Description
Generate synthetic normal before values and after=before+offset+independent normal noise, then delegate the paired t statistic for after-minus-before; preserve inherited 12-significant-digit results and report undefined/nonfinite statistics explicitly rather than fabricating 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.
Generate synthetic normal before values and after=before+offset+independent normal noise, then delegate the paired t statistic for after-minus-before; preserve inherited 12-significant-digit results and report undefined/nonfinite statistics explicitly rather than fabricating p-values.
When to use this tool
Use this generator to create reproducible paired t test 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 beforeMean, beforeStandardDeviation, offset, noiseStandardDeviation, count 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, before, after, analysis. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Draw Gaussian before values and corresponding after values centered on before plus offset with additional Gaussian noise. Delegate the paired t calculation as after minus before, retaining finite, undefined-statistic, or numeric-overflow status.1
Delegated operations used for this result: paired t test. Their calculation or parsing conventions apply to the corresponding result fields.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| beforeMean | Before Mean | Required. Finite number. |
| beforeStandardDeviation | Before Standard Deviation | Required. Finite number; minimum 0. |
| offset | Offset | Required. Finite number. |
| noiseStandardDeviation | Noise Standard Deviation | Required. Finite number; minimum 0. |
| count | Requested count; the mechanics explain whether one draw expands into several returned records. | Required. Safe integer; minimum 2; maximum 1024. |
| 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.beforeMean | Before Mean | Required. Finite number. |
| model.beforeStandardDeviation | Before Standard Deviation | Required. Finite number; minimum 0. |
| model.offset | Offset | Required. Finite number. |
| model.noiseStandardDeviation | Noise Standard Deviation | Required. Finite number; minimum 0. |
| before | Before | Required. Array of Finite number.; minimum items 2; maximum items 1024. |
| after | After | Required. Array of Finite number.; minimum items 2; maximum items 1024. |
| analysis | Analysis | Required. Object; no unknown keys. |
| analysis.status | Named outcome; inspect null and error fields before interpreting associated values. | Required. Text; one of "finite", "undefined-statistic", "numeric-overflow". |
| analysis.result | Result | Required. Object; no unknown keys. or Null. |
| 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.
{
"input": {
"count": 3,
"beforeMean": 10,
"beforeStandardDeviation": 1,
"offset": 2,
"noiseStandardDeviation": 1,
"seed": 42
},
"output": {
"model": {
"beforeMean": 10,
"beforeStandardDeviation": 1,
"offset": 2,
"noiseStandardDeviation": 1
},
"before": [
9.043837770615852,
9.72697389511739,
8.158372815216403
],
"after": [
9.902955699661828,
11.197540101400975,
11.386963488279507
],
"analysis": {
"status": "finite",
"result": {
"degreesOfFreedom": 2,
"meanDifference": 1.85275826946,
"sampleSize": 3,
"standardDeviation": 1.23010298391,
"standardError": 0.710200288892,
"tStatistic": 2.60878275951
}
},
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- The samples are matched pairs, not independent groups. A constant difference can make the statistic undefined. Synthetic test results do not establish a real effect or validate normality assumptions.
- 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
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