Description
Calculate effectiveSize=sumWeights²/sumSquaredWeights and return the same number as rescaledEffectiveSize with invariant true.
A statistical term depends on its data summaries, weighting convention, centering, denominator, and boundary rules. A contribution, derivative, domain check, or converted summary answers a narrower question than a complete estimator. Those conventions must match before terms are combined or compared.
Calculate effectiveSize=sumWeights²/sumSquaredWeights and return the same number as rescaledEffectiveSize with invariant true.
When to use this tool
Use Weight Rescale Standard Error Invariance Check when you need this specific summary conversion, contribution, domain rule, or sensitivity term with matching statistical conventions.
How to use the tool and how it works
- Enter sumWeights, sumSquaredWeights, factor. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read effectiveSize, rescaledEffectiveSize, invariant. Inspect invariant before interpreting the associated values.
Calculate effectiveSize=sumWeights²/sumSquaredWeights and return the same number as rescaledEffectiveSize with invariant true. Require positive summaries and factor and sumSquaredWeights no greater than sumWeights².1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| sumWeights | Sum Weights | Required. Finite number; strictly above 0. |
| sumSquaredWeights | Sum Squared Weights | Required. Finite number; strictly above 0. |
| factor | Positive common scale validated but not numerically applied. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| effectiveSize | Effective Size | Required. Finite number. |
| rescaledEffectiveSize | Rescaled Effective Size | Required. Finite number. |
| invariant | Statement of the effective-size identity, not an empirical standard-error check. | Required. Boolean. |
{
"input": {
"sumWeights": 4,
"sumSquaredWeights": 8,
"factor": 3
},
"output": {
"effectiveSize": 2,
"rescaledEffectiveSize": 2,
"invariant": true
}
}Limitations and assumptions
- Factor is validated but not numerically applied. The tool states common-weight-scale invariance of effective size; it neither rescales actual weights nor computes a standard error or verifies the supplied summaries.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Use a complete estimator or model when a contribution, sensitivity, or domain check is insufficient. Verify the weight semantics, centering, denominator, and sampling assumptions before combining summaries.
References
Similar or alternative tools
- Standard Error Cluster Weight Reference
Return clusterError=independentError*sqrt(designEffect), requiring nonnegative independent error and positive design effect.
- Correlation Sign Rescale Policy
Correlation under nonzero linear rescaling; a collapsed variable returns an undefined flag and zero placeholder.