adaptivetest

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name: adaptive-testing
description: Design and implement adaptive testing systems using Item Response Theory (IRT). Use when working with computerized adaptive tests (CAT), psychometric assessment, ability estimation, question calibration, test design, or IRT models (1PL/2PL/3PL). Covers test algorithms, stopping rules, item selection strategies, and practical implementation patterns for K-12, certification, placement, and diagnostic assessments.
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# Adaptive Testing with IRT

Design computerized adaptive tests that measure ability efficiently and accurately using Item Response Theory.

## Core Concept

Adaptive tests adjust difficulty in real-time based on student responses. A correct answer → harder question. Incorrect → easier question. The result: accurate ability estimates in ~50% fewer questions than fixed-length tests.

**Key advantage:** Traditional tests waste time on too-easy or too-hard questions. Adaptive tests spend time where measurement matters most — near the student's ability level.

## Quick Decision Tree

| You need to... | See |
|----------------|-----|
| Understand IRT models and parameters | [IRT Fundamentals](#irt-fundamentals) |
| Design a new adaptive test | [Test Design Workflow](#test-design-workflow) |
| Choose item selection algorithm | [Item Selection](#item-selection-strategies) |
| Decide when to stop the test | [Stopping Rules](#stopping-rules) |
| Calibrate new questions | `references/calibration.md` |
| Implement CAT algorithm | `references/implementation.md` |

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## IRT Fundamentals

### The 3-Parameter Logistic (3PL) Model

Most adaptive tests use the 3PL model. Each question has three parameters:

- **a** (discrimination) — How well the question differentiates ability levels. Higher = steeper curve. Typical range: 0.5 to 2.5
- **b** (difficulty) — The ability level where P(correct) = 0.5. Range: -3 to +3 (standardized scale)
- **c** (guessing) — Probability of guessing correctly. Usually 0.2 to 0.25 for multiple choice