Description
Calculate denominator=sampleCount-correction, expectedVariance=sumSquaredDeviations/denominator, and residual=reportedVariance-expectedVariance.
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 denominator=sampleCount-correction, expectedVariance=sumSquaredDeviations/denominator, and residual=reportedVariance-expectedVariance.
When to use this tool
Use Sample Variance Denominator Residual 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 sumSquaredDeviations, sampleCount, reportedVariance, correction. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read expectedVariance, residual, denominator. Use the output convention below.
Calculate denominator=sampleCount-correction, expectedVariance=sumSquaredDeviations/denominator, and residual=reportedVariance-expectedVariance. Require nonnegative variances and integer correction from zero through sampleCount minus one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| sumSquaredDeviations | Sum Squared Deviations | Required. Finite number; minimum 0. |
| sampleCount | Sample Count | Required. Safe integer; minimum 1. |
| reportedVariance | Reported Variance | Required. Finite number; minimum 0. |
| correction | Correction | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| expectedVariance | Expected Variance | Required. Finite number. |
| residual | Signed discrepancy under the formula stated above. | Required. Finite number. |
| denominator | Denominator | Required. Safe integer. |
{
"input": {
"sumSquaredDeviations": 12,
"sampleCount": 5,
"reportedVariance": 4,
"correction": 1
},
"output": {
"expectedVariance": 3,
"residual": 1,
"denominator": 4
}
}Limitations and assumptions
- The correction is supplied rather than chosen as a statistical convention. The tool does not verify centering, raw observations, weighting, or whether the reported variance is substantively appropriate.
- 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
- Sample Variance One Point Deletion Term
Remove one observation from count, mean, and centered sum m2, update the mean, and subtract its centered contribution.
- Variance Denominator Rescale
Return rescaledVariance=variance*oldDenominator/newDenominator, requiring nonnegative variance and positive denominators.