\u002F06-hypothesis-method\u002Findex",[1720],{"title":1716,"path":1717,"stem":1718},{"title":1722,"path":1723,"stem":1724,"children":1725},"第十二章：Bootstrap 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process",[1798,1799,1800],"p",{},"Scholarship recipients have higher prior scores and stronger adviser support than non-recipients. Matching can align observed scores and support. It cannot align unrecorded motivation merely because the propensity-score model predicts receipt well.",[1798,1802,1803],{},"The identifying claim is conditional exchangeability:",[1805,1806,1809],"span",{"className":1807},[1808],"katex-display",[1805,1810,1813,1880],{"className":1811},[1812],"katex",[1805,1814,1817],{"className":1815},[1816],"katex-mathml",[1818,1819,1822],"math",{"xmlns":1820,"display":1821},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[1823,1824,1825,1875],"semantics",{},[1826,1827,1828,1833,1837,1839,1843,1846,1850,1852,1854,1857,1859,1861,1864,1867,1870,1873],"mrow",{},[1829,1830,1832],"mo",{"stretchy":1831},"false","(",[1834,1835,1836],"mi",{},"Y",[1829,1838,1832],{"stretchy":1831},[1840,1841,1842],"mn",{},"1",[1829,1844,1845],{"stretchy":1831},")",[1829,1847,1849],{"separator":1848},"true",",",[1834,1851,1836],{},[1829,1853,1832],{"stretchy":1831},[1840,1855,1856],{},"0",[1829,1858,1845],{"stretchy":1831},[1829,1860,1845],{"stretchy":1831},[1829,1862,1863],{},"⊥",[1834,1865,1866],{},"D",[1829,1868,1869],{},"∣",[1834,1871,1872],{},"X",[1829,1874,1849],{"separator":1848},[1876,1877,1879],"annotation",{"encoding":1878},"application\u002Fx-tex","(Y(1),Y(0))\\perp D\\mid X,",[1805,1881,1884,1946,1965],{"className":1882,"ariaHidden":1848},[1883],"katex-html",[1805,1885,1888,1893,1897,1903,1906,1909,1913,1917,1922,1925,1928,1931,1935,1939,1943],{"className":1886},[1887],"base",[1805,1889],{"className":1890,"style":1892},[1891],"strut","height:1em;vertical-align:-0.25em;",[1805,1894,1832],{"className":1895},[1896],"mopen",[1805,1898,1836],{"className":1899,"style":1902},[1900,1901],"mord","mathnormal","margin-right:0.2222em;",[1805,1904,1832],{"className":1905},[1896],[1805,1907,1842],{"className":1908},[1900],[1805,1910,1845],{"className":1911},[1912],"mclose",[1805,1914,1849],{"className":1915},[1916],"mpunct",[1805,1918],{"className":1919,"style":1921},[1920],"mspace","margin-right:0.1667em;",[1805,1923,1836],{"className":1924,"style":1902},[1900,1901],[1805,1926,1832],{"className":1927},[1896],[1805,1929,1856],{"className":1930},[1900],[1805,1932,1934],{"className":1933},[1912],"))",[1805,1936],{"className":1937,"style":1938},[1920],"margin-right:0.2778em;",[1805,1940,1863],{"className":1941},[1942],"mrel",[1805,1944],{"className":1945,"style":1938},[1920],[1805,1947,1949,1952,1956,1959,1962],{"className":1948},[1887],[1805,1950],{"className":1951,"style":1892},[1891],[1805,1953,1866],{"className":1954,"style":1955},[1900,1901],"margin-right:0.0278em;",[1805,1957],{"className":1958,"style":1938},[1920],[1805,1960,1869],{"className":1961},[1942],[1805,1963],{"className":1964,"style":1938},[1920],[1805,1966,1968,1972,1976],{"className":1967},[1887],[1805,1969],{"className":1970,"style":1971},[1891],"height:0.8778em;vertical-align:-0.1944em;",[1805,1973,1872],{"className":1974,"style":1975},[1900,1901],"margin-right:0.0785em;",[1805,1977,1849],{"className":1978},[1916],[1798,1980,1981],{},"plus positivity: every covariate profile of interest has a non-zero chance of each treatment. These are substantive claims about assignment, not consequences of balance.",[1793,1983,1985],{"id":1984},"choose-the-target-before-the-weights","Choose the target before the weights",[1798,1987,1988,1989,2118],{},"Let ",[1805,1990,1992,2033],{"className":1991},[1812],[1805,1993,1995],{"className":1994},[1816],[1818,1996,1997],{"xmlns":1820},[1823,1998,1999,2030],{},[1826,2000,2001,2004,2006,2008,2010,2013,2016,2018,2020,2022,2024,2026,2028],{},[1834,2002,2003],{},"e",[1829,2005,1832],{"stretchy":1831},[1834,2007,1872],{},[1829,2009,1845],{"stretchy":1831},[1829,2011,2012],{},"=",[1834,2014,2015],{},"P",[1829,2017,1832],{"stretchy":1831},[1834,2019,1866],{},[1829,2021,2012],{},[1840,2023,1842],{},[1829,2025,1869],{},[1834,2027,1872],{},[1829,2029,1845],{"stretchy":1831},[1876,2031,2032],{"encoding":1878},"e(X)=P(D=1\\mid