FA-74646 / Experiment statistics / Open access
Bootstrap difference interval: Resampling draws without replacement · case 01
Every replicate reproduces the observed difference, so the interval has zero width.
ROOT CAUSE
rng.sample is used, which merely permutes each arm.
THE FAILURE
rng.sample is used, which merely permutes each arm.
Unsuccessful approach: Resampling from the pooled data simulates the null instead of the effect.
Case contract
rng = random.Random(seed). Each of reps replicates resamples control then treatment with replacement (rng.choices, same sizes) and records mean(t) - mean(c). After sorting, the interval is diffs[floor((1 - level)/2 * reps)] to diffs[ceil((1 + level)/2 * reps) - 1]. Return both ends rounded to 6.
Why this case matters
Bootstrap intervals are the fallback for skewed metrics; reproducibility and indexing must be exact.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import random
N = 1
observations = []
def solve(control, treatment, reps, seed, level):
rng = random.Random(seed)
diffs = []
for _ in range(reps):
c = rng.sample(control, len(control))
t = rng.sample(treatment, len(treatment))
diffs.append(sum(t) / len(t) - sum(c) / len(c))
diffs.sort()
lo = diffs[math.floor((1 - level) / 2 * reps)]
hi = diffs[math.ceil((1 + level) / 2 * reps) - 1]
return [round(lo, 6), round(hi, 6)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('ninety percent interval', [[1, 2, 3, 4], [2, 3, 5, 8], 101, 7, 0.9], [0.0, 4.5]),
('eighty percent interval', [[0, 0, 1, 5], [1, 1, 2], 50, 11, 0.8], [-2.333333, 1.083333]),
('treatment larger than control', [[1, 2], [6, 9, 7], 41, 3, 0.9], [4.833333, 7.0]),
('ninety-five percent interval', [[3, 1, 4, 1, 5], [9, 2, 6, 5], 200, 42, 0.95], [-0.2, 5.65]),
('bootstrap sample 1', [[6, 3, 2, 7], [7, 9, 2, 9, 7], 200, 662, 0.9], [-0.35, 4.95]),
('bootstrap sample 2', [[4, 4, 4, 8, 2], [10, 9, 6, 3, 2], 50, 548, 0.8], [-0.4, 3.0]),
('bootstrap sample 3', [[6, 9, 2, 1], [3, 3, 11, 8, 2], 50, 269, 0.9], [-2.15, 4.35]),
('bootstrap sample 4', [[4, 6, 4], [3, 11], 200, 10, 0.9], [-2.333333, 7.0])],
[('ninety percent interval', [[1, 2, 3, 4], [2, 3, 5, 8], 101, 7, 0.9], [0.0, 4.5]),
('eighty percent interval', [[0, 0, 1, 5], [1, 1, 2], 50, 11, 0.8], [-2.333333, 1.083333]),
('treatment larger than control', [[1, 2], [6, 9, 7], 41, 3, 0.9], [4.833333, 7.0]),
('ninety-five percent interval', [[3, 1, 4, 1, 5], [9, 2, 6, 5], 200, 42, 0.95], [-0.2, 5.65]),
('bootstrap sample 4', [[4, 6, 4], [3, 11], 200, 10, 0.9], [-2.333333, 7.0]),
('bootstrap sample 6', [[9, 8], [11, 10, 6], 50, 172, 0.95], [-3.0, 2.5]),
('bootstrap sample 7', [[5, 7, 2, 9], [1, 10], 41, 416, 0.9], [-6.0, 5.5]),
