Item Difficulty p-Value Calculator
Actual item difficulty pvalue=fraction correct, NOTa statistical significance pvalue. Actual independently qualified instrument/cohort/matching units; no diagnosis, causal outcome, validated personal prediction or universal clinical cutoff.
Description
An item's difficulty p-value is its fraction of correct responses.
An item's difficulty p-value is its fraction of correct responses.1
It is distinct from a significance-test p-value. The calculation and input requirements are explained below.
When to use Item Difficulty p-Value Calculator
Enter integer correct count 0–1000000 and eligible count 1–1000000.
How to use Item Difficulty p-Value 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 Item Difficulty p-Value 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 |
|---|---|---|---|
| actualCorrectResponseCount | Actual Correct Response Count. Use the units and matching context stated in the calculation below. | number | Required; integer 0–1000000; finite; other constraints below |
| actualEligibleResponseCount | Actual Eligible Response Count. Use the units and matching context stated in the calculation below. | number | Required; integer 1–1000000; finite; other constraints below |
Enter integer correct count 0–1000000 and eligible count 1–1000000. Correct cannot exceed eligible. Return a fraction, not percentage or statistical significance p-value.
itemP=correctCount/eligibleCount 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": {
"actualCorrectResponseCount": 2,
"actualEligibleResponseCount": 4
},
"output": {
"result": {
"value": 0.5
}
}
}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 Brogden-Cronbach-Gleser Utility Gain Calculator for a complementary operation: A BCG utility model combines selection size, tenure, performance variation and predictive parameters.
Use Sociometric Status Z From Nominations Calculator for a complementary operation: A sociometric nomination z-score compares a count with a matched reference mean and standard deviation.
References
-
Item Difficulty p-Value Calculator — tool.io
Similar or alternative tools
- Brogden-Cronbach-Gleser Utility Gain Calculator
A BCG utility model combines selection size, tenure, performance variation and predictive parameters.
- Sociometric Status Z From Nominations Calculator
A sociometric nomination z-score compares a count with a matched reference mean and standard deviation.