The Science Behind the Calculator

This calculator implements a research-backed approximation of the College Board's proprietary scoring algorithm:

The Science Behind the Calculator

This calculator implements a research-backed approximation of the College Board's proprietary scoring algorithm:

1. Module 1 Analysis: We estimate your ability level (theta θ) based on your Module 1 performance using Expected A Posteriori (EAP) estimation with a Bayesian prior distribution.
2. Adaptive Routing: If your estimated theta exceeds the threshold (~0.10-0.15), you're routed to the harder Module 2. Otherwise, you receive the easier module.
3. Maximum Likelihood Estimation: After Module 2, we calculate your final theta using Maximum Likelihood Estimation (MLE) with Newton-Raphson optimization, considering all responses and item parameters.
4. Polynomial Scaling: Your theta value is converted to a section score (200-800) using an 8th-degree polynomial transformation: Score = β₀ + β₁θ + β₂θ² + ... + β₈θ⁸
5. Confidence Intervals: We calculate ±30-40 point ranges based on the Standard Error of Measurement (SEM), which reflects the inherent uncertainty in adaptive testing.

Why Official Practice Tests Matter

While this calculator provides research-backed estimates, the most accurate way to predict your SAT score is through official College Board practice tests. Here's why:

• Official tests use the exact item parameters (difficulty, discrimination, guessing) from real SAT questions
• They implement the proprietary polynomial coefficients College Board uses for score conversion
• They account for pretest items and experimental sections
• They provide calibrated adaptive routing based on actual test data