Random Bootstrap Interval Experiment Generator

Description

Generate bounded normal datasets and delegate mean/median percentile-bootstrap intervals with equal two-sided tail probabilities, adapting the older core level convention; retain nearest-rank endpoints and 12-significant-digit summary rounding, not BCa intervals or guaranteed nominal coverage.

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 bootstrap interval experiment 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 datasetCount, sampleCount, mean, standardDeviation, statistic, confidenceLevel, resamples 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 model, experiments. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.

Generate Gaussian datasets and delegate percentile bootstrap intervals for their mean or median using the same advancing random source. Map the requested central confidence fraction to core level (1+confidenceLevel)/2 so its two percentile tails are symmetric.^[1]

Delegated operations used for this result: bootstrap confidence interval. Their calculation or parsing conventions apply to the corresponding result fields.^[2]

Input field	Meaning and units	Accepted input
datasetCount	Dataset Count	Required. Safe integer; minimum 1; maximum 32.
sampleCount	Sample Count	Required. Safe integer; minimum 2; maximum 128.
mean	Mean	Required. Finite number.
standardDeviation	Standard Deviation	Required. Finite number; minimum 0.
statistic	Statistic	Required. Text; one of "mean", "median".
confidenceLevel	Confidence Level	Required. Finite number; strictly above 0; strictly below 1.
resamples	Resamples	Required. Safe integer; minimum 2; maximum 4096.
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
model	Model	Required. Object; no unknown keys.
model.mean	Mean	Required. Finite number.
model.standardDeviation	Standard Deviation	Required. Finite number; minimum 0.
experiments	Experiments	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 32.
experiments[].values	Values	Required. Array of Finite number.; minimum items 2; maximum items 128.
experiments[].interval	Interval	Required. Object; no unknown keys.
experiments[].interval.estimate	Estimate	Required. Finite number.
experiments[].interval.low	Low	Required. Finite number.
experiments[].interval.high	High	Required. Finite number.
experiments[].interval.confidenceLevel	Confidence Level	Required. Finite number; strictly above 0; strictly below 1.
experiments[].interval.resamples	Resamples	Required. Safe integer; minimum 2; maximum 4096.
experiments[].interval.statistic	Statistic	Required. Text; one of "mean", "median".
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": {
    "datasetCount": 1,
    "sampleCount": 3,
    "mean": 0,
    "standardDeviation": 1,
    "statistic": "mean",
    "confidenceLevel": 0.5,
    "resamples": 4,
    "seed": 42
  },
  "output": {
    "model": {
      "mean": 0,
      "standardDeviation": 1
    },
    "experiments": [
      {
        "values": [
          -0.956162229384149,
          -0.2730261048826104,
          -1.8416271847835968
        ],
        "interval": {
          "estimate": -1.02360517302,
          "low": -1.25131721452,
          "high": -1.02360517302,
          "confidenceLevel": 0.5,
          "resamples": 4,
          "statistic": "mean"
        }
      }
    ],
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

This uses percentile resampling rather than BCa or studentized bootstrap and reports no coverage experiment. Finite sample and resample counts affect results; output estimates and endpoints inherit the core's rounding.
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 Bootstrap Interval Experiment Generator — tool.io
Calculation or validation: statistics/bootstrap-confidence-interval — tool.io

Similar or alternative tools

Random Confidence Interval Coverage Experiment Generator
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Random A/B Test Experiment Generator
Generate paired batches of independent synthetic binomial conversion counts under supplied visitor totals/rates and delegate the existing pooled two-proportion z-test plus Wald interval; retain 12-significant-digit summaries, including degenerate endpoint conventions, not exact small-sample inference or real-study advice.