Description
Propagate a supplied center-uncertainty bound through positive-scale normalization.
Normalization requires an explicit order of operations, center, scale and reference convention. Centering before scaling generally differs from subtracting the same center after scaling. A normalized weight or bounded uncertainty interval inherits supplied assumptions; zero entries, sentinel collisions and reference-category coding need separate interpretation.
Propagate a supplied center-uncertainty bound through positive-scale normalization.
When to use this tool
Use Robust Center Uncertainty Shift when you already have value, suppliedCenter, suppliedScale, centerUncertainty and need to propagate a supplied center-uncertainty bound through positive-scale normalization.
How to use the tool and how it works
- Enter value, suppliedCenter, suppliedScale, centerUncertainty. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read normalized, lower, upper. Use the output convention below.
Require suppliedScale>0 and centerUncertainty>=0; return (value-center)/scale and endpoints (value-center±uncertainty)/scale.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| value | Value | Required. Finite number. |
| suppliedCenter | Supplied Center | Required. Finite number. |
| suppliedScale | Supplied Scale | Required. Finite number; strictly above 0. |
| centerUncertainty | Nonnegative symmetric uncertainty bound in the value/center unit; not a confidence level. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| normalized | Normalized | Required. Finite number. |
| lower | (value-suppliedCenter-centerUncertainty)/suppliedScale. | Required. Finite number. |
| upper | (value-suppliedCenter+centerUncertainty)/suppliedScale. | Required. Finite number. |
{
"input": {
"value": 10,
"suppliedCenter": 4,
"suppliedScale": 2,
"centerUncertainty": 1
},
"output": {
"normalized": 3,
"lower": 2.5,
"upper": 3.5
}
}Limitations and assumptions
- These are bounds due only to supplied center uncertainty, not an inferred confidence interval or a complete measurement-uncertainty model.
- 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
Specify the intended transformation and data basis before estimating or applying parameters. Review missing-value handling and reference coding across the full dataset; one affine term or normalized vector does not establish comparable measurements or a fitted model.
References
Similar or alternative tools
- Scalar Centering After Scaling Delta
Compare centering before scaling with centering after scaling.
- Reference Index Base Year Factor
Express a value relative to a supplied nonzero base value and index base.