FAILURE MAP
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FA-74486 / Experiment statistics / Open access

Holm correction across metrics: Adjusted p-values are not made monotone · case 01

A metric with a smaller raw p-value reports a larger adjusted p-value than a later one.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Each adjusted value is min(1, (m - k) p) without the running maximum.

VERIFIED REPAIR

Carry the running maximum over the sorted adjusted values.

Unsuccessful approach: Keeping the running maximum but dropping the cap reports adjusted values above one.

Case contract

Holm step-down: sort p-values ascending (ties by position); reject while p_(k) <= alpha / (m - k) for k = 0, 1, ... and stop at the first failure. Adjusted p_(k) = running max of min(1, (m - k) p_(k)). Return [rejections, adjusted p-values rounded to 6] in the original metric order.

Why this case matters

Experiments track many metrics; multiplicity control keeps secondary wins honest.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(pvalues, alpha):
    m = len(pvalues)
    order = sorted(range(m), key=lambda i: (pvalues[i], i))
    reject = [False] * m
    adjusted = [0.0] * m
    running = 0.0
    stopped = False
    for rank, i in enumerate(order):
        running = min(1.0, (m - rank) * pvalues[i])
        adjusted[i] = round(running, 6)
        if not stopped and pvalues[i] <= alpha / (m - rank):
            reject[i] = True
        else:
            stopped = True
    return [reject, adjusted]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('all three pass their step thresholds',
   [[0.01, 0.04, 0.012], 0.05],
   [[True, True, True], [0.03, 0.04, 0.03]]),
  ('step-down stops at first non-rejection',
   [[0.03, 0.02, 0.04], 0.05],
   [[False, False, False], [0.06, 0.06, 0.06]]),
  ('boundary p equals alpha over remaining',
   [[0.0125, 0.5, 0.9, 0.9], 0.05],
   [[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]),
  ('adjusted values are monotone', [[0.01, 0.011, 0.5], 0.05], [[True, True, False], [0.03, 0.03, 0.5]]),
  ('adjusted values cap at one', [[0.4, 0.6], 0.05], [[False, False], [0.8, 0.8]]),
  ('metric p-value sample 1',
   [[0.025, 0.02, 0.05, 0.6], 0.05],
   [[False, False, False, False], [0.08, 0.08, 0.1, 0.6]]),
  ('metric p-value sample 2', [[0.0125, 0.03, 0.0167], 0.05], [[True, True, True], [0.0375, 0.0375, 0.0375]]),
  ('metric p-value sample 3', [[0.025], 0.05], [[True], [0.025]])],
 [('step-down stops at first non-rejection',
   [[0.03, 0.02, 0.04], 0.05],
   [[False, False, False], [0.06, 0.06, 0.06]]),
  ('boundary p equals alpha over remaining',
   [[0.0125, 0.5, 0.9, 0.9], 0.05],
   [[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]),
  ('adjusted values are monotone', [[0.01, 0.011, 0.5], 0.05], [[True, True, False], [0.03, 0.03, 0.5]]),
  ('adjusted values cap at one', [[0.4, 0.6], 0.05], [[False, False], [0.8, 0.8]]),
  ('original order is preserved', [[0.3, 0.001, 0.02], 0.05], [[False, True, True], [0.3, 0.003, 0.04]]),
  ('metric p-value sample 4', [[0.0125, 0.0167, 0.05], 0.05], [[True, True, True], [0.0375, 0.0375, 0.05]]),
  ('metric p-value sample 6', [[0.01, 0.05], 0.05], [[True, True], [0.02, 0.05]]),
  ('metric p-value sample 7', [[0.02, 0.0167], 0.05], [[True, True], [0.0334, 0.0334]])],
 [('boundary p equals alpha over remaining',
   [[0.0125, 0.5, 0.9, 0.9], 0.05],
   [[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]),
  ('adjusted values are monotone', [[0.01, 0.011, 0.5], 0.05], [[True, True, False], [0.03, 0.03, 0.5]]),
