Adaptive Testing Engine: Item Response Theory Simulator

Computerized adaptive tests don't ask a fixed list of questions — they pick the next question in real time based on everything answered so far. This simulator runs a real 2-parameter logistic Item Response Theory model over a bank of items, each with its own difficulty and discrimination, and re-estimates an examinee's ability θ by Newton–Raphson maximum likelihood after every response. Switch between a maximum-information item-selection rule (genuine CAT logic, as used in exams like the GRE) and random ordering to see directly how much faster targeted item selection narrows the standard error of the ability estimate for the same number of questions.