Description
Compare two explicit tied-rank intervals using midpoint, minimum and maximum distances.
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.
Compare two explicit tied-rank intervals using midpoint, minimum and maximum distances.
When to use this tool
Use Rank Distance Tie Gap 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 firstMinimumRank, firstMaximumRank, secondMinimumRank, secondMaximumRank. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read midrankGap, closestGap, largestGap. Use the output convention below.
Return the signed gap between interval midranks, the smallest nonnegative separation between ordered rank intervals, and the greatest absolute endpoint gap.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstMinimumRank | First Minimum Rank | Required. Finite number. |
| firstMaximumRank | First Maximum Rank | Required. Finite number. |
| secondMinimumRank | Second Minimum Rank | Required. Finite number. |
| secondMaximumRank | Second Maximum Rank | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| midrankGap | Midrank Gap | Required. Finite number. |
| closestGap | Closest Gap | Required. Finite number. |
| largestGap | Largest Gap | Required. Finite number. |
{
"input": {
"firstMinimumRank": 1,
"firstMaximumRank": 3,
"secondMinimumRank": 5,
"secondMaximumRank": 7
},
"output": {
"midrankGap": 4,
"closestGap": 2,
"largestGap": 6
}
}Limitations and assumptions
- Ranks are supplied numeric intervals and need not be integer positions. This does not assign tied ranks, compare full rankings, or calculate a rank-correlation statistic.
- 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
- Empirical Cdf One Tie Jump
Return leftLimit=less/count, rightLimit=(less+tied)/count, and jump=tied/count after feasible nonnegative integer count checks with positive total.
- Median Tie Middle Gap
Sort a copy of nonempty values numerically and return lowerMiddle, upperMiddle, and gap=upperMiddle-lowerMiddle.