A/B Testing Module Abstract

High-level Purpose and Responsibility

The A/B testing module provides specialized infrastructure for conducting controlled experiments comparing two or more variants of learning interventions. It implements both classical and Bayesian A/B testing frameworks with real-time statistical monitoring, early stopping criteria, and effect size estimation for learning optimization studies.

Key Data Structures and Relationships

  • ABTest: Core A/B testing framework with variant management and statistical tracking
  • BayesianABTest: Bayesian implementation with posterior belief updates and credible intervals
  • TestVariant: Individual treatment conditions with performance tracking and sample management
  • ConversionMetric: Outcome measures including accuracy, response time, and learning rate metrics
  • StatisticalResult: Hypothesis test outcomes with p-values, confidence intervals, and effect sizes
  • BayesianResult: Posterior distributions, credible intervals, and probability of superiority

Main Data Flows and Transformations

  1. Participant Assignment: Incoming participants → Random allocation to test variants
  2. Performance Tracking: Task responses → Aggregated conversion metrics per variant
  3. Statistical Testing: Accumulated data → Hypothesis tests and significance calculations
  4. Bayesian Updates: New observations → Posterior belief updates using conjugate priors
  5. Decision Making: Statistical results → Recommendations for variant selection or continued testing

External Dependencies and Interfaces

  • Statistics Module: Hypothesis testing, effect size calculations, and confidence interval estimation
  • Learning Module: Integration with learning metrics and performance indicators
  • Tasks Module: Task generation and response collection for each test variant
  • Data Module: Persistent storage of test results and participant assignments

State Management Patterns

  • Immutable Test Configuration: Test parameters fixed after initialization
  • Dynamic Performance Tracking: Real-time accumulation of conversion metrics
  • Statistical State Updates: Incremental computation of test statistics as data arrives
  • Early Stopping Monitoring: Continuous evaluation of stopping criteria and statistical power

Core Algorithms or Business Logic Abstractions

  • Sequential Testing: Continuous monitoring with alpha spending functions and early stopping rules
  • Bayesian Belief Updates: Conjugate prior-posterior calculations for rapid inference
  • Effect Size Estimation: Cohen's d, odds ratios, and other standardized effect measures
  • Multiple Comparisons Correction: Bonferroni, FDR, and other corrections for multiple variant testing
  • Power Analysis: Real-time power calculations and sample size recommendations
  • Confidence Interval Construction: Bootstrap, asymptotic, and exact methods for interval estimation