('bootstrap sample 8', [[3, 2, 8, 5, 4], [4, 3, 6, 8, 6], 101, 427, 0.9], [-1.2, 2.8])],
[('ninety percent interval', [[1, 2, 3, 4], [2, 3, 5, 8], 101, 7, 0.9], [0.0, 4.5]),
('eighty percent interval', [[0, 0, 1, 5], [1, 1, 2], 50, 11, 0.8], [-2.333333, 1.083333]),
('treatment larger than control', [[1, 2], [6, 9, 7], 41, 3, 0.9], [4.833333, 7.0]),
('ninety-five percent interval', [[3, 1, 4, 1, 5], [9, 2, 6, 5], 200, 42, 0.95], [-0.2, 5.65]),
('bootstrap sample 11', [[7, 5, 6, 7, 6], [6, 4, 6, 3], 41, 117, 0.9], [-2.9, -0.3]),
('bootstrap sample 12', [[3, 5, 5, 0, 4], [5, 8], 41, 271, 0.95], [1.0, 5.6]),
('bootstrap sample 13', [[4, 8, 1, 1], [8, 8], 200, 78, 0.9], [2.0, 7.0]),
('bootstrap sample 14', [[2, 0, 8, 3], [4, 6, 7], 99, 617, 0.95], [-0.333333, 5.416667])],
[('ninety percent interval', [[1, 2, 3, 4], [2, 3, 5, 8], 101, 7, 0.9], [0.0, 4.5]),
('eighty percent interval', [[0, 0, 1, 5], [1, 1, 2], 50, 11, 0.8], [-2.333333, 1.083333]),
('treatment larger than control', [[1, 2], [6, 9, 7], 41, 3, 0.9], [4.833333, 7.0]),
('ninety-five percent interval', [[3, 1, 4, 1, 5], [9, 2, 6, 5], 200, 42, 0.95], [-0.2, 5.65]),
('bootstrap sample 16', [[3, 4], [5, 7, 7, 7], 101, 604, 0.95], [2.0, 4.0]),
('bootstrap sample 17', [[0, 1], [10, 2, 5, 8, 11], 50, 644, 0.8], [4.5, 8.7]),
('bootstrap sample 18', [[3, 4, 9], [0, 8], 101, 541, 0.95], [-9.0, 4.666667]),
('bootstrap sample 19', [[3, 3, 9], [2, 2], 99, 846, 0.9], [-7.0, -1.0])],
[('ninety percent interval', [[1, 2, 3, 4], [2, 3, 5, 8], 101, 7, 0.9], [0.0, 4.5]),
('eighty percent interval', [[0, 0, 1, 5], [1, 1, 2], 50, 11, 0.8], [-2.333333, 1.083333]),
('treatment larger than control', [[1, 2], [6, 9, 7], 41, 3, 0.9], [4.833333, 7.0]),
('ninety-five percent interval', [[3, 1, 4, 1, 5], [9, 2, 6, 5], 200, 42, 0.95], [-0.2, 5.65]),
('bootstrap sample 21', [[2, 6, 8, 0, 8], [9, 10, 5, 7, 10], 41, 153, 0.8], [1.2, 5.2]),
('bootstrap sample 22', [[8, 3], [0, 7, 11, 7, 1], 99, 38, 0.8], [-4.0, 3.4]),
('bootstrap sample 23', [[1, 2], [3, 4, 10, 3, 3], 99, 27, 0.9], [1.2, 5.7]),
('bootstrap sample 25', [[5, 9, 1, 0], [7, 6, 11, 8], 41, 751, 0.8], [2.0, 6.25])]]
for label, args, expected in fixtures[N - 1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| ninety percent interval | [2.0, 2.0] | [0.0, 4.5] | Failed |
| eighty percent interval | [-0.166667, -0.166667] | [-2.333333, 1.083333] | Failed |
| treatment larger than control | [5.833333, 5.833333] | [4.833333, 7.0] | Failed |
| ninety-five percent interval | [2.7, 2.7] | [-0.2, 5.65] | Failed |
| bootstrap sample 1 | [2.3, 2.3] | [-0.35, 4.95] | Failed |
| bootstrap sample 2 | [1.6, 1.6] | [-0.4, 3.0] | Failed |
| bootstrap sample 3 | [0.9, 0.9] | [-2.15, 4.35] | Failed |
