Point-Biserial Item-Total Correlation Calculator
Point biserial from actual conditional means, POPU lationtotal-scoreSD, and correct fraction; item excluded/total convention independent. Not ordinary sample SD substitution. Actual independently qualified instrument/cohort/matching units; no diagnosis, causal outcome, validated personal prediction or universal clinical cutoff.
Description
Point-biserial correlation relates a binary item outcome to a total-score measure.
Point-biserial correlation relates a binary item outcome to a total-score measure.1
Conditional means, population standard deviation and the correct-response fraction must use the same scoring convention. The calculation and input requirements are explained below.
When to use Point-Biserial Item-Total Correlation Calculator
Enter finite correct- and incorrect-group means, positive total-score population SD and correct fraction from 0 to 1.
How to use Point-Biserial Item-Total Correlation 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 Point-Biserial Item-Total Correlation 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 |
|---|---|---|---|
| actualCorrectGroupMean | Actual Correct Group Mean. Use the units and matching context stated in the calculation below. | number | Required; finite; other constraints below |
| actualIncorrectGroupMean | Actual Incorrect Group Mean. Use the units and matching context stated in the calculation below. | number | Required; finite; other constraints below |
| actualTotalScorePopulationSd | Actual Total Score Population Sd. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
| actualCorrectFraction | Actual Correct Fraction. Use the units and matching context stated in the calculation below. | number | Required; fraction from 0 to 1; finite; other constraints below |
Enter finite correct- and incorrect-group means, positive total-score population SD and correct fraction from 0 to 1. Multiply mean difference/SD by sqrt(p(1-p)). Sample-SD substitution and item-total conventions are not selected by the tool.
rPointBiserial=(meanCorrect-meanIncorrect)/populationSD*sqrt(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": {
"actualCorrectGroupMean": 3,
"actualIncorrectGroupMean": 1,
"actualTotalScorePopulationSd": 2,
"actualCorrectFraction": 0.5
},
"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 Item Difficulty p-Value Calculator for a complementary operation: An item's difficulty p-value is its fraction of correct responses.
Use Item Discrimination Index Calculator for a complementary operation: An item discrimination index compares correct-response fractions in two independently defined groups.
References
Similar or alternative tools
- Item Difficulty p-Value Calculator
An item's difficulty p-value is its fraction of correct responses.
- Item Discrimination Index Calculator
An item discrimination index compares correct-response fractions in two independently defined groups.