Statistics Core Module Abstract
High-level Purpose and Responsibility
The statistics core module provides fundamental statistical functions and probability distributions for the experimental learning system. It serves as the mathematical foundation for all statistical inference, hypothesis testing, and probabilistic modeling throughout the platform, ensuring numerical accuracy and statistical validity.
Key Data Structures and Relationships
- StatisticalFunction: Core statistical computations including descriptive statistics and probability functions
- ProbabilityDistribution: Standard probability distributions with parameter estimation and sampling
- HypothesisTest: Framework for statistical significance testing with multiple test procedures
- ConfidenceInterval: Interval estimation procedures with various construction methods
- EffectSize: Standardized effect size measures for practical significance assessment
- StatisticalSummary: Comprehensive statistical summaries with diagnostic information
Main Data Flows and Transformations
- Data Summarization: Raw observations → Descriptive statistics → Statistical summaries
- Distribution Fitting: Empirical data → Parameter estimation → Fitted probability distributions
- Hypothesis Testing: Data + Null hypothesis → Test statistics → P-values and decisions
- Interval Estimation: Sample data → Confidence intervals → Uncertainty quantification
- Effect Size Calculation: Group differences → Standardized measures → Practical significance assessment
External Dependencies and Interfaces
- Learning Module: Statistical assessment of learning progress and proficiency estimation
- Experiments Module: Hypothesis testing for experimental outcomes and treatment effects
- Bayesian Module: Prior and posterior distribution support for Bayesian inference
- Validation Module: Statistical validation and assumption checking for model appropriateness
State Management Patterns
- Immutable Statistical Results: Statistical computations produce immutable result objects
- Cached Distribution Parameters: Performance optimization for repeated distribution operations
- Numerical Precision Management: Careful handling of floating-point precision in statistical calculations
- Error Propagation: Systematic propagation of numerical errors through statistical procedures
Core Algorithms or Business Logic Abstractions
- Descriptive Statistics: Mean, median, variance, skewness, and kurtosis with numerical stability
- Probability Density Functions: Implementation of standard statistical distributions (normal, beta, gamma, etc.)
- Statistical Tests: t-tests, chi-square tests, ANOVA, and non-parametric alternatives
- Maximum Likelihood Estimation: Parameter estimation for probability distributions
- Bootstrap Methods: Resampling procedures for robust statistical inference
- Multiple Comparisons Correction: Bonferroni, FDR, and other corrections for simultaneous inference