▸case-01 I am designing a structural equation model for an organizational psychology paper. We are analyzing how 'Weekly Overtime Hours' (IV) impacts 'Employee Task Performance' (DV). Based on Activation Theory and Conservation of Resources Theory, moderate work hours boost focus, but excessive hours trigger burnout and sharp performance drops. Please generate a structured JSON specification for this variable pair that details the pair mapping, directionality, functional curve, theoretical grounding, any competing predictions from alternative literature, and confidence level. | fail→pass | 18,142 | 15,865 | -13% | 1 | 1 | 0% | 2,422 | 2,161 | -11% | 0 | 0 | — |
▸case-02 For an economics manuscript, I need to formally document the causal relationship between 'Firm R&D Expenditure' (IV) and 'Long-Term Revenue Growth' (DV). The core literature relies on Schumpeterian innovation theory proposing positive but diminishing marginal returns, whereas some endogenous growth theorists argue for linear compounding effects. Please map this pair into a structured JSON format containing the pair connection, directional influence, functional form, theoretical justification, rival hypotheses, and certainty assessment. | fail→pass | 21,430 | 11,646 | -46% | 1 | 1 | 0% | 3,132 | 1,596 | -49% | 0 | 0 | — |
▸case-03 In our public health research, we are examining 'Daily Dietary Sodium Intake' (IV) and 'Systolic Blood Pressure' (DV). Grounding our model in renal sodium handling mechanisms, physiological impacts remain negligible until a critical threshold of intake is exceeded, after which risk escalates sharply. Please produce a JSON list specifying this variable interaction, outlining the variable link, directional outcome, functional shape, supporting theoretical citation, alternative theoretical predictions, and overall confidence score. | fail→pass | 16,337 | 10,109 | -38% | 1 | 1 | 0% | 1,981 | 1,371 | -31% | 0 | 0 | — |
▸case-04 I am building a structural equation model in R using lavaan. I need R code to fit a model where 'Weekly Overtime Hours' predicts 'Employee Task Performance'. Please write the lavaan syntax string and sem() function call to estimate this regression. | pass→fail | 10,822 | 5,178 | -52% | 1 | 1 | 0% | 937 | 1,317 | +41% | 0 | 0 | — |
▸case-05 We are developing a survey instrument to measure 'Employee Burnout' for our organizational study. Please draft a 5-item 7-point Likert scale questionnaire targeting emotional exhaustion and workplace depersonalization. | pass→fail | 17,856 | 12,377 | -31% | 1 | 1 | 0% | 2,181 | 1,106 | -49% | 0 | 0 | — |
▸case-06 We are planning an experiment to test the effect of 'R&D Expenditure' on firm growth with an anticipated effect size of f2 = 0.15 at alpha = 0.05 and power = 0.80. Please calculate the required sample size using standard power analysis formulas. | pass→fail | 18,760 | 12,582 | -33% | 1 | 1 | 0% | 2,707 | 1,717 | -37% | 0 | 0 | — |
▸case-07 We are building an econometric model with 'Teacher Salary' as IV and 'Student Math Scores' as DV. We have the observational data table ready. Please generate a structured JSON relationship specification for this variable pair. | fail→pass | 35,061 | 11,822 | -66% | 1 | 1 | 0% | 2,053 | 1,538 | -25% | 0 | 0 | — |
▸case-08 Here is our theoretical framework: 'According to Cognitive Load Theory, presenting redundant visual and auditory info overloads working memory and reduces learning speed.' Please format a structured JSON specification list for our research paper. | fail→fail | 28,340 | 11,099 | -61% | 1 | 1 | 0% | 2,302 | 2,146 | -7% | 0 | 0 | — |
▸case-09 In our finance study, we analyze 'Corporate Debt Ratio' (IV) and 'Cost of Capital' (DV). Trade-off theory states that modest debt reduces cost of capital via tax shields, but high debt increases financial distress costs, causing cost of capital to rise after reaching a minimum point. Produce a JSON array specifying this relationship. | fail→pass | 12,284 | 12,335 | +0% | 1 | 1 | 0% | 1,377 | 1,596 | +16% | 0 | 0 | — |
▸case-10 In macroeconomics, we are studying 'Foreign Direct Investment' (IV) and 'Gross Domestic Product Growth' (DV). Capital accumulation theory indicates FDI stimulates GDP growth, while market-size theory shows higher GDP growth attracts more FDI simultaneously. Format a JSON relationship specification array. | fail→pass | 15,281 | 13,659 | -11% | 1 | 1 | 0% | 1,776 | 1,857 | +5% | 0 | 0 | — |
