Description
Calculate covariance=(sumXY-sumX*sumY/count)/(count-1), requiring integer count at least two.
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 covariance=(sumXY-sumX*sumY/count)/(count-1), requiring integer count at least two.
When to use this tool
Use Unbiased Covariance Centering Correction 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 count, sumX, sumY, sumXY. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read covariance. Use the output convention below.
Calculate covariance=(sumXY-sumX*sumY/count)/(count-1), requiring integer count at least two.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| count | Count under the stated input or output convention. | Required. Safe integer; minimum 2. |
| sumX | Sum X | Required. Finite number. |
| sumY | Sum Y | Required. Finite number. |
| sumXY | Sum XY | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| covariance | Covariance | Required. Finite number. |
{
"input": {
"count": 3,
"sumX": 6,
"sumY": 12,
"sumXY": 28
},
"output": {
"covariance": 2
}
}Limitations and assumptions
- The sums must represent the same paired observations and units. This sample-denominator formula does not verify summary consistency and can lose accuracy through subtraction of large close terms.
- 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
- Covariance Denominator Convention Factor
Multiply covariance by (count-1)/count when fromSample, otherwise by count/(count-1), returning the factor.
- Covariance One Pair Sign Contribution
Return product=(x-meanX)*(y-meanY) and its sign.