Power Analysis Module Abstract
High-level Purpose and Responsibility
The power analysis module provides statistical power calculations and sample size determination for experimental learning studies. It implements power analysis procedures for various statistical tests, enables optimal experimental design through sample size planning, and supports post-hoc power analysis for interpreting experimental results.
Key Data Structures and Relationships
- PowerAnalysis: Comprehensive power calculation framework for different statistical tests
- SampleSizeCalculator: Optimal sample size determination given effect sizes and power requirements
- EffectSizeEstimator: Estimation and specification of expected effect sizes for power calculations
- PowerCurve: Visualization and analysis of statistical power across different parameter values
- PostHocPower: Retrospective power analysis for completed experiments
- OptimalDesign: Integration of power analysis with experimental design optimization
Main Data Flows and Transformations
- Effect Size Specification: Domain knowledge → Expected effect sizes → Power calculation inputs
- Sample Size Planning: Power requirements + Effect sizes → Optimal sample size recommendations
- Power Calculation: Sample sizes + Effect sizes → Statistical power estimates
- Design Optimization: Multiple design options → Power comparison → Optimal design selection
- Post-Hoc Analysis: Completed experiment data → Retrospective power assessment → Result interpretation
External Dependencies and Interfaces
- Statistics Module: Integration with statistical tests and effect size calculations
- Experiments Module: Power-informed experimental design and sample size planning
- Learning Module: Effect size estimation for learning interventions and treatments
- Validation Module: Validation of power analysis assumptions and calculations
State Management Patterns
- Power Calculation Caching: Performance optimization for repeated power analyses
- Effect Size Library: Repository of empirical effect sizes for different learning interventions
- Design History Tracking: Maintains records of power analysis decisions for experimental designs
- Sensitivity Analysis State: Tracking of power sensitivity to assumption violations
Core Algorithms or Business Logic Abstractions
- Parametric Power Calculations: Analytical power formulas for t-tests, ANOVA, and regression
- Non-Parametric Power: Bootstrap and simulation-based power analysis for non-parametric tests
- Bayesian Power Analysis: Power calculations for Bayesian experimental designs
- Adaptive Power Monitoring: Sequential power analysis for adaptive experimental designs
- Multi-Objective Power Optimization: Balancing statistical power across multiple outcome measures
- Sensitivity Analysis: Assessment of power robustness to assumption violations and parameter uncertainty