| bootstrap sample 4 | [2.333333, 2.333333] | [-2.333333, 7.0] | Failed |
SHA-256 / 64e227f3902b8956b4f12cf0942a1f55336a3ad416f29ba24ea730de0370ec0b
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import random
N = 1
observations = []
def solve(control, treatment, reps, seed, level):
rng = random.Random(seed)
diffs = []
for _ in range(reps):
c = rng.choices(control + treatment, k=len(control))
t = rng.choices(control + treatment, k=len(treatment))
diffs.append(sum(t) / len(t) - sum(c) / len(c))
diffs.sort()
lo = diffs[math.floor((1 - level) / 2 * reps)]
hi = diffs[math.ceil((1 + level) / 2 * reps) - 1]
return [round(lo, 6), round(hi, 6)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('ninety percent interval', [[1, 2, 3, 4], [2, 3, 5, 8], 101, 7, 0.9], [0.0, 4.5]),
('eighty percent interval', [[0, 0, 1, 5], [1, 1, 2], 50, 11, 0.8], [-2.333333, 1.083333]),
('treatment larger than control', [[1, 2], [6, 9, 7], 41, 3, 0.9], [4.833333, 7.0]),
('ninety-five percent interval', [[3, 1, 4, 1, 5], [9, 2, 6, 5], 200, 42, 0.95], [-0.2, 5.65]),
('bootstrap sample 1', [[6, 3, 2, 7], [7, 9, 2, 9, 7], 200, 662, 0.9], [-0.35, 4.95]),
('bootstrap sample 2', [[4, 4, 4, 8, 2], [10, 9, 6, 3, 2], 50, 548, 0.8], [-0.4, 3.0]),
('bootstrap sample 3', [[6, 9, 2, 1], [3, 3, 11, 8, 2], 50, 269, 0.9], [-2.15, 4.35]),
('bootstrap sample 4', [[4, 6, 4], [3, 11], 200, 10, 0.9], [-2.333333, 7.0])],
[('ninety percent interval', [[1, 2, 3, 4], [2, 3, 5, 8], 101, 7, 0.9], [0.0, 4.5]),
('eighty percent interval', [[0, 0, 1, 5], [1, 1, 2], 50, 11, 0.8], [-2.333333, 1.083333]),
('treatment larger than control', [[1, 2], [6, 9, 7], 41, 3, 0.9], [4.833333, 7.0]),
('ninety-five percent interval', [[3, 1, 4, 1, 5], [9, 2, 6, 5], 200, 42, 0.95], [-0.2, 5.65]),
('bootstrap sample 4', [[4, 6, 4], [3, 11], 200, 10, 0.9], [-2.333333, 7.0]),
('bootstrap sample 6', [[9, 8], [11, 10, 6], 50, 172, 0.95], [-3.0, 2.5]),
('bootstrap sample 7', [[5, 7, 2, 9], [1, 10], 41, 416, 0.9], [-6.0, 5.5]),
('bootstrap sample 8', [[3, 2, 8, 5, 4], [4, 3, 6, 8, 6], 101, 427, 0.9], [-1.2, 2.8])],
[('ninety percent interval', [[1, 2, 3, 4], [2, 3, 5, 8], 101, 7, 0.9], [0.0, 4.5]),
('eighty percent interval', [[0, 0, 1, 5], [1, 1, 2], 50, 11, 0.8], [-2.333333, 1.083333]),
('treatment larger than control', [[1, 2], [6, 9, 7], 41, 3, 0.9], [4.833333, 7.0]),
('ninety-five percent interval', [[3, 1, 4, 1, 5], [9, 2, 6, 5], 200, 42, 0.95], [-0.2, 5.65]),
('bootstrap sample 11', [[7, 5, 6, 7, 6], [6, 4, 6, 3], 41, 117, 0.9], [-2.9, -0.3]),
('bootstrap sample 12', [[3, 5, 5, 0, 4], [5, 8], 41, 271, 0.95], [1.0, 5.6]),
('bootstrap sample 13', [[4, 8, 1, 1], [8, 8], 200, 78, 0.9], [2.0, 7.0]),
