Test Information At Theta Calculator
Actual independently evaluated2PL test informationΣa²P(1−P) at one independently statedθ, D=1, no guessing/lapse. Local independence/calibration external. Actual independently qualified instrument/cohort/matching units; no diagnosis, causal outcome, validated personal prediction or universal clinical cutoff.
Description
Two-parameter logistic item information depends on discrimination and correct-response probability at a chosen ability.
Two-parameter logistic item information depends on discrimination and correct-response probability at a chosen ability.1
Summing information assumes matched calibration and local independence. The calculation and input requirements are explained below.
When to use Test Information At Theta Calculator
Enter nonempty aligned correct-response probabilities from 0 to 1 and positive calibrated discrimination parameters.
How to use Test Information At Theta Calculator and how it works
- Prepare the measurements or independently established model inputs described below, with matching units and observation scope.
- Enter the required fields and run Test Information At Theta Calculator.
- Read the result fields using the formula, output units, signs and ordering explained below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualTwoPlCorrectProbabilities | Actual Two Pl Correct Probabilities. Use the units and matching context stated in the calculation below. | array of number | Required; other constraints below |
| callerCalibratedDiscriminations | Caller Calibrated Discriminations. Use the units and matching context stated in the calculation below. | array of number | Required; other constraints below |
Enter nonempty aligned correct-response probabilities from 0 to 1 and positive calibrated discrimination parameters. Sum a squared times P(1-P), using the D=1 two-parameter logistic convention. No ability or item calibration is fitted and endpoint probabilities contribute zero.
testInformation=sum(discrimination^2*P*(1-P)) Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.value | Numeric result under the formula and output units explained above. | number |
{
"input": {
"actualTwoPlCorrectProbabilities": [
0.5,
0.5
],
"callerCalibratedDiscriminations": [
1,
2
]
},
"output": {
"result": {
"value": 1.25
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Wright Map Item Position Lookup for a complementary operation: A Wright map places person measures and item locations on a common calibrated scale.
Use Rasch Item Difficulty Logits Calculator for a complementary operation: A restricted Rasch difficulty estimate transforms an observed correct-response fraction into logits.
References
-
Test Information At Theta Calculator — tool.io
Similar or alternative tools
- Wright Map Item Position Lookup
A Wright map places person measures and item locations on a common calibrated scale.
- Rasch Item Difficulty Logits Calculator
A restricted Rasch difficulty estimate transforms an observed correct-response fraction into logits.