  ('adjusted values cap at one', [[0.4, 0.6], 0.05], [[False, False], [0.8, 0.8]]),
  ('original order is preserved', [[0.3, 0.001, 0.02], 0.05], [[False, True, True], [0.3, 0.003, 0.04]]),
  ('holm rejects more than bonferroni', [[0.01, 0.02], 0.05], [[True, True], [0.02, 0.02]]),
  ('metric p-value sample 11', [[0.01, 0.001, 0.02], 0.05], [[True, True, True], [0.02, 0.003, 0.02]]),
  ('metric p-value sample 12',
   [[0.04, 0.025, 0.01, 0.0167, 0.0125], 0.05],
   [[False, False, True, False, True], [0.0501, 0.0501, 0.05, 0.0501, 0.05]]),
  ('metric p-value sample 16',
   [[0.03, 0.02, 0.2, 0.6, 0.0167], 0.05],
   [[False, False, False, False, False], [0.09, 0.0835, 0.4, 0.6, 0.0835]])],
 [('boundary p equals alpha over remaining',
   [[0.0125, 0.5, 0.9, 0.9], 0.05],
   [[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]),
  ('adjusted values are monotone', [[0.01, 0.011, 0.5], 0.05], [[True, True, False], [0.03, 0.03, 0.5]]),
  ('adjusted values cap at one', [[0.4, 0.6], 0.05], [[False, False], [0.8, 0.8]]),
  ('original order is preserved', [[0.3, 0.001, 0.02], 0.05], [[False, True, True], [0.3, 0.003, 0.04]]),
  ('holm rejects more than bonferroni', [[0.01, 0.02], 0.05], [[True, True], [0.02, 0.02]]),
  ('single metric', [[0.05], 0.05], [[True], [0.05]]),
  ('metric p-value sample 16',
   [[0.03, 0.02, 0.2, 0.6, 0.0167], 0.05],
   [[False, False, False, False, False], [0.09, 0.0835, 0.4, 0.6, 0.0835]]),
  ('metric p-value sample 28', [[0.01, 0.05, 0.03], 0.05], [[True, False, False], [0.03, 0.06, 0.06]])],
 [('all three pass their step thresholds',
   [[0.01, 0.04, 0.012], 0.05],
   [[True, True, True], [0.03, 0.04, 0.03]]),
  ('boundary p equals alpha over remaining',
   [[0.0125, 0.5, 0.9, 0.9], 0.05],
   [[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]),
  ('adjusted values cap at one', [[0.4, 0.6], 0.05], [[False, False], [0.8, 0.8]]),
  ('original order is preserved', [[0.3, 0.001, 0.02], 0.05], [[False, True, True], [0.3, 0.003, 0.04]]),
  ('holm rejects more than bonferroni', [[0.01, 0.02], 0.05], [[True, True], [0.02, 0.02]]),
  ('single metric', [[0.05], 0.05], [[True], [0.05]]),
  ('metric p-value sample 21',
   [[0.0167, 0.6, 0.2, 0.02, 0.01], 0.05],
   [[False, False, False, False, True], [0.0668, 0.6, 0.4, 0.0668, 0.05]]),
  ('metric p-value sample 48',
   [[0.02, 0.2, 0.0167, 0.2, 0.025], 0.05],
   [[False, False, False, False, False], [0.0835, 0.4, 0.0835, 0.4, 0.0835]])]]
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 fixtureActualExpectedOutcome
all three pass their step thresholds[[True, True, True], [0.03, 0.04, 0.024]][[True, True, True], [0.03, 0.04, 0.03]]Failed
step-down stops at first non-rejection[[False, False, False], [0.06, 0.06, 0.04]][[False, False, False], [0.06, 0.06, 0.06]]Failed
boundary p equals alpha over remaining[[True, False, False, False], [0.05, 1.0, 1.0, 0.9]][[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]Failed
adjusted values are monotone[[True, True, False], [0.03, 0.022, 0.5]][[True, True, False], [0.03, 0.03, 0.5]]Failed
adjusted values cap at one[[False, False], [0.8, 0.6]][[False, False], [0.8, 0.8]]Failed
metric p-value sample 1[[False, False, False, False], [0.075, 0.08, 0.1, 0.6]][[False, False, False, False], [0.08, 0.08, 0.1, 0.6]]Failed
metric p-value sample 2[[True, True, True], [0.0375, 0.03, 0.0334]][[True, True, True], [0.0375, 0.0375, 0.0375]]Failed
metric p-value sample 3[[True], [0.025]][[True], [0.025]]Passed

