Description
Return a paired-lot difference and correlated uncertainty ratio.
Standard uncertainties combine through the measurement model and the covariance of its inputs. Correlated errors may reinforce or cancel, and treating a scale or volume as exact is a substantive assumption. A propagated value is different from a complete uncertainty budget or a statistical decision.
Return a paired-lot difference and correlated uncertainty ratio.
When to use this tool
Use Biomonitoring Lablot Reference Uncertainty when checking the stated uncertainty-propagation term under supplied correlation and exact-input assumptions.
How to use the tool and how it works
- Enter first, second, firstUncertainty, secondUncertainty, correlation. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read difference, differenceUncertainty, normalizedDifference. Use the output convention below.
Return a paired-lot difference and correlated uncertainty ratio. Require nonnegative uncertainties, correlation [-1,1] and positive resulting difference uncertainty; difference = second-first, uncertainty = sqrt(u1²+u2²-2*rho*u1*u2), evaluated with scaling.1
Uncertainty propagation depends on the measurement model and input covariance. Omitting correlations or treating volume as exact requires justification; this helper is only one specified contribution.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| first | First | Required. Finite number. |
| second | Second | Required. Finite number. |
| firstUncertainty | First Uncertainty | Required. Finite number; minimum 0. |
| secondUncertainty | Second Uncertainty | Required. Finite number. |
| correlation | Correlation | Required. Finite number; minimum -1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| difference | second-first on a common measurement scale. | Required. Finite number. |
| differenceUncertainty | Positive propagated standard uncertainty including the supplied correlation. | Required. Finite number. |
| normalizedDifference | Difference divided by its standard uncertainty; not automatically a z-test or equivalence decision. | Required. Finite number. |
{
"input": {
"first": 10,
"second": 12,
"firstUncertainty": 1,
"secondUncertainty": 1,
"correlation": 0
},
"output": {
"difference": 2,
"differenceUncertainty": 1.4142135623730951,
"normalizedDifference": 1.414213562373095
}
}Limitations and assumptions
- Inputs must be compatible standard uncertainties with a justified correlation; the normalized difference is not automatically a significance test.
- 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
Construct a justified measurement model and complete uncertainty budget, including correlations, calibration and omitted scale/volume terms, for reliable uncertainty reporting.
References
Similar or alternative tools
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