Description
Return equal-uncertainty correlated dispense uncertainty.
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 equal-uncertainty correlated dispense uncertainty.
When to use this tool
Use Aliquot Volume Uncertainty Term when checking the stated uncertainty-propagation term under supplied correlation and exact-input assumptions.
How to use the tool and how it works
- Enter dispenses, perDispenseStandardUncertainty, correlation. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read standardUncertainty. Use the output convention below.
Return equal-uncertainty correlated dispense uncertainty. Require whole dispenses >= 1, per-dispense uncertainty >= 0 and correlation in [-1/(n-1),1] for n>1, otherwise [-1,1]; result = u*sqrt(n*(1+(n-1)*rho)).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 |
|---|---|---|
| dispenses | Dispenses | Required. Safe integer; minimum 1. |
| perDispenseStandardUncertainty | Per Dispense Standard Uncertainty | Required. Finite number; minimum 0. |
| correlation | Common pairwise correlation rho, bounded to keep the equal-correlation covariance model nonnegative. | Required. Finite number; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| standardUncertainty | Standard Uncertainty | Required. Finite number. |
{
"input": {
"dispenses": 4,
"perDispenseStandardUncertainty": 0.1,
"correlation": 0
},
"output": {
"standardUncertainty": 0.2
}
}Limitations and assumptions
- This assumes equal standard uncertainties and equal pairwise correlation; no actual pipette calibration or full uncertainty budget is determined.
- 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
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