Description
Return minimum=max(0,rounded-resolution/2) and maximum=rounded+resolution/2, requiring nonnegative rounded standard deviation and positive resolution.
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 minimum=max(0,rounded-resolution/2) and maximum=rounded+resolution/2, requiring nonnegative rounded standard deviation and positive resolution.
When to use this tool
Use Standard Deviation Rounding Interval Envelope 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 rounded, resolution. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read minimum, maximum. Use the output convention below.
Return minimum=max(0,rounded-resolution/2) and maximum=rounded+resolution/2, requiring nonnegative rounded standard deviation and positive resolution.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| rounded | Rounded | Required. Finite number; minimum 0. |
| resolution | Resolution | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| minimum | Minimum | Required. Finite number. |
| maximum | Maximum | Required. Finite number. |
{
"input": {
"rounded": 2,
"resolution": 0.2
},
"output": {
"minimum": 1.9,
"maximum": 2.1
}
}Limitations and assumptions
- This is a supplied half-resolution rounding envelope with a nonnegative floor. It does not specify endpoint closure, probability coverage, sample uncertainty, or the actual rounding method.
- 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
- Sample Size Rounding Achieved Margin
Round positive unroundedSize upward for sampleSize and return achievedMargin=margin*sqrt(unroundedSize/sampleSize), requiring nonnegative margin.
- Standard Error Cluster Weight Reference
Return clusterError=independentError*sqrt(designEffect), requiring nonnegative independent error and positive design effect.