Random ANOVA Test Case Generator

Description

Generate independent normal groups from supplied group-specific means, deviations, and sizes, then delegate one-way ANOVA sums of squares and F ratio; retain 12-significant-digit summaries and explicit nonfinite/undefined cases, without fitting parameters or inventing p-values.

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 anova 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 groups 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, groups, analysis. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.

Draw independent Gaussian groups from their supplied means, deviations, and counts, then delegate one-way ANOVA. Return original models and samples with finite analysis or a null result under not-finite status.^[1]

Delegated operations used for this result: one way anova. Their calculation or parsing conventions apply to the corresponding result fields.^[2]

Input field	Meaning and units	Accepted input
groups	Groups	Required. Array of Object; no unknown keys.; minimum items 2; maximum items 16.
groups[].mean	Mean	Required. Finite number.
groups[].standardDeviation	Standard Deviation	Required. Finite number; minimum 0.
groups[].count	Count	Required. Safe integer; minimum 2; maximum 256.
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. Array of Object; no unknown keys.; minimum items 2; maximum items 16.
models[].mean	Mean	Required. Finite number.
models[].standardDeviation	Standard Deviation	Required. Finite number; minimum 0.
models[].count	Count	Required. Safe integer; minimum 2; maximum 256.
groups	Groups	Required. Array of Array of Finite number.; minimum items 2; maximum items 256.; minimum items 2; maximum items 16.
analysis	Analysis	Required. Object; no unknown keys.
analysis.status	Named outcome; interpret associated null fields and error evidence under the stated convention.	Required. Text; one of "finite", "not-finite".
analysis.result	Result	Required. Object; no unknown keys. or Null.
randomness	Replay source and normalized 32-bit seed, or null seed for an advancing context source.	Required. Object; no unknown keys.
randomness.seed	Optional safe-integer 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": {
    "groups": [
      {
        "mean": 0,
        "standardDeviation": 1,
        "count": 3
      },
      {
        "mean": 2,
        "standardDeviation": 1,
        "count": 3
      }
    ],
    "seed": 42
  },
  "output": {
    "models": [
      {
        "mean": 0,
        "standardDeviation": 1,
        "count": 3
      },
      {
        "mean": 2,
        "standardDeviation": 1,
        "count": 3
      }
    ],
    "groups": [
      [
        -0.956162229384149,
        -0.2730261048826104,
        -1.8416271847835968
      ],
      [
        0.8591179290459758,
        1.4705662062835847,
        3.2285906730631044
      ]
    ],
    "analysis": {
      "status": "finite",
      "result": {
        "betweenDegreesOfFreedom": 1,
        "betweenSumSquares": 12.4101999799,
        "fRatio": 11.6435201633,
        "grandMean": 0.414576548224,
        "groupMeans": [
          -1.02360517302,
          1.85275826946
        ],
        "withinDegreesOfFreedom": 4,
        "withinSumSquares": 4.26338420196
      }
    },
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Synthetic normal groups do not validate assumptions for real data. Zero within-group variation or extreme arithmetic can prevent a finite analysis, and an observed statistic is not proof of a real-world group effect.
A replay requires the same complete input and implementation. The stated sampling convention applies within its eligible space. A finite draw does not exhaust all possible outputs; repeats remain possible unless a distinct-selection rule is explicit.
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 ANOVA Test Case Generator — tool.io
Calculation or validation: statistics/one-way-anova — tool.io

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