Description
Pool supplied unbiased sample variances with n−1 degrees-of-freedom weights.
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.
Pool supplied unbiased sample variances with n−1 degrees-of-freedom weights.
When to use this tool
Use Pooled Within Group Sum Squares 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 groupSizes, sampleVariances. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read sumSquares, degreesOfFreedom, pooledVariance. Use the output convention below.
Sum (groupSize-1)*sampleVariance and groupSize-1 over aligned nonempty groups, then divide for pooledVariance. Require integer group sizes at least two and nonnegative sample variances.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| groupSizes | Group Sizes | Required. Array of safe integer; maximum items 256. |
| sampleVariances | Within-group variances using each groupSize-1 denominator. | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| sumSquares | Sum Squares | Required. Finite number. |
| degreesOfFreedom | Degrees Of Freedom | Required. Safe integer. |
| pooledVariance | Pooled Variance | Required. Finite number. |
{
"input": {
"groupSizes": [
3,
5
],
"sampleVariances": [
4,
9
]
},
"output": {
"sumSquares": 44,
"degreesOfFreedom": 6,
"pooledVariance": 7.333333333333333
}
}Limitations and assumptions
- Input variances must use the sample denominator and compatible units. This gives within-group pooling under a shared-variance interpretation without testing homogeneity or incorporating between-group mean differences.
- 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
- Centered Sum Observation Update
Update count to count+1, mean by (value-mean)/(count+1), and m2 by the product of the old-mean and new-mean deviations.
- Pooled Variance One Stratum Numerator
Return degreesOfFreedom=sampleSize-1 and numerator=degreesOfFreedom*sampleVariance.