Description
Return degreesOfFreedom=sampleSize-1 and numerator=degreesOfFreedom*sampleVariance.
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.
Return degreesOfFreedom=sampleSize-1 and numerator=degreesOfFreedom*sampleVariance.
When to use this tool
Use Pooled Variance One Stratum Numerator 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 sampleSize, sampleVariance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read degreesOfFreedom, numerator. Use the output convention below.
Return degreesOfFreedom=sampleSize-1 and numerator=degreesOfFreedom*sampleVariance. Require integer sample size at least two and nonnegative variance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| sampleSize | Sample Size | Required. Safe integer; minimum 2. |
| sampleVariance | Sample Variance | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| degreesOfFreedom | Degrees Of Freedom | Required. Safe integer. |
| numerator | Numerator | Required. Finite number. |
{
"input": {
"sampleSize": 5,
"sampleVariance": 3
},
"output": {
"degreesOfFreedom": 4,
"numerator": 12
}
}Limitations and assumptions
- This is one group's within-group pooling contribution, not the final pooled variance. The variance must already use the sample denominator and share units with other groups.
- 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
- Finite Population Variance Sampling Factor
Calculate factor=(population-sample)/(population-1) and correctedVariance=varianceOfMean*factor.
- Pooled Within Group Sum Squares
Pool supplied unbiased sample variances with n−1 degrees-of-freedom weights.