Description
Calculate one weighted squared-deviation contribution about a supplied origin.
Statistical summaries depend on weights, reference origins, denominator definitions and sign conventions. A squared deviation about an arbitrary origin is not automatically a variance, and a scale label does not studentize a residual. Keep the stated measurement and model conventions attached to a quantity before comparing or interpreting it.
Calculate one weighted squared-deviation contribution about a supplied origin.
When to use this tool
Use Weighted Second Moment Contribution when you already have value, referenceOrigin, weight, totalWeight and need to calculate one weighted squared-deviation contribution about a supplied origin.
How to use the tool and how it works
- Enter value, referenceOrigin, weight, totalWeight. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read contribution. Use the output convention below.
Require totalWeight>0 and weight in [0,totalWeight]; return weight/totalWeight*(value-referenceOrigin)².1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| value | Value | Required. Finite number. |
| referenceOrigin | Supplied origin in the value unit; need not be the weighted mean. | Required. Finite number. |
| weight | Weight | Required. Finite number; minimum 0. |
| totalWeight | Total Weight | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| contribution | Contribution | Required. Finite number. |
{
"input": {
"value": 5,
"referenceOrigin": 1,
"weight": 2,
"totalWeight": 8
},
"output": {
"contribution": 4
}
}Limitations and assumptions
- This is one contribution, not a full variance or centered moment unless the origin, all observations and normalization justify that interpretation.
- 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
Calculate the full weighted statistic from all observations and its defined centering and normalization. Consult the original model or reporting method for studentization and effect-size conventions, keeping a supplied scale label separate from a computed statistical quantity.
References
Similar or alternative tools
- Weighted Share Denominator Rebase
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- Paired Difference Reference Sign
Calculate a paired difference under an explicit reference direction.