X)",[1805,2034,2036,2063,2088,2106],{"className":2035,"ariaHidden":1848},[1883],[1805,2037,2039,2042,2045,2048,2051,2054,2057,2060],{"className":2038},[1887],[1805,2040],{"className":2041,"style":1892},[1891],[1805,2043,2003],{"className":2044},[1900,1901],[1805,2046,1832],{"className":2047},[1896],[1805,2049,1872],{"className":2050,"style":1975},[1900,1901],[1805,2052,1845],{"className":2053},[1912],[1805,2055],{"className":2056,"style":1938},[1920],[1805,2058,2012],{"className":2059},[1942],[1805,2061],{"className":2062,"style":1938},[1920],[1805,2064,2066,2069,2073,2076,2079,2082,2085],{"className":2065},[1887],[1805,2067],{"className":2068,"style":1892},[1891],[1805,2070,2015],{"className":2071,"style":2072},[1900,1901],"margin-right:0.1389em;",[1805,2074,1832],{"className":2075},[1896],[1805,2077,1866],{"className":2078,"style":1955},[1900,1901],[1805,2080],{"className":2081,"style":1938},[1920],[1805,2083,2012],{"className":2084},[1942],[1805,2086],{"className":2087,"style":1938},[1920],[1805,2089,2091,2094,2097,2100,2103],{"className":2090},[1887],[1805,2092],{"className":2093,"style":1892},[1891],[1805,2095,1842],{"className":2096},[1900],[1805,2098],{"className":2099,"style":1938},[1920],[1805,2101,1869],{"className":2102},[1942],[1805,2104],{"className":2105,"style":1938},[1920],[1805,2107,2109,2112,2115],{"className":2108},[1887],[1805,2110],{"className":2111,"style":1892},[1891],[1805,2113,1872],{"className":2114,"style":1975},[1900,1901],[1805,2116,1845],{"className":2117},[1912],".",[2120,2121,2122,2142],"table",{},[2123,2124,2125],"thead",{},[2126,2127,2128,2132,2136,2139],"tr",{},[2129,2130,2131],"th",{},"Target",[2129,2133,2135],{"align":2134},"right","Treated weight",[2129,2137,2138],{"align":2134},"Control weight",[2129,2140,2141],{},"Question",[2143,2144,2145,2297,2407],"tbody",{},[2126,2146,2147,2151,2207,2294],{},[2148,2149,2150],"td",{},"ATE",[2148,2152,2153],{"align":2134},[1805,2154,2156,2182],{"className":2155},[1812],[1805,2157,2159],{"className":2158},[1816],[1818,2160,2161],{"xmlns":1820},[1823,2162,2163,2179],{},[1826,2164,2165,2167,2171,2173,2175,2177],{},[1840,2166,1842],{},[1834,2168,2170],{"mathvariant":2169},"normal","\u002F",[1834,2172,2003],{},[1829,2174,1832],{"stretchy":1831},[1834,2176,1872],{},[1829,2178,1845],{"stretchy":1831},[1876,2180,2181],{"encoding":1878},"1\u002Fe(X)",[1805,2183,2185],{"className":2184,"ariaHidden":1848},[1883],[1805,2186,2188,2191,2195,2198,2201,2204],{"className":2187},[1887],[1805,2189],{"className":2190,"style":1892},[1891],[1805,2192,2194],{"className":2193},[1900],"1\u002F",[1805,2196,2003],{"className":2197},[1900,1901],[1805,2199,1832],{"className":2200},[1896],[1805,2202,1872],{"className":2203,"style":1975},[1900,1901],[1805,2205,1845],{"className":2206},[1912],[2148,2208,2209],{"align":2134},[1805,2210,2212,2247],{"className":2211},[1812],[1805,2213,2215],{"className":2214},[1816],[1818,2216,2217],{"xmlns":1820},[1823,2218,2219,2244],{},[1826,2220,2221,2223,2225,2228,2230,2233,2235,2237,2239,2241],{},[1840,2222,1842],{},[1834,2224,2170],{"mathvariant":2169},[1829,2226,2227],{"stretchy":1831},"[",[1840,2229,1842],{},[1829,2231,2232],{},"−",[1834,2234,2003],{},[1829,2236,1832],{"stretchy":1831},[1834,2238,1872],{},[1829,2240,1845],{"stretchy":1831},[1829,2242,2243],{"stretchy":1831},"]",[1876,2245,2246],{"encoding":1878},"1\u002F[1-e(X)]",[1805,2248,2250,2275],{"className":2249,"ariaHidden":1848},[1883],[1805,2251,2253,2256,2259,2262,2265,2268,2272],{"className":2252},[1887],[1805,2254],{"className":2255,"style":1892},[1891],[1805,2257,2194],{"className":2258},[1900],[1805,2260,2227],{"className":2261},[1896],[1805,2263,1842],{"className":2264},[1900],[1805,2266],{"className":2267,"style":1902},[1920],[1805,2269,2232],{"className":2270},[2271],"mbin",[1805,2273],{"className":2274,"style":1902},[1920],[1805,2276,2278,2281,2284,2287,2290],{"className":2277},[1887],[1805,2279],{"className":2280,"style":1892},[1891],[1805,2282,2003],{"className":2283},[1900,1901],[1805,2285,1832],{"className":2286},[1896],[1805,2288,1872],{"className":2289,"style":1975},[1900,1901],[1805,2291,2293],{"className":2292},[1912],")]",[2148,2295,2296],{},"effect