Rank Order Agreement Pairs

Classify numeric rank-order pair agreement and disagreement while retaining all pairs tied in either observation; not a normalized correlation coefficient.

Description

Classify numeric rank-order pair agreement and disagreement while retaining all pairs tied in either observation; not a normalized correlation coefficient.

Paired rankings agree or disagree on each observation pair. A tie in either list needs its own class.

When to use this tool

Classify numeric rank-order pair agreement and disagreement while retaining all pairs tied in either observation; not a normalized correlation coefficient.

Prepare the supplied left, right fields for this operation.
Compare the complete example with the representation used by your own input before carrying the result into another step.

How to use the tool and how it works

Enter left, right. Use the exact text syntax, units and index conventions explained below.
Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
Read result.concordant, result.discordant, result.tied. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.

Require equal-length numeric lists. For every index pair j before k, compare the two within-list difference signs. Put the pair in tied when either sign is zero, otherwise concordant for equal signs or discordant.^[1]

Input field	Meaning and representation	Accepted input
left	left.	List of finite numbers; at most 128 entries
right	right.	List of finite numbers; at most 128 entries

Output field	Interpretation
result	Object containing the named outputs below.
result.concordant	The concordant list in the ordering and representation described above.
result.discordant	The discordant list in the ordering and representation described above.
result.tied	The tied list in the ordering and representation described above.

json

{
  "input": {
    "left": [
      1,
      2,
      3
    ],
    "right": [
      1,
      3,
      2
    ]
  },
  "output": {
    "result": {
      "concordant": [
        [
          0,
          1
        ],
        [
          0,
          2
        ]
      ],
      "discordant": [
        [
          1,
          2
        ]
      ],
      "tied": []
    }
  }
}

Limitations and assumptions

No correlation coefficient or significance estimate is calculated. Ties use exact numeric equality.
All declared input fields are required and unexpected top-level fields are rejected. Numbers must be finite; lists are limited to 128 entries and ordinary text fields to 8,192 UTF-16 code units, with tighter limits where stated.
JSON text inputs must parse within bounded nesting and size limits. Numeric outputs outside the safe finite range are rejected; large exact integer results use decimal strings. Indexes and half-open spans are zero-based unless a rank is explicitly described as one-based.

Alternative or Complementary methods

Choose the tie policy and whether you need values, original indexes, sorted positions or one-based ranks. Use a complete sort verifier when a local stability or adjacent-comparison check is insufficient.

References

Tool behavior and example: Rank Order Agreement Pairs — tool.io

Similar or alternative tools

Competition Rank Tie Table
Assign one-based ascending competition numeric ranks; exact numeric ties are preserved according to the stated policy.
Dense Rank Tie Table
Assign one-based ascending dense numeric ranks; exact numeric ties are preserved according to the stated policy.