SHA-256 / 2286904f5db44c6f7fc7abfa5b6620a81aef742c8d38b756f23e3f98915ddc9d

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(pvalues, alpha):
    m = len(pvalues)
    order = sorted(range(m), key=lambda i: (pvalues[i], i))
    reject = [False] * m
    adjusted = [0.0] * m
    running = 0.0
    stopped = False
    for rank, i in enumerate(order):
        running = max(running, (m - rank) * pvalues[i])
        adjusted[i] = round(running, 6)
        if not stopped and pvalues[i] <= alpha / (m - rank):
            reject[i] = True
        else:
            stopped = True
    return [reject, adjusted]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('all three pass their step thresholds',
   [[0.01, 0.04, 0.012], 0.05],
   [[True, True, True], [0.03, 0.04, 0.03]]),
  ('step-down stops at first non-rejection',
   [[0.03, 0.02, 0.04], 0.05],
   [[False, False, False], [0.06, 0.06, 0.06]]),
  ('boundary p equals alpha over remaining',
   [[0.0125, 0.5, 0.9, 0.9], 0.05],
   [[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]),
  ('adjusted values are monotone', [[0.01, 0.011, 0.5], 0.05], [[True, True, False], [0.03, 0.03, 0.5]]),
  ('adjusted values cap at one', [[0.4, 0.6], 0.05], [[False, False], [0.8, 0.8]]),
  ('metric p-value sample 1',
   [[0.025, 0.02, 0.05, 0.6], 0.05],
   [[False, False, False, False], [0.08, 0.08, 0.1, 0.6]]),
  ('metric p-value sample 2', [[0.0125, 0.03, 0.0167], 0.05], [[True, True, True], [0.0375, 0.0375, 0.0375]]),
  ('metric p-value sample 3', [[0.025], 0.05], [[True], [0.025]])],
 [('step-down stops at first non-rejection',
   [[0.03, 0.02, 0.04], 0.05],
   [[False, False, False], [0.06, 0.06, 0.06]]),
  ('boundary p equals alpha over remaining',
   [[0.0125, 0.5, 0.9, 0.9], 0.05],
   [[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]),
  ('adjusted values are monotone', [[0.01, 0.011, 0.5], 0.05], [[True, True, False], [0.03, 0.03, 0.5]]),
  ('adjusted values cap at one', [[0.4, 0.6], 0.05], [[False, False], [0.8, 0.8]]),
  ('original order is preserved', [[0.3, 0.001, 0.02], 0.05], [[False, True, True], [0.3, 0.003, 0.04]]),
  ('metric p-value sample 4', [[0.0125, 0.0167, 0.05], 0.05], [[True, True, True], [0.0375, 0.0375, 0.05]]),
  ('metric p-value sample 6', [[0.01, 0.05], 0.05], [[True, True], [0.02, 0.05]]),
  ('metric p-value sample 7', [[0.02, 0.0167], 0.05], [[True, True], [0.0334, 0.0334]])],
 [('boundary p equals alpha over remaining',
   [[0.0125, 0.5, 0.9, 0.9], 0.05],
   [[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]),
  ('adjusted values are monotone', [[0.01, 0.011, 0.5], 0.05], [[True, True, False], [0.03, 0.03, 0.5]]),
  ('adjusted values cap at one', [[0.4, 0.6], 0.05], [[False, False], [0.8, 0.8]]),
  ('original order is preserved', [[0.3, 0.001, 0.02], 0.05], [[False, True, True], [0.3, 0.003, 0.04]]),
  ('holm rejects more than bonferroni', [[0.01, 0.02], 0.05], [[True, True], [0.02, 0.02]]),
  ('metric p-value sample 11', [[0.01, 0.001, 0.02], 0.05], [[True, True, True], [0.02, 0.003, 0.02]]),
  ('metric p-value sample 12',