for the combined target population",[2126,2298,2299,2302,2304,2404],{},[2148,2300,2301],{},"ATT",[2148,2303,1842],{"align":2134},[2148,2305,2306],{"align":2134},[1805,2307,2309,2347],{"className":2308},[1812],[1805,2310,2312],{"className":2311},[1816],[1818,2313,2314],{"xmlns":1820},[1823,2315,2316,2344],{},[1826,2317,2318,2320,2322,2324,2326,2328,2330,2332,2334,2336,2338,2340,2342],{},[1834,2319,2003],{},[1829,2321,1832],{"stretchy":1831},[1834,2323,1872],{},[1829,2325,1845],{"stretchy":1831},[1834,2327,2170],{"mathvariant":2169},[1829,2329,2227],{"stretchy":1831},[1840,2331,1842],{},[1829,2333,2232],{},[1834,2335,2003],{},[1829,2337,1832],{"stretchy":1831},[1834,2339,1872],{},[1829,2341,1845],{"stretchy":1831},[1829,2343,2243],{"stretchy":1831},[1876,2345,2346],{"encoding":1878},"e(X)\u002F[1-e(X)]",[1805,2348,2350,2386],{"className":2349,"ariaHidden":1848},[1883],[1805,2351,2353,2356,2359,2362,2365,2368,2371,2374,2377,2380,2383],{"className":2352},[1887],[1805,2354],{"className":2355,"style":1892},[1891],[1805,2357,2003],{"className":2358},[1900,1901],[1805,2360,1832],{"className":2361},[1896],[1805,2363,1872],{"className":2364,"style":1975},[1900,1901],[1805,2366,1845],{"className":2367},[1912],[1805,2369,2170],{"className":2370},[1900],[1805,2372,2227],{"className":2373},[1896],[1805,2375,1842],{"className":2376},[1900],[1805,2378],{"className":2379,"style":1902},[1920],[1805,2381,2232],{"className":2382},[2271],[1805,2384],{"className":2385,"style":1902},[1920],[1805,2387,2389,2392,2395,2398,2401],{"className":2388},[1887],[1805,2390],{"className":2391,"style":1892},[1891],[1805,2393,2003],{"className":2394},[1900,1901],[1805,2396,1832],{"className":2397},[1896],[1805,2399,1872],{"className":2400,"style":1975},[1900,1901],[1805,2402,2293],{"className":2403},[1912],[2148,2405,2406],{},"effect for treated units",[2126,2408,2409,2412,2481,2527],{},[2148,2410,2411],{},"overlap",[2148,2413,2414],{"align":2134},[1805,2415,2417,2441],{"className":2416},[1812],[1805,2418,2420],{"className":2419},[1816],[1818,2421,2422],{"xmlns":1820},[1823,2423,2424,2438],{},[1826,2425,2426,2428,2430,2432,2434,2436],{},[1840,2427,1842],{},[1829,2429,2232],{},[1834,2431,2003],{},[1829,2433,1832],{"stretchy":1831},[1834,2435,1872],{},[1829,2437,1845],{"stretchy":1831},[1876,2439,2440],{"encoding":1878},"1-e(X)",[1805,2442,2444,2463],{"className":2443,"ariaHidden":1848},[1883],[1805,2445,2447,2451,2454,2457,2460],{"className":2446},[1887],[1805,2448],{"className":2449,"style":2450},[1891],"height:0.7278em;vertical-align:-0.0833em;",[1805,2452,1842],{"className":2453},[1900],[1805,2455],{"className":2456,"style":1902},[1920],[1805,2458,2232],{"className":2459},[2271],[1805,2461],{"className":2462,"style":1902},[1920],[1805,2464,2466,2469,2472,2475,2478],{"className":2465},[1887],[1805,2467],{"className":2468,"style":1892},[1891],[1805,2470,2003],{"className":2471},[1900,1901],[1805,2473,1832],{"className":2474},[1896],[1805,2476,1872],{"className":2477,"style":1975},[1900,1901],[1805,2479,1845],{"className":2480},[1912],[2148,2482,2483],{"align":2134},[1805,2484,2486,2506],{"className":2485},[1812],[1805,2487,2489],{"className":2488},[1816],[1818,2490,2491],{"xmlns":1820},[1823,2492,2493,2503],{},[1826,2494,2495,2497,2499,2501],{},[1834,2496,2003],{},[1829,2498,1832],{"stretchy":1831},[1834,2500,1872],{},[1829,2502,1845],{"stretchy":1831},[1876,2504,2505],{"encoding":1878},"e(X)",[1805,2507,2509],{"className":2508,"ariaHidden":1848},[1883],[1805,2510,2512,2515,2518,2521,2524],{"className":2511},[1887],[1805,2513],{"className":2514,"style":1892},[1891],[1805,2516,2003],{"className":2517},[1900,1901],[1805,2519,1832],{"className":2520},[1896],[1805,2522,1872],{"className":2523,"style":1975},[1900,1901],[1805,2525,1845],{"className":2526},[1912],[2148,2528,2529],{},"effect where treatment choice was most uncertain",[1798,2531,2532],{},"Changing