Description
Calculate a dichotomous Rasch response probability from supplied ability and item difficulty.
Item-response models link a latent ability scale to response probabilities, odds and information. Parameters must share the intended calibrated scale, and one item or category term is different from a full test model or parameter estimate.
Calculate a dichotomous Rasch response probability from supplied ability and item difficulty.
When to use this tool
Use Item Response Rasch Logit One Point when checking one supplied item-response model term.
How to use the tool and how it works
- Enter ability, difficulty. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read logit, probability. Use the output convention below.
logit = ability-difficulty; probability is the logistic transform using a sign-dependent form to reduce exponential overflow.1
The dichotomous Rasch model links response probability to the difference between person ability and item difficulty on the logit scale.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| ability | Ability | Required. Finite number. |
| difficulty | Difficulty | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| logit | Logit | Required. Finite number. |
| probability | Dimensionless probability from zero to one under the stated model. | Required. Finite number. |
{
"input": {
"ability": 1.5,
"difficulty": 0.5
},
"output": {
"logit": 1,
"probability": 0.7310585786300049
}
}Limitations and assumptions
- Ability and difficulty must share a calibrated logit scale. Numerical probabilities can round to zero or one at extremes; this one Rasch-model point does not estimate parameters or validate item fit.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a fitted, validated measurement model with appropriate item and population evidence for interpretation of ability or test precision.
References
-
Calculation and input contract: educational-psychology/item-response-rasch-logit-one-point — tool.io
-
MESA Memo 42: Solving Measurement Problems — Rasch Measurement Transactions
Similar or alternative tools
- Partial Credit One Step Logit Term
adjacentLogOdds = discrimination*(ability-stepDifficulty); odds = exp(adjacentLogOdds).
- Test Information One Item Term
information = probabilityDerivative²/[probability*(1-probability)].