Description
Calculate alpha=1-confidence, lowerTail=alpha*lowerShare, and upperTail=alpha-lowerTail.
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 alpha=1-confidence, lowerTail=alpha*lowerShare, and upperTail=alpha-lowerTail.
When to use this tool
Use Confidence Level Tail Allocation 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 confidence, lowerShare. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read alpha, lowerTail, upperTail. Use the output convention below.
Calculate alpha=1-confidence, lowerTail=alpha*lowerShare, and upperTail=alpha-lowerTail. Require confidence and lowerShare within zero through one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| confidence | Confidence | Required. Finite number; minimum 0; maximum 1. |
| lowerShare | Lower Share | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| alpha | Alpha | Required. Finite number. |
| lowerTail | Lower Tail | Required. Finite number. |
| upperTail | Upper Tail | Required. Finite number. |
{
"input": {
"confidence": 0.9,
"lowerShare": 0.5
},
"output": {
"alpha": 0.09999999999999998,
"lowerTail": 0.04999999999999999,
"upperTail": 0.04999999999999999
}
}Limitations and assumptions
- These are tail-probability allocations, not interval endpoints. The tool does not choose a sampling distribution, test direction, coverage method, or appropriate confidence level.
- 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
- Percentage Trim One Tail Count
Calculate trimmed=floor(count*fraction) and remaining=count-2*trimmed.
- Arithmetic Geometric Mean Gap Two Values
Return arithmetic=(left+right)/2, geometric=sqrt(left)*sqrt(right), and gap=arithmetic-geometric for nonnegative inputs.