weights changes the population. It is not merely a technical stabilisation.",[1793,2534,2536],{"id":2535},"a-four-student-example","A four-student example",[2120,2538,2539,2658],{},[2123,2540,2541],{},[2126,2542,2543,2546,2578,2609,2655],{},[2129,2544,2545],{},"Student",[2129,2547,2548,2549],{"align":2134},"Receipt ",[1805,2550,2552,2565],{"className":2551},[1812],[1805,2553,2555],{"className":2554},[1816],[1818,2556,2557],{"xmlns":1820},[1823,2558,2559,2563],{},[1826,2560,2561],{},[1834,2562,1866],{},[1876,2564,1866],{"encoding":1878},[1805,2566,2568],{"className":2567,"ariaHidden":1848},[1883],[1805,2569,2571,2575],{"className":2570},[1887],[1805,2572],{"className":2573,"style":2574},[1891],"height:0.6833em;",[1805,2576,1866],{"className":2577,"style":1955},[1900,1901],[2129,2579,2580,2581],{"align":2134},"Completion ",[1805,2582,2584,2597],{"className":2583},[1812],[1805,2585,2587],{"className":2586},[1816],[1818,2588,2589],{"xmlns":1820},[1823,2590,2591,2595],{},[1826,2592,2593],{},[1834,2594,1836],{},[1876,2596,1836],{"encoding":1878},[1805,2598,2600],{"className":2599,"ariaHidden":1848},[1883],[1805,2601,2603,2606],{"className":2602},[1887],[1805,2604],{"className":2605,"style":2574},[1891],[1805,2607,1836],{"className":2608,"style":1902},[1900,1901],[2129,2610,2611,2612],{"align":2134},"Propensity ",[1805,2613,2615,2634],{"className":2614},[1812],[1805,2616,2618],{"className":2617},[1816],[1818,2619,2620],{"xmlns":1820},[1823,2621,2622,2632],{},[1826,2623,2624,2626,2628,2630],{},[1834,2625,2003],{},[1829,2627,1832],{"stretchy":1831},[1834,2629,1872],{},[1829,2631,1845],{"stretchy":1831},[1876,2633,2505],{"encoding":1878},[1805,2635,2637],{"className":2636,"ariaHidden":1848},[1883],[1805,2638,2640,2643,2646,2649,2652],{"className":2639},[1887],[1805,2641],{"className":2642,"style":1892},[1891],[1805,2644,2003],{"className":2645},[1900,1901],[1805,2647,1832],{"className":2648},[1896],[1805,2650,1872],{"className":2651,"style":1975},[1900,1901],[1805,2653,1845],{"className":2654},[1912],[2129,2656,2657],{"align":2134},"ATE weight",[2143,2659,2660,2675,2690,2704],{},[2126,2661,2662,2665,2667,2669,2672],{},[2148,2663,2664],{},"A",[2148,2666,1842],{"align":2134},[2148,2668,1842],{"align":2134},[2148,2670,2671],{"align":2134},"0.80",[2148,2673,2674],{"align":2134},"1.25",[2126,2676,2677,2680,2682,2684,2687],{},[2148,2678,2679],{},"B",[2148,2681,1842],{"align":2134},[2148,2683,1856],{"align":2134},[2148,2685,2686],{"align":2134},"0.55",[2148,2688,2689],{"align":2134},"1.82",[2126,2691,2692,2695,2697,2699,2702],{},[2148,2693,2694],{},"C",[2148,2696,1856],{"align":2134},[2148,2698,1842],{"align":2134},[2148,2700,2701],{"align":2134},"0.45",[2148,2703,2689],{"align":2134},[2126,2705,2706,2708,2710,2712,2715],{},[2148,2707,1866],{},[2148,2709,1856],{"align":2134},[2148,2711,1856],{"align":2134},[2148,2713,2714],{"align":2134},"0.05",[2148,2716,2717],{"align":2134},"1.05",[1798,2719,2720,2721,2789],{},"Student B and C receive more weight because their observed treatment was less predictable. If a treated student had ",[1805,2722,2724,2749],{"className":2723},[1812],[1805,2725,2727],{"className":2726},[1816],[1818,2728,2729],{"xmlns":1820},[1823,2730,2731,2746],{},[1826,2732,2733,2735,2737,2739,2741,2743],{},[1834,2734,2003],{},[1829,2736,1832],{"stretchy":1831},[1834,2738,1872],{},[1829,2740,1845],{"stretchy":1831},[1829,2742,2012],{},[1840,2744,2745],{},"0.02",[1876,2747,2748],{"encoding":1878},"e(X)=0.02",[1805,2750,2752,2779],{"className":2751,"ariaHidden":1848},[1883],[1805,2753,2755,2758,2761,2764,2767,2770,2773,2776],{"className":2754},[1887],[1805,2756],{"className":2757,"style":1892},[1891],[1805,2759,2003],{"className":2760},[1900,1901],[1805,2762,1832],{"className":2763},[1896],[1805,2765,1872],{"className":2766,"style":1975},[1900,1901],[1805,2768,1845],{"className":2769},[1912],[1805,2771],{"className":2772,"style":1938},[1920],[1805,2774,2012],{"className":2775},[1942],[1805,2777],{"className":2778,"style":1938},[1920],[1805,2780,2782,2786],{"className":2781},[1887],[1805,2783],{"className":2784,"style":2785},[1891],"height:0.6444em;",[1805,2787,2745],{"className":2788},[1900],", the