Description
For positive variance return standardized=residual/sqrt(variance) and squared=standardized^2.
Normalization depends on the supplied center, scale, norm, range, reference distribution, or denominator. A zero spread and a missing denominator need an explicit policy, and clipping differs from fitting a scaler. Evaluating one scalar or derivative term does not estimate every parameter or establish a distributional improvement.
For positive variance return standardized=residual/sqrt(variance) and squared=standardized^2.
When to use this tool
Use Standardized Residual Reference Variance Pair when you already have the required normalization parameters and need this local scalar, range, policy, or derivative term.
How to use the tool and how it works
- Enter residual, variance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read standardized, squared. Use the output convention below.
For positive variance return standardized=residual/sqrt(variance) and squared=standardized^2.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| residual | Signed supplied-minus-reconstructed discrepancy under the stated formula. | Required. Finite number. |
| variance | Positive supplied variance in squared residual units, or returned variance under the stated branch. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| standardized | Standardized | Required. Finite number. |
| squared | Squared | Required. Finite number. |
{
"input": {
"residual": -6,
"variance": 9
},
"output": {
"standardized": -2,
"squared": 4
}
}Limitations and assumptions
- Variance must be in the residual's unit squared and supplied for the intended model. The term is not a fitted z-score distribution, goodness-of-fit test, probability, or automatic outlier classification.
- 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
Fit or verify the intended scaler parameters and statistical model separately. Check units, zero policies, missingness, clipping, inverse conventions, and whether supplied norms or denominators belong to the same data.
References
Similar or alternative tools
- Row Standardization One Missing Denominator
For nonnegative sumSquares and integer 0<=missing<=count set denominator=count-missing minus one if sample.
- Reference Zscore Offset Recovery
For positive scale return location=value-score*scale.