Random Rank-Sum Test Case Generator

Description

Generate independent samples on caller-specified inclusive integer lattices, controlling ties and range separation, and delegate tie-aware Mann–Whitney U statistics; report cross-sample tie pairs and model ranges without inventing p-values or a continuous-distribution assumption.

Synthetic statistical data separates a specified generating model from the values observed in a finite draw. A model parameter, a sample summary, and the result of a fitted analysis answer different questions; retaining them separately makes numerical and statistical checks easier to interpret.

When to use this tool

Use this generator to create reproducible rank sum test case cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.

How to use the tool and how it works

Supply first, second in the field shapes below. Set seed when you need an explicit replay.
Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
Read models, first, second, crossSampleTiePairs, analysis. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

For each sample, draw integers from minimum plus step times a uniformly sampled eligible step index. Delegate Mann-Whitney analysis and count all equal-valued cross-sample pairs separately.^[1]

Delegated operations used for this result: mann whitney u. Their calculation or parsing conventions apply to the corresponding result fields.^[2]

Input field	Meaning and units	Accepted input
first	First	Required. Object; no unknown keys.
first.count	Requested count; the mechanics explain whether one draw expands into several returned records.	Required. Safe integer; minimum 1; maximum 512.
first.minimum	Minimum	Required. Safe integer.
first.maximum	Maximum	Required. Safe integer.
first.step	Step	Required. Safe integer; minimum 1.
second	Second	Required. Object; no unknown keys.
second.count	Requested count; the mechanics explain whether one draw expands into several returned records.	Required. Safe integer; minimum 1; maximum 512.
second.minimum	Minimum	Required. Safe integer.
second.maximum	Maximum	Required. Safe integer.
second.step	Step	Required. Safe integer; minimum 1.
seed	Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed.	Optional. Safe integer.

Output field	Interpretation	Returned shape
models	Models	Required. Object; no unknown keys.
models.first	First	Required. Object; no unknown keys.
models.first.count	Requested count; the mechanics explain whether one draw expands into several returned records.	Required. Safe integer; minimum 1; maximum 512.
models.first.minimum	Minimum	Required. Safe integer.
models.first.maximum	Maximum	Required. Safe integer.
models.first.step	Step	Required. Safe integer; minimum 1.
models.second	Second	Required. Object; no unknown keys.
models.second.count	Requested count; the mechanics explain whether one draw expands into several returned records.	Required. Safe integer; minimum 1; maximum 512.
models.second.minimum	Minimum	Required. Safe integer.
models.second.maximum	Maximum	Required. Safe integer.
models.second.step	Step	Required. Safe integer; minimum 1.
first	First	Required. Array of Safe integer.; minimum items 1; maximum items 512.
second	Second	Required. Array of Safe integer.; minimum items 1; maximum items 512.
crossSampleTiePairs	Cross Sample Tie Pairs	Required. Safe integer; minimum 0; maximum 262144.
analysis	Analysis	Required. Object; no unknown keys.
analysis.firstU	First U	Required. Finite number; minimum 0.
analysis.secondU	Second U	Required. Finite number; minimum 0.
analysis.statistic	Statistic	Required. Finite number; minimum 0.
randomness	Replay metadata: source is seed or context; seed is the normalized 32-bit seed or null for a context source.	Required. Object; no unknown keys.
randomness.seed	Optional numeric replay seed; normalization and precedence are explained below.	Required. Safe integer. or Null.
randomness.source	Source	Required. Text; one of "context", "seed".

An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.

json

{
  "input": {
    "first": {
      "count": 4,
      "minimum": 0,
      "maximum": 2,
      "step": 1
    },
    "second": {
      "count": 3,
      "minimum": 1,
      "maximum": 3,
      "step": 1
    },
    "seed": 42
  },
  "output": {
    "models": {
      "first": {
        "count": 4,
        "minimum": 0,
        "maximum": 2,
        "step": 1
      },
      "second": {
        "count": 3,
        "minimum": 1,
        "maximum": 3,
        "step": 1
      }
    },
    "first": [
      1,
      1,
      2,
      2
    ],
    "second": [
      1,
      2,
      1
    ],
    "crossSampleTiePairs": 6,
    "analysis": {
      "firstU": 7,
      "secondU": 5,
      "statistic": 5
    },
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

A maximum not on the step grid is not reached. Ties can occur within and between samples; analysis inherits the linked rank-sum conventions and is not evidence of a real treatment or population effect.
A replay requires the same complete input and implementation. Randomized construction does not guarantee uniform coverage of every feasible output; finite samples can repeat unless a distinct-selection rule is explicitly stated.
The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.

Alternative or Complementary methods

For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.

References

Tool behavior and example: Random Rank-Sum Test Case Generator — tool.io
Calculation or validation: statistics/mann-whitney-u — tool.io

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