1PL Rasch Item Response Theory Calculator
Compute the probability of a correct response and the odds ratio under the one-parameter logistic (Rasch) item response model from examinee ability θ and item difficulty b.
How to Use the 1PL Rasch Item Response Theory Calculator
- Enter the examinee ability θ in logits.
- Enter the item difficulty b in logits.
- Click Calculate to see the probability correct and odds ratio.
Casos de Uso
- •Psychometrics and test construction.
- •Computerised adaptive testing (CAT).
- •Education research.
Fórmula
P(correct | θ, b) = 1 / (1 + exp(−(θ − b))). Odds ratio = exp(θ − b).
Preguntas Frecuentes
What does θ = b mean?
When ability equals difficulty, the probability of a correct answer is exactly 0.5 — the defining property of the Rasch model.
Why the logit scale?
The logit transform puts ability and difficulty on the same additive scale. A +1 logit shift corresponds to an e ≈ 2.72 odds increase in getting the item right.