Description
Partition observed score variance into modeled true and error components using a supplied reliability.
Classical score reliability partitions observed variance into modeled true-score and error components. A supplied reliability coefficient supports an arithmetic decomposition but is not an estimate generated by that decomposition.
Partition observed score variance into modeled true and error components using a supplied reliability.
When to use this tool
Use Reliability Item Error Variance Term when checking a declared score-variance and standard-error relationship.
How to use the tool and how it works
- Enter observedVariance, reliability. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read trueVariance, errorVariance, standardError. Use the output convention below.
Require nonnegative observedVariance and reliability in [0,1]. trueVariance = observedVariance*reliability; errorVariance = observedVariance*(1-reliability); standardError = sqrt(errorVariance).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| observedVariance | Observed Variance | Required. Finite number; minimum 0. |
| reliability | Reliability | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| trueVariance | True Variance | Required. Finite number. |
| errorVariance | Error Variance | Required. Finite number. |
| standardError | Standard Error | Required. Finite number. |
{
"input": {
"observedVariance": 100,
"reliability": 0.75
},
"output": {
"trueVariance": 75,
"errorVariance": 25,
"standardError": 5
}
}Limitations and assumptions
- Variance is in squared score units and the error is in score units. Reliability is supplied rather than estimated; classical-test-theory assumptions and individual uncertainty require separate review.
- 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 an appropriate reliability study and measurement model for population-specific score interpretation and individual uncertainty.
References
Similar or alternative tools
- Test Information One Item Term
information = probabilityDerivative²/[probability*(1-probability)].
- Logit Marginal Effect One Covariate
effect = coefficient*probability*(1-probability).