Description
Calculate leverage=1/count+(value-mean)²/centeredSumSquares with positive centered sum of squares and integer count at least one.
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 leverage=1/count+(value-mean)²/centeredSumSquares with positive centered sum of squares and integer count at least one.
When to use this tool
Use Normal Score One Observation Leverage 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, value, mean, centeredSumSquares. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read leverage. Use the output convention below.
Calculate leverage=1/count+(value-mean)²/centeredSumSquares with positive centered sum of squares and integer count at least one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| count | Count under the stated input or output convention. | Required. Safe integer; minimum 1. |
| value | Value | Required. Finite number. |
| mean | Mean | Required. Finite number. |
| centeredSumSquares | Centered Sum Squares | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| leverage | Leverage | Required. Finite number. |
{
"input": {
"count": 4,
"value": 3,
"mean": 2,
"centeredSumSquares": 4
},
"output": {
"leverage": 0.5
}
}Limitations and assumptions
- The supplied summaries are not constrained to one consistent dataset, so leverage can exceed one. This term does not fit a model, validate a regression design, or identify outliers.
- 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.
- Empirical Cdf Single Observation Step
Return one/sampleSize when observation is below evaluation under strict or below-or-equal otherwise, and zero when it fails.