ATE weight would be 50: one observation could dominate the result. That is a lack-of-overlap warning, not a request for a more elaborate classifier.",[1793,2791,2793],{"id":2792},"design-stage-outcomes-stay-hidden","Design stage: outcomes stay hidden",[2795,2796,2797,2801,2804,2807,2810,2813,2816],"ol",{},[2798,2799,2800],"li",{},"define pre-treatment covariates from an assignment story;",[2798,2802,2803],{},"estimate or construct a distance\u002Fpropensity score;",[2798,2805,2806],{},"inspect common support and extreme weights;",[2798,2808,2809],{},"match, subclassify or weight;",[2798,2811,2812],{},"assess balance and effective sample size;",[2798,2814,2815],{},"revise the design without looking for a favourable outcome effect;",[2798,2817,2818],{},"estimate effects and uncertainty for the retained target population.",[1798,2820,2821,2822,2913],{},"For weights ",[1805,2823,2825,2846],{"className":2824},[1812],[1805,2826,2828],{"className":2827},[1816],[1818,2829,2830],{"xmlns":1820},[1823,2831,2832,2843],{},[1826,2833,2834],{},[2835,2836,2837,2840],"msub",{},[1834,2838,2839],{},"w",[1834,2841,2842],{},"i",[1876,2844,2845],{"encoding":1878},"w_i",[1805,2847,2849],{"className":2848,"ariaHidden":1848},[1883],[1805,2850,2852,2856],{"className":2851},[1887],[1805,2853],{"className":2854,"style":2855},[1891],"height:0.5806em;vertical-align:-0.15em;",[1805,2857,2859,2863],{"className":2858},[1900],[1805,2860,2839],{"className":2861,"style":2862},[1900,1901],"margin-right:0.0269em;",[1805,2864,2867],{"className":2865},[2866],"msupsub",[1805,2868,2872,2904],{"className":2869},[2870,2871],"vlist-t","vlist-t2",[1805,2873,2876,2899],{"className":2874},[2875],"vlist-r",[1805,2877,2881],{"className":2878,"style":2880},[2879],"vlist","height:0.3117em;",[1805,2882,2884,2889],{"style":2883},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[1805,2885],{"className":2886,"style":2888},[2887],"pstrut","height:2.7em;",[1805,2890,2896],{"className":2891},[2892,2893,2894,2895],"sizing","reset-size6","size3","mtight",[1805,2897,2842],{"className":2898},[1900,1901,2895],[1805,2900,2903],{"className":2901},[2902],"vlist-s","​",[1805,2905,2907],{"className":2906},[2875],[1805,2908,2911],{"className":2909,"style":2910},[2879],"height:0.15em;",[1805,2912],{},", a useful information diagnostic is",[1805,2915,2917],{"className":2916},[1808],[1805,2918,2920,2996],{"className":2919},[1812],[1805,2921,2923],{"className":2922},[1816],[1818,2924,2925],{"xmlns":1820,"display":1821},[1823,2926,2927,2993],{},[1826,2928,2929,2943,2945,2991],{},[2835,2930,2931,2934],{},[1834,2932,2933],{},"n",[1826,2935,2936,2938,2941],{},[1834,2937,2003],{},[1834,2939,2940],{},"f",[1834,2942,2940],{},[1829,2944,2012],{},[2946,2947,2948,2974],"mfrac",{},[1826,2949,2950,2952,2960,2966],{},[1829,2951,1832],{"stretchy":1831},[2953,2954,2955,2958],"munder",{},[1829,2956,2957],{},"∑",[1834,2959,2842],{},[2835,2961,2962,2964],{},[1834,2963,2839],{},[1834,2965,2842],{},[2967,2968,2969,2971],"msup",{},[1829,2970,1845],{"stretchy":1831},[1840,2972,2973],{},"2",[1826,2975,2976,2982],{},[2953,2977,2978,2980],{},[1829,2979,2957],{},[1834,2981,2842],{},[2983,2984,2985,2987,2989],"msubsup",{},[1834,2986,2839],{},[1834,2988,2842],{},[1840,2990,2973],{},[1834,2992,2118],{"mathvariant":2169},[1876,2994,2995],{"encoding":1878},"n_{eff}=\\frac{(\\sum_i w_i)^2}{\\sum_i w_i^2}.",[1805,2997,2999,3068],{"className":2998,"ariaHidden":1848},[1883],[1805,3000,3002,3006,3059,3062,3065],{"className":3001},[1887],[1805,3003],{"className":3004,"style":3005},[1891],"height:0.7167em;vertical-align:-0.2861em;",[1805,3007,3009,3012],{"className":3008},[1900],[1805,3010,2933],{"className":3011},[1900,1901],[1805,3013,3015],{"className":3014},[2866],[1805,3016,3018,3050],{"className":3017},[2870,2871],[1805,3019,3021,3047],{"className":3020},[2875],[1805,3022,3025],{"className":3023,"style":3024},[2879],"height:0.3361em;",[1805,3026,3028,3031],{"style":3027},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1805,3029],{"className":3030,"style":2888},[2887],[1805,