Description
Sum t^3-t over exact numeric rank tie blocks for finite observations; no rank-test p-value or independence inference.
A descriptive statistic depends on what is counted, how observations are weighted, and which reference or denominator is used. Removing observations differs from replacing them at cutoffs, and a ratio of totals differs from a mean of individual ratios. Keep those conventions and measurement units explicit when comparing results.
Sum t^3-t over exact numeric rank tie blocks for finite observations; no rank-test p-value or independence inference.
When to use this tool
Use this tool to sum t^3-t over exact numeric rank tie blocks for finite observations; no rank-test p-value or independence inference.
How to use the tool and how it works
- Enter values using the field definitions below.
- Run the operation. Correct input errors before interpreting an output.
- Read result.sum. Use the ordering, boundary rules and absence conditions described below.
Group exactly equal values into tie blocks and sum t³ − t for their sizes t.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| values | Finite observations in the measurement units used by reference or cutoffs. | Dense list of at most 128 finite numbers; integer/shape constraints above also apply. |
| Output field | Interpretation |
|---|---|
| result | Object containing the named fields below. |
| result.sum | The explicitly defined pairwise-difference or tie-block sum, without extra normalization. |
{
"input": {
"values": [
1,
1,
2,
2,
2
]
},
"output": {
"result": {
"sum": 30
}
}
}Limitations and assumptions
- No rank test or significance calculation is performed; near-equal floating-point values are not automatically tied.
- Use consistent units within each measured list and its reference/cutoffs. Ratios carry numerator units divided by denominator units unless those units cancel. Ordinary floating-point arithmetic is used; input validation does not establish statistical suitability.
- Every declared top-level input field is required and unexpected fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
- Numeric outputs must be finite and no larger in absolute magnitude than the safe-integer limit; operations returning exact large integers use decimal text. Positions are zero-based and spans end exclusively unless the operation explicitly states a different convention.
Alternative or Complementary methods
Check the descriptive convention and denominator before comparing results. Use a separate inferential model when you need uncertainty, significance, causal interpretation or population estimates.
References
Similar or alternative tools
- Rank Tie Correction Factor
Compute the exact-tie cubic correction factor 1-sum(t^3-t)/(n^3-n) for n>=2; does not itself correct a named test statistic.
- Pairwise Absolute Difference Sum
Sum absolute differences over every unordered observation pair exactly once; no normalization into Gini or dispersion estimators.