('bootstrap sample 14', [[2, 0, 8, 3], [4, 6, 7], 99, 617, 0.95], [-0.333333, 5.416667])],
[('ninety percent interval', [[1, 2, 3, 4], [2, 3, 5, 8], 101, 7, 0.9], [0.0, 4.5]),
('eighty percent interval', [[0, 0, 1, 5], [1, 1, 2], 50, 11, 0.8], [-2.333333, 1.083333]),
('treatment larger than control', [[1, 2], [6, 9, 7], 41, 3, 0.9], [4.833333, 7.0]),
('ninety-five percent interval', [[3, 1, 4, 1, 5], [9, 2, 6, 5], 200, 42, 0.95], [-0.2, 5.65]),
('bootstrap sample 16', [[3, 4], [5, 7, 7, 7], 101, 604, 0.95], [2.0, 4.0]),
('bootstrap sample 17', [[0, 1], [10, 2, 5, 8, 11], 50, 644, 0.8], [4.5, 8.7]),
('bootstrap sample 18', [[3, 4, 9], [0, 8], 101, 541, 0.95], [-9.0, 4.666667]),
('bootstrap sample 19', [[3, 3, 9], [2, 2], 99, 846, 0.9], [-7.0, -1.0])],
[('ninety percent interval', [[1, 2, 3, 4], [2, 3, 5, 8], 101, 7, 0.9], [0.0, 4.5]),
('eighty percent interval', [[0, 0, 1, 5], [1, 1, 2], 50, 11, 0.8], [-2.333333, 1.083333]),
('treatment larger than control', [[1, 2], [6, 9, 7], 41, 3, 0.9], [4.833333, 7.0]),
('ninety-five percent interval', [[3, 1, 4, 1, 5], [9, 2, 6, 5], 200, 42, 0.95], [-0.2, 5.65]),
('bootstrap sample 21', [[2, 6, 8, 0, 8], [9, 10, 5, 7, 10], 41, 153, 0.8], [1.2, 5.2]),
('bootstrap sample 22', [[8, 3], [0, 7, 11, 7, 1], 99, 38, 0.8], [-4.0, 3.4]),
('bootstrap sample 23', [[1, 2], [3, 4, 10, 3, 3], 99, 27, 0.9], [1.2, 5.7]),
('bootstrap sample 25', [[5, 9, 1, 0], [7, 6, 11, 8], 41, 751, 0.8], [2.0, 6.25])]]
for label, args, expected in fixtures[N - 1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| ninety percent interval | [-2.25, 2.0] | [0.0, 4.5] | Failed |
| eighty percent interval | [-1.833333, 0.916667] | [-2.333333, 1.083333] | Failed |
| treatment larger than control | [-3.5, 3.333333] | [4.833333, 7.0] | Failed |
| ninety-five percent interval | [-3.4, 3.3] | [-0.2, 5.65] | Failed |
| bootstrap sample 1 | [-2.7, 2.9] | [-0.35, 4.95] | Failed |
| bootstrap sample 2 | [-2.4, 2.2] | [-0.4, 3.0] | Failed |
| bootstrap sample 3 | [-2.3, 3.8] | [-2.15, 4.35] | Failed |
| bootstrap sample 4 | [-4.166667, 4.166667] | [-2.333333, 7.0] | Failed |
SHA-256 / 5224ffaa7d80326d842c556ebf67c5a52ccd7e6f809cb2af83f53c2d54decf90
HELD IN THE MEMBER ARCHIVE
The verified repair and its recorded checks are member-only.
This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.
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Sign in to the archive ↗Verification & scope
A deterministic toy experiment-analysis model with a stipulated contract; results are rounded and are not a substitute for a validated statistics package. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:48:58.621419+00:00.
Case digest / 68e279b68449d68b729615e2a9e8e6c3a8ef20e00b79e6eb38e6cab3094ef1ee