3032,3034],{"className":3033},[2892,2893,2894,2895],[1805,3035,3037,3040,3044],{"className":3036},[1900,2895],[1805,3038,2003],{"className":3039},[1900,1901,2895],[1805,3041,2940],{"className":3042,"style":3043},[1900,1901,2895],"margin-right:0.1076em;",[1805,3045,2940],{"className":3046,"style":3043},[1900,1901,2895],[1805,3048,2903],{"className":3049},[2902],[1805,3051,3053],{"className":3052},[2875],[1805,3054,3057],{"className":3055,"style":3056},[2879],"height:0.2861em;",[1805,3058],{},[1805,3060],{"className":3061,"style":1938},[1920],[1805,3063,2012],{"className":3064},[1942],[1805,3066],{"className":3067,"style":1938},[1920],[1805,3069,3071,3075,3362],{"className":3070},[1887],[1805,3072],{"className":3073,"style":3074},[1891],"height:2.4895em;vertical-align:-0.9857em;",[1805,3076,3078,3082,3359],{"className":3077},[1900],[1805,3079],{"className":3080},[1896,3081],"nulldelimiter",[1805,3083,3085],{"className":3084},[2946],[1805,3086,3088,3350],{"className":3087},[2870,2871],[1805,3089,3091,3347],{"className":3090},[2875],[1805,3092,3095,3210,3221],{"className":3093,"style":3094},[2879],"height:1.5038em;",[1805,3096,3098,3102],{"style":3097},"top:-2.314em;",[1805,3099],{"className":3100,"style":3101},[2887],"height:3em;",[1805,3103,3105,3152,3155],{"className":3104},[1900],[1805,3106,3109,3115],{"className":3107},[3108],"mop",[1805,3110,2957],{"className":3111,"style":3114},[3108,3112,3113],"op-symbol","small-op","position:relative;top:0em;",[1805,3116,3118],{"className":3117},[2866],[1805,3119,3121,3143],{"className":3120},[2870,2871],[1805,3122,3124,3140],{"className":3123},[2875],[1805,3125,3128],{"className":3126,"style":3127},[2879],"height:0.162em;",[1805,3129,3131,3134],{"style":3130},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1805,3132],{"className":3133,"style":2888},[2887],[1805,3135,3137],{"className":3136},[2892,2893,2894,2895],[1805,3138,2842],{"className":3139},[1900,1901,2895],[1805,3141,2903],{"className":3142},[2902],[1805,3144,3146],{"className":3145},[2875],[1805,3147,3150],{"className":3148,"style":3149},[2879],"height:0.2997em;",[1805,3151],{},[1805,3153],{"className":3154,"style":1921},[1920],[1805,3156,3158,3161],{"className":3157},[1900],[1805,3159,2839],{"className":3160,"style":2862},[1900,1901],[1805,3162,3164],{"className":3163},[2866],[1805,3165,3167,3201],{"className":3166},[2870,2871],[1805,3168,3170,3198],{"className":3169},[2875],[1805,3171,3174,3186],{"className":3172,"style":3173},[2879],"height:0.7959em;",[1805,3175,3177,3180],{"style":3176},"top:-2.4231em;margin-left:-0.0269em;margin-right:0.05em;",[1805,3178],{"className":3179,"style":2888},[2887],[1805,3181,3183],{"className":3182},[2892,2893,2894,2895],[1805,3184,2842],{"className":3185},[1900,1901,2895],[1805,3187,3189,3192],{"style":3188},"top:-3.0448em;margin-right:0.05em;",[1805,3190],{"className":3191,"style":2888},[2887],[1805,3193,3195],{"className":3194},[2892,2893,2894,2895],[1805,3196,2973],{"className":3197},[1900,2895],[1805,3199,2903],{"className":3200},[2902],[1805,3202,3204],{"className":3203},[2875],[1805,3205,3208],{"className":3206,"style":3207},[2879],"height:0.2769em;",[1805,3209],{},[1805,3211,3213,3216],{"style":3212},"top:-3.23em;",[1805,3214],{"className":3215,"style":3101},[2887],[1805,3217],{"className":3218,"style":3220},[3219],"frac-line","border-bottom-width:0.04em;",[1805,3222,3224,3227],{"style":3223},"top:-3.6897em;",[1805,3225],{"className":3226,"style":3101},[2887],[1805,3228,3230,3233,3273,3276,3316],{"className":3229},[1900],[1805,3231,1832],{"className":3232},[1896],[1805,3234,3236,3239],{"className":3235},[3108],[1805,3237,2957],{"className":3238,"style":3114},[3108,3112,3113],[1805,3240,3242],{"className":3241},[2866],[1805,3243,3245,3265],{"className":3244},[2870,2871],[1805,3246,3248,3262],{"className":3247},[2875],[1805,3249,3251],{"className":3250,"style":3127},[2879],[1805,3252,3253,3256],{"style":3130},[1805,3254],{"className":3255,"style":2888},[2887],[1805,3257,3259],{"className":3258},[2892,2893,2894,2895],[1805,3260,2842],{"className":3261},[1900,1901,2895],[1805,3263,2903],{"className":