### What is Item Response Theory (IRT)?

In simple terms, Item Response Theory (IRT) models examine the relationship between a person's IQ (in the case of an IQ test) and their answers to the test questions. The models assess how well a person performs on each question, how difficult each question is (item difficulty), and how much information the question provides about the person's IQ (What is the Point of Maximum Information?).
In contrast to classical test theory, where the difficulty of a question is determined by the percentage of people who answered it correctly, IRT models take all answers from all test-takers into account.
Based on all the answers, IRT models predict the likelihood that someone with a given IQ (based on their answers to other questions) will answer a question correctly. A question is considered difficult if a high IQ is required to answer it correctly, and easy if people with low IQs have a high chance of answering it correctly. This is known as item difficulty.
If someone with a high IQ is far more likely to give the correct answer to a question than someone with a low IQ, the question has a high item discrimination. Questions with high discrimination are considered good questions, as they provide a lot of information about the IQ of the person answering it.
The point at which discrimination is highest is referred to as the Point of Maximum Information. For example, if someone with an IQ of 100 has a 20% chance of giving the correct answer to a question, and someone with an IQ of 105 has an 80% chance of getting it right, the answer to that question can provide a strong indication that the person's IQ is 105 or higher if they give the correct answer, and 100 or lower if they give an incorrect answer. The Point of Maximum Information for the question is likely to be somewhere between 100 and 105, meaning the question provides the most information if it is answered by someone with an IQ between 100 and 105.
By selecting the right questions for the right people, the system can provide an accurate estimation of a person's IQ based on a relatively small number of questions.
The item difficulty, item discrimination, and Point of Maximum Information can be visualized in the Item Characteristic Curve, which is created for each question in the database of brght.