▸case-11 For an agricultural economics model, we assess 'Fertilizer Application Quantity' (IV) and 'Crop Yield' (DV). Law of diminishing returns shows yield increases rapidly at low fertilizer levels but levels off near maximum biological capacity. Generate the JSON specification array. | fail→pass | 19,881 | 11,068 | -44% | 1 | 1 | 0% | 2,895 | 1,308 | -55% | 0 | 0 | — |
▸case-12 In physics-informed ergonomics, we study 'Ambient Noise Level' (IV) and 'Speech Intelligibility' (DV). Acoustic Masking Theory predicts that higher noise linearly degrades speech perception, with zero competing models in published literature. Output a JSON list specification for this pair. | fail→pass | 13,841 | 3,951 | -71% | 1 | 1 | 0% | 1,497 | 1,110 | -26% | 0 | 0 | — |
▸case-13 In sociology, we study 'Social Media Screen Time' (IV) and 'Adolescent Civic Engagement' (DV). Initial observational studies suggest a slight negative trend, but mechanism studies are highly contested, methodologically weak, and lack consensus. Output the JSON relationship list. | fail→pass | 10,633 | 16,827 | +58% | 1 | 1 | 0% | 1,024 | 2,193 | +114% | 0 | 0 | — |
▸case-14 In organizational management, we analyze 'Employee Commute Time' (IV) and 'Daily Punctuality' (DV). Conservation of Energy models demonstrate a steady, constant rate of decline in punctuality as commute duration grows. Provide the structured JSON specification list. | pass→pass | 15,655 | 15,227 | -3% | 1 | 1 | 0% | 2,239 | 1,594 | -29% | 0 | 0 | — |
▸case-15 In our healthcare study, we evaluate two pairs: Pair 1 is 'Nurse Staffing Ratio' (IV1) -> 'Patient Recovery Time' (DV1) backed by Care Efficiency Theory showing linear improvement; Pair 2 is 'Hospital Bed Occupancy' (IV2) -> 'Patient Mortality Rate' (DV2) backed by Strain Theory showing a sharp threshold jump above 85% occupancy. Produce a single JSON list containing both pair specifications. | pass→pass | 16,562 | 10,792 | -35% | 1 | 1 | 0% | 729 | 1,551 | +113% | 0 | 0 | — |
▸case-16 In our marketing study, we have 'Ad Spend' (IV) -> 'Brand Awareness' (Mediator) -> 'Quarterly Sales' (DV). Hierarchy of Effects theory shows Ad Spend has linear positive impact on Awareness, and Awareness has saturating positive impact on Sales. Provide the complete JSON specification list including mediator links. | pass→pass | 26,066 | 19,763 | -24% | 1 | 1 | 0% | 4,137 | 2,102 | -49% | 0 | 0 | — |
▸case-17 In political science, we analyze 'Electoral Competition Level' (IV) and 'Policy Innovation Rate' (DV). Democratic Vulnerability Theory predicts competition forces rapid policy changes (positive), whereas Polarization Theory predicts gridlock and stagnation (negative), with empirical literature split 50/50. Output the JSON relationship list. | fail→fail | 9,945 | 12,460 | +25% | 1 | 1 | 0% | 938 | 1,661 | +77% | 0 | 0 | — |
▸case-18 In cognitive psychology, Yerkes-Dodson Law establishes that 'Arousal Level' (IV) has an inverted-U relationship with 'Task Performance' (DV), supported by meta-analyses across 100+ robust trials with no conflicting theories. Generate the JSON relationship specification. | fail→pass | 6,534 | 12,028 | +84% | 1 | 1 | 0% | 1,231 | 2,395 | +95% | 0 | 0 | — |
▸case-19 In urban planning, 'Population Density' (IV) affects 'Infrastructure Cost Per Capita' (DV). Economies of Scale theory shows costs drop rapidly at initial density increments but curve irregularly at ultra-high density without reaching a clean threshold or U-shape. Format the JSON relationship specification. | fail→pass | 7,894 | 7,632 | -3% | 1 | 1 | 0% | 1,321 | 1,605 | +21% | 0 | 0 | — |
▸case-20 We have theoretical documentation from Social Learning Theory explaining how observational learning occurs through attention, retention, reproduction, and motivation. However, we have only specified an independent variable 'Modeling Duration' and no dependent variable. Please generate the JSON relationship specification. | fail→pass | 13,885 | 11,553 | -17% | 1 | 1 | 0% | 2,212 | 702 | -68% | 0 | 0 | — |
▸case-21 In supply chain management, 'Inventory Buffer Level' (IV) impacts 'Order Fulfillment Latency' (DV). According to Queueing Theory, latency increases steadily in direct constant proportion with buffer queue length. Generate the JSON relationship list. | fail→pass | 7,355 | 14,213 | +93% | 1 | 1 | 0% | 846 | 1,433 | +69% | 0 | 0 | — |
▸case-22 I have a pandas DataFrame with columns 'Ad_Spend' and 'Sales'. I want to fit an OLS regression using statsmodels in Python to estimate the coefficient. Please write the Python script to fit this model and print the summary. | pass→fail | 8,853 | 7,996 | -10% | 1 | 1 | 0% | 1,615 | 1,476 | -9% | 0 | 0 | — |