   [[0.04, 0.025, 0.01, 0.0167, 0.0125], 0.05],
   [[False, False, True, False, True], [0.0501, 0.0501, 0.05, 0.0501, 0.05]]),
  ('metric p-value sample 16',
   [[0.03, 0.02, 0.2, 0.6, 0.0167], 0.05],
   [[False, False, False, False, False], [0.09, 0.0835, 0.4, 0.6, 0.0835]])],
 [('boundary p equals alpha over remaining',
   [[0.0125, 0.5, 0.9, 0.9], 0.05],
   [[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]),
  ('adjusted values are monotone', [[0.01, 0.011, 0.5], 0.05], [[True, True, False], [0.03, 0.03, 0.5]]),
  ('adjusted values cap at one', [[0.4, 0.6], 0.05], [[False, False], [0.8, 0.8]]),
  ('original order is preserved', [[0.3, 0.001, 0.02], 0.05], [[False, True, True], [0.3, 0.003, 0.04]]),
  ('holm rejects more than bonferroni', [[0.01, 0.02], 0.05], [[True, True], [0.02, 0.02]]),
  ('single metric', [[0.05], 0.05], [[True], [0.05]]),
  ('metric p-value sample 16',
   [[0.03, 0.02, 0.2, 0.6, 0.0167], 0.05],
   [[False, False, False, False, False], [0.09, 0.0835, 0.4, 0.6, 0.0835]]),
  ('metric p-value sample 28', [[0.01, 0.05, 0.03], 0.05], [[True, False, False], [0.03, 0.06, 0.06]])],
 [('all three pass their step thresholds',
   [[0.01, 0.04, 0.012], 0.05],
   [[True, True, True], [0.03, 0.04, 0.03]]),
  ('boundary p equals alpha over remaining',
   [[0.0125, 0.5, 0.9, 0.9], 0.05],
   [[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]),
  ('adjusted values cap at one', [[0.4, 0.6], 0.05], [[False, False], [0.8, 0.8]]),
  ('original order is preserved', [[0.3, 0.001, 0.02], 0.05], [[False, True, True], [0.3, 0.003, 0.04]]),
  ('holm rejects more than bonferroni', [[0.01, 0.02], 0.05], [[True, True], [0.02, 0.02]]),
  ('single metric', [[0.05], 0.05], [[True], [0.05]]),
  ('metric p-value sample 21',
   [[0.0167, 0.6, 0.2, 0.02, 0.01], 0.05],
   [[False, False, False, False, True], [0.0668, 0.6, 0.4, 0.0668, 0.05]]),
  ('metric p-value sample 48',
   [[0.02, 0.2, 0.0167, 0.2, 0.025], 0.05],
   [[False, False, False, False, False], [0.0835, 0.4, 0.0835, 0.4, 0.0835]])]]
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 fixtureActualExpectedOutcome
all three pass their step thresholds[[True, True, True], [0.03, 0.04, 0.03]][[True, True, True], [0.03, 0.04, 0.03]]Passed
step-down stops at first non-rejection[[False, False, False], [0.06, 0.06, 0.06]][[False, False, False], [0.06, 0.06, 0.06]]Passed
boundary p equals alpha over remaining[[True, False, False, False], [0.05, 1.5, 1.8, 1.8]][[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]Failed
adjusted values are monotone[[True, True, False], [0.03, 0.03, 0.5]][[True, True, False], [0.03, 0.03, 0.5]]Passed
adjusted values cap at one[[False, False], [0.8, 0.8]][[False, False], [0.8, 0.8]]Passed
metric p-value sample 1[[False, False, False, False], [0.08, 0.08, 0.1, 0.6]][[False, False, False, False], [0.08, 0.08, 0.1, 0.6]]Passed
metric p-value sample 2[[True, True, True], [0.0375, 0.0375, 0.0375]][[True, True, True], [0.0375, 0.0375, 0.0375]]Passed
metric p-value sample 3[[True], [0.025]][[True], [0.025]]Passed