3264},[2902],[1805,3266,3268],{"className":3267},[2875],[1805,3269,3271],{"className":3270,"style":3149},[2879],[1805,3272],{},[1805,3274],{"className":3275,"style":1921},[1920],[1805,3277,3279,3282],{"className":3278},[1900],[1805,3280,2839],{"className":3281,"style":2862},[1900,1901],[1805,3283,3285],{"className":3284},[2866],[1805,3286,3288,3308],{"className":3287},[2870,2871],[1805,3289,3291,3305],{"className":3290},[2875],[1805,3292,3294],{"className":3293,"style":2880},[2879],[1805,3295,3296,3299],{"style":2883},[1805,3297],{"className":3298,"style":2888},[2887],[1805,3300,3302],{"className":3301},[2892,2893,2894,2895],[1805,3303,2842],{"className":3304},[1900,1901,2895],[1805,3306,2903],{"className":3307},[2902],[1805,3309,3311],{"className":3310},[2875],[1805,3312,3314],{"className":3313,"style":2910},[2879],[1805,3315],{},[1805,3317,3319,3322],{"className":3318},[1912],[1805,3320,1845],{"className":3321},[1912],[1805,3323,3325],{"className":3324},[2866],[1805,3326,3328],{"className":3327},[2870],[1805,3329,3331],{"className":3330},[2875],[1805,3332,3335],{"className":3333,"style":3334},[2879],"height:0.8141em;",[1805,3336,3338,3341],{"style":3337},"top:-3.063em;margin-right:0.05em;",[1805,3339],{"className":3340,"style":2888},[2887],[1805,3342,3344],{"className":3343},[2892,2893,2894,2895],[1805,3345,2973],{"className":3346},[1900,2895],[1805,3348,2903],{"className":3349},[2902],[1805,3351,3353],{"className":3352},[2875],[1805,3354,3357],{"className":3355,"style":3356},[2879],"height:0.9857em;",[1805,3358],{},[1805,3360],{"className":3361},[1912,3081],[1805,3363,2118],{"className":3364},[1900],[1798,3366,3367,3368,3476],{},"Ten thousand records with ",[1805,3369,3371,3400],{"className":3370},[1812],[1805,3372,3374],{"className":3373},[1816],[1818,3375,3376],{"xmlns":1820},[1823,3377,3378,3397],{},[1826,3379,3380,3392,3394],{},[2835,3381,3382,3384],{},[1834,3383,2933],{},[1826,3385,3386,3388,3390],{},[1834,3387,2003],{},[1834,3389,2940],{},[1834,3391,2940],{},[1829,3393,2012],{},[1840,3395,3396],{},"420",[1876,3398,3399],{"encoding":1878},"n_{eff}=420",[1805,3401,3403,3467],{"className":3402,"ariaHidden":1848},[1883],[1805,3404,3406,3409,3458,3461,3464],{"className":3405},[1887],[1805,3407],{"className":3408,"style":3005},[1891],[1805,3410,3412,3415],{"className":3411},[1900],[1805,3413,2933],{"className":3414},[1900,1901],[1805,3416,3418],{"className":3417},[2866],[1805,3419,3421,3450],{"className":3420},[2870,2871],[1805,3422,3424,3447],{"className":3423},[2875],[1805,3425,3427],{"className":3426,"style":3024},[2879],[1805,3428,3429,3432],{"style":3027},[1805,3430],{"className":3431,"style":2888},[2887],[1805,3433,3435],{"className":3434},[2892,2893,2894,2895],[1805,3436,3438,3441,3444],{"className":3437},[1900,2895],[1805,3439,2003],{"className":3440},[1900,1901,2895],[1805,3442,2940],{"className":3443,"style":3043},[1900,1901,2895],[1805,3445,2940],{"className":3446,"style":3043},[1900,1901,2895],[1805,3448,2903],{"className":3449},[2902],[1805,3451,3453],{"className":3452},[2875],[1805,3454,3456],{"className":3455,"style":3056},[2879],[1805,3457],{},[1805,3459],{"className":3460,"style":1938},[1920],[1805,3462,2012],{"className":3463},[1942],[1805,3465],{"className":3466,"style":1938},[1920],[1805,3468,3470,3473],{"className":3469},[1887],[1805,3471],{"className":3472,"style":2785},[1891],[1805,3474,3396],{"className":3475},[1900]," do not provide ten thousand equally informative comparisons.",[1793,3478,3480,3481,3510],{"id":3479},"balance-is-not-a-propensity-score-ppp-value","Balance is not a propensity-score ",[1805,3482,3484,3497],{"className":3483},[1812],[1805,3485,3487],{"className":3486},[1816],[1818,3488,3489],{"xmlns":1820},[1823,3490,3491,3495],{},[1826,3492,3493],{},[1834,3494,1798],{},[1876,3496,1798],{"encoding":1878},[1805,3498,3500],{"className":3499,"ariaHidden":1848},[1883],[1805,3501,3503,3507],{"className":3502},[1887],[1805,3504],{"className":3505,"style":3506},[1891],"height:0.625em;vertical-align:-0.1944em;",[1805,3508,1798],{"className":3509},[1900,1901],"-value",[1798,3512,3513],{},"Use standardised mean