Statistics Module - Abstract Documentation

Purpose and Responsibility

Provides comprehensive statistical analysis framework for research applications including mixed-effects modeling, power analysis, validation testing, and publication-ready statistical reporting.

Key Data Structures and Relationships

Statistical Components

core: Core statistical analysis with learning curves and strategy classification
mixed_effects: Mixed-effects modeling for hierarchical experimental data
power_analysis: Statistical power calculation and sample size estimation
prediction: Predictive modeling and cross-validation frameworks
validation: Statistical validation and assumption testing
math_validation: Mathematical correctness verification and numerical stability

Analysis Architecture

StatisticalAnalyzer → LearningCurves + StrategyAnalysis + ErrorPatterns + RTModeling
MixedEffectsModel → FixedEffects + RandomEffects + Covariance Structure
PowerAnalysis → EffectSize + SampleSize + Power + AlphaLevel

Main Data Flows and Transformations

Analysis Pipeline

Data Validation: Assumption testing and outlier detection
Descriptive Analysis: Summary statistics and exploratory data analysis
Inferential Testing: Hypothesis testing with multiple comparison correction
Model Fitting: Mixed-effects models with optimal structure selection

Research Integration

Publication Standards: APA-compliant statistical reporting
Effect Sizes: Cohen's d, eta-squared, and confidence interval calculation
Power Analysis: Pre-study planning and post-hoc sensitivity analysis
Reproducible Analysis: Complete statistical pipeline with version control

Core Algorithms and Business Logic Abstractions

Mixed-Effects Modeling: Hierarchical linear models with random effects
Learning Curve Analysis: Non-linear growth modeling and plateau detection
Strategy Classification: Model-based clustering and mixture modeling
Response Time Modeling: Ex-Gaussian distribution fitting and parameter estimation

ABCDeez Documentation