statsmodels
Statistical modeling toolkit. OLS, GLM, logistic, ARIMA, time series, hypothesis tests, diagnostics, AIC/BIC, for rigorous statistical inference and econometric analysis.
statistical-analysis
Statistical analysis toolkit. Hypothesis tests (t-test, ANOVA, chi-square), regression, correlation, Bayesian stats, power analysis, assumption checks, APA reporting, for academic research.
hypothesis-generation
Generate testable hypotheses. Formulate from observations, design experiments, explore competing explanations, develop predictions, propose mechanisms, for scientific inquiry across domains.
systematic-debugging
Use when encountering any bug, test failure, or unexpected behavior, before proposing fixes - four-phase framework (root cause investigation, pattern analysis, hypothesis testing, implementation) that ensures understanding before attempting solutions
sequential-thinking
Structured reflective problem-solving methodology. Process: decompose, analyze, hypothesize, verify, revise. Capabilities: complex problem decomposition, adaptive planning, course correction, hypothesis verification, multi-step analysis. Actions: decompose, analyze, plan, revise, verify solutions step-by-step. Keywords: sequential thinking, problem decomposition, multi-step analysis, hypothesis verification, adaptive planning, course correction, reflective thinking, step-by-step, thought sequence, dynamic adjustment, unclear scope, complex problem, structured analysis. Use when: decomposing complex problems, planning with revision capability, analyzing unclear scope, verifying hypotheses, needing course correction, solving multi-step problems.
systematic-debugging
Use when encountering any bug, test failure, or unexpected behavior, before proposing fixes - four-phase framework (root cause investigation, pattern analysis, hypothesis testing, implementation) that ensures understanding before attempting solutions
sequential-thinking
Apply structured, reflective problem-solving for complex tasks requiring multi-step analysis, revision capability, and hypothesis verification. Use for complex problem decomposition, adaptive planning, analysis needing course correction, problems with unclear scope, multi-step solutions, and hypothesis-driven work. | Sử dụng khi: suy nghĩ từng bước, phân tích, vấn đề phức tạp, chia nhỏ.
statistical-analyzer
Perform statistical hypothesis testing, regression analysis, ANOVA, and t-tests with plain-English interpretations and visualizations.
statistical-power-calculator
Use when asked to calculate statistical power, determine sample size, or plan experiments for hypothesis testing.
statistics
Statistical analysis methods, hypothesis testing, and probability for data analytics
statistical-analysis
Probability, distributions, hypothesis testing, and statistical inference. Use for A/B testing, experimental design, or statistical validation.
systematic-debugging
Use when encountering any bug, test failure, or unexpected behavior, before proposing fixes - four-phase framework (root cause investigation, pattern analysis, hypothesis testing, implementation) that ensures understanding before attempting solutions
debug-like-expert
Deep analysis debugging mode for complex issues. Activates methodical investigation protocol with evidence gathering, hypothesis testing, and rigorous verification. Use when standard troubleshooting fails or when issues require systematic root cause analysis.
causal-inference-root-cause
Use when investigating why something happened and need to distinguish correlation from causation, identify root causes vs symptoms, test competing hypotheses, control for confounding variables, or design experiments to validate causal claims. Invoke when debugging systems, analyzing failures, researching health outcomes, evaluating policy impacts, or when user mentions root cause, causal chain, confounding, spurious correlation, or asks "why did this really happen?"
bayesian-reasoning-calibration
Use when making predictions or judgments under uncertainty and need to explicitly update beliefs with new evidence. Invoke when forecasting outcomes, evaluating probabilities, testing hypotheses, calibrating confidence, assessing risks with uncertain data, or avoiding overconfidence bias. Use when user mentions priors, likelihoods, Bayes theorem, probability updates, forecasting, calibration, or belief revision.
prototyping-pretotyping
Use when testing ideas cheaply before building (pretotyping with fake doors, concierge MVPs, paper prototypes) to validate desirability/feasibility, choosing appropriate prototype fidelity (paper/clickable/coded), running experiments to test assumptions (demand, pricing, workflow), or when user mentions prototype, MVP, fake door test, concierge, Wizard of Oz, landing page test, smoke test, or asks "how can we validate this idea before building?".
hypothesis-testing-engine
Take any claim and design + execute a complete research protocol to test it. Apply scientific method automatically: design study, gather data, run analysis, provide verdict with confidence level.
Statistical Hypothesis Testing
Conduct statistical tests including t-tests, chi-square, ANOVA, and p-value analysis for statistical significance, hypothesis validation, and A/B testing
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