Description
information = probabilityDerivative²/[probability*(1-probability)].
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.
information = probabilityDerivative²/[probability*(1-probability)].
When to use this tool
Use Test Information One Item Term when checking one supplied item-response model term.
How to use the tool and how it works
- Enter probability, probabilityDerivative. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read information. Use the output convention below.
Require probability strictly between zero and one. information = probabilityDerivative²/[probability*(1-probability)].1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| probability | Dimensionless probability from zero to one under the stated model. | Required. Finite number; strictly above 0; strictly below 1. |
| probabilityDerivative | Response-probability derivative with respect to ability on its chosen scale. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| information | Information | Required. Finite number. |
{
"input": {
"probability": 0.5,
"probabilityDerivative": 0.25
},
"output": {
"information": 0.25
}
}Limitations and assumptions
- The derivative must be with respect to the intended ability parameter and on its scale. This one-item Bernoulli information term does not fit a model or sum test information.
- 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
Similar or alternative tools
- Item Response Rasch Logit One Point
Calculate a dichotomous Rasch response probability from supplied ability and item difficulty.
- Partial Credit One Step Logit Term
adjacentLogOdds = discrimination*(ability-stepDifficulty); odds = exp(adjacentLogOdds).