differences, distribution plots and substantively important interactions. A large sample can make a negligible imbalance statistically significant; a small sample can hide important imbalance.",[2120,3515,3516,3526],{},[2123,3517,3518],{},[2126,3519,3520,3523],{},[2129,3521,3522],{},"Diagnostic",[2129,3524,3525],{},"Useful question",[2143,3527,3528,3536,3544,3552,3560],{},[2126,3529,3530,3533],{},[2148,3531,3532],{},"standardised difference",[2148,3534,3535],{},"are covariate means close on a scale-free metric?",[2126,3537,3538,3541],{},[2148,3539,3540],{},"variance\u002Fquantile comparison",[2148,3542,3543],{},"do distributions align beyond the mean?",[2126,3545,3546,3549],{},[2148,3547,3548],{},"propensity overlap",[2148,3550,3551],{},"are both treatments represented in the target region?",[2126,3553,3554,3557],{},[2148,3555,3556],{},"maximum weight",[2148,3558,3559],{},"can one unit control the estimate?",[2126,3561,3562,3565],{},[2148,3563,3564],{},"effective sample size",[2148,3566,3567],{},"how much information remains after weighting?",[1793,3569,3571],{"id":3570},"doubly-robust-does-not-mean-assumption-free","Doubly robust does not mean assumption-free",[1798,3573,3574,3575,3579],{},"An augmented inverse-probability estimator combines an outcome model and a treatment model. Under regularity conditions it can remain consistent when one nuisance model is correct. It does ",[3576,3577,3578],"strong",{},"not"," survive unmeasured confounding, failed positivity, post-treatment controls or two badly misspecified models.",[1798,3581,3582,3589,3590,3595],{},[3583,3584,3588],"a",{"href":3585,"rel":3586},"https:\u002F\u002Fdoi.org\u002F10.1214\u002F09-STS313",[3587],"nofollow","Stuart (2010)"," reviews matching as a design strategy. ",[3583,3591,3594],{"href":3592,"rel":3593},"https:\u002F\u002Fdoi.org\u002F10.1080\u002F01621459.2016.1260466",[3587],"Li, Morgan and Zaslavsky (2018)"," develop overlap weights that target the region with greatest covariate overlap.",[1793,3597,3599],{"id":3598},"a-defensible-conclusion","A defensible conclusion",[1798,3601,3602],{},"Weak: “After propensity-score matching, treatment is as good as random.”",[1798,3604,3605],{},"Stronger: “Among applicants in the shared-support region, weighted pre-treatment covariates are closely balanced. The estimate is causal if the recorded covariates suffice to control joint causes of receipt and completion; adviser motivation remains a plausible unmeasured confounder.”",[1793,3607,3609],{"id":3608},"quick-check","Quick check",[1798,3611,3612],{},"Trimming removes all high-need applicants because every high-need applicant received the scholarship. What changed?",[3614,3615,3617],"legacy-details",{"title":3616},"Answer","The data contain no untreated comparison for high-need applicants. Trimming may improve internal credibility, but the estimand now excludes that group. State the new target population; do not generalise the trimmed estimate back without extra assumptions or evidence.",[1798,3619,3620],{},[3583,3621,3623],{"href":3622},".\u002F15-synthetic-control","Next: Synthetic Control",{"title":10,"searchDepth":3625,"depth":3625,"links":3626},2,[3627,3628,3629,3630,3631,3633,3634,3635],{"id":1795,"depth":3625,"text":1796},{"id":1984,"depth":3625,"text":1985},{"id":2535,"depth":3625,"text":2536},{"id":2792,"depth":3625,"text":2793},{"id":3479,"depth":3625,"text":3632},"Balance is not a propensity-score ppp-value",{"id":3570,"depth":3625,"text":3571},{"id":3598,"depth":3625,"text":3599},{"id":3608,"depth":3625,"text":3609},"Construct observable comparison groups while keeping exchangeability, balance and positivity distinct","md",{},true,{"title":622,"description":3636},"sbSJHsNz7RL4VjH-t68KkcPurOYbaSiWPDAPwK9vuuw",[3643,3645],{"title":618,"path":619,"stem":620,"description":3644,"children":-1},"Turn a treatment threshold into a local causal comparison and audit continuity, manipulation and bandwidth",{"title":626,"path":627,"stem":628,"description":3646,"children":-1},"Build and stress-test a weighted counterfactual for one or a few treated aggregate units",1785754728818]