SHA-256 / d255f5200ea7ccfaaf53ddc06f2ff8383ce3a8d604eddfe5821b808c0e97bd60

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(pvalues, alpha):
    m = len(pvalues)
    order = sorted(range(m), key=lambda i: (pvalues[i], i))
    reject = [False] * m
    adjusted = [0.0] * m
    running = 0.0
    stopped = False
    for rank, i in enumerate(order):
        running = max(running, min(1.0, (m - rank) * pvalues[i]))
        adjusted[i] = round(running, 6)
        if not stopped and pvalues[i] <= alpha / (m - rank):
            reject[i] = True
        else:
            stopped = True
    return [reject, adjusted]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('all three pass their step thresholds',
   [[0.01, 0.04, 0.012], 0.05],
   [[True, True, True], [0.03, 0.04, 0.03]]),
  ('step-down stops at first non-rejection',
   [[0.03, 0.02, 0.04], 0.05],
   [[False, False, False], [0.06, 0.06, 0.06]]),
  ('boundary p equals alpha over remaining',
   [[0.0125, 0.5, 0.9, 0.9], 0.05],
   [[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]),
  ('adjusted values are monotone', [[0.01, 0.011, 0.5], 0.05], [[True, True, False], [0.03, 0.03, 0.5]]),
  ('adjusted values cap at one', [[0.4, 0.6], 0.05], [[False, False], [0.8, 0.8]]),
  ('metric p-value sample 1',
   [[0.025, 0.02, 0.05, 0.6], 0.05],
   [[False, False, False, False], [0.08, 0.08, 0.1, 0.6]]),
  ('metric p-value sample 2', [[0.0125, 0.03, 0.0167], 0.05], [[True, True, True], [0.0375, 0.0375, 0.0375]]),
  ('metric p-value sample 3', [[0.025], 0.05], [[True], [0.025]])],
 [('step-down stops at first non-rejection',
   [[0.03, 0.02, 0.04], 0.05],
   [[False, False, False], [0.06, 0.06, 0.06]]),
  ('boundary p equals alpha over remaining',
   [[0.0125, 0.5, 0.9, 0.9], 0.05],
   [[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]),
  ('adjusted values are monotone', [[0.01, 0.011, 0.5], 0.05], [[True, True, False], [0.03, 0.03, 0.5]]),
  ('adjusted values cap at one', [[0.4, 0.6], 0.05], [[False, False], [0.8, 0.8]]),
  ('original order is preserved', [[0.3, 0.001, 0.02], 0.05], [[False, True, True], [0.3, 0.003, 0.04]]),
  ('metric p-value sample 4', [[0.0125, 0.0167, 0.05], 0.05], [[True, True, True], [0.0375, 0.0375, 0.05]]),
  ('metric p-value sample 6', [[0.01, 0.05], 0.05], [[True, True], [0.02, 0.05]]),
  ('metric p-value sample 7', [[0.02, 0.0167], 0.05], [[True, True], [0.0334, 0.0334]])],
 [('boundary p equals alpha over remaining',
   [[0.0125, 0.5, 0.9, 0.9], 0.05],
   [[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]),
  ('adjusted values are monotone', [[0.01, 0.011, 0.5], 0.05], [[True, True, False], [0.03, 0.03, 0.5]]),
  ('adjusted values cap at one', [[0.4, 0.6], 0.05], [[False, False], [0.8, 0.8]]),
  ('original order is preserved', [[0.3, 0.001, 0.02], 0.05], [[False, True, True], [0.3, 0.003, 0.04]]),
  ('holm rejects more than bonferroni', [[0.01, 0.02], 0.05], [[True, True], [0.02, 0.02]]),
  ('metric p-value sample 11', [[0.01, 0.001, 0.02], 0.05], [[True, True, True], [0.02, 0.003, 0.02]]),
  ('metric p-value sample 12',
   [[0.04, 0.025, 0.01, 0.0167, 0.0125], 0.05],
   [[False, False, True, False, True], [0.0501, 0.0501, 0.05, 0.0501, 0.05]]),
  ('metric p-value sample 16',
   [[0.03, 0.02, 0.2, 0.6, 0.0167], 0.05],
   [[False, False, False, False, False], [0.09, 0.0835, 0.4, 0.6, 0.0835]])],
 [('boundary p equals alpha over remaining',
   [[0.0125, 0.5, 0.9, 0.9], 0.05],
   [[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]),
  ('adjusted values are monotone', [[0.01, 0.011, 0.5], 0.05], [[True, True, False], [0.03, 0.03, 0.5]]),
  ('adjusted values cap at one', [[0.4, 0.6], 0.05], [[False, False], [0.8, 0.8]]),
  ('original order is preserved', [[0.3, 0.001, 0.02], 0.05], [[False, True, True], [0.3, 0.003, 0.04]]),
  ('holm rejects more than bonferroni', [[0.01, 0.02], 0.05], [[True, True], [0.02, 0.02]]),
  ('single metric', [[0.05], 0.05], [[True], [0.05]]),
  ('metric p-value sample 16',
   [[0.03, 0.02, 0.2, 0.6, 0.0167], 0.05],
   [[False, False, False, False, False], [0.09, 0.0835, 0.4, 0.6, 0.0835]]),
  ('metric p-value sample 28', [[0.01, 0.05, 0.03], 0.05], [[True, False, False], [0.03, 0.06, 0.06]])],
 [('all three pass their step thresholds',
   [[0.01, 0.04, 0.012], 0.05],
   [[True, True, True], [0.03, 0.04, 0.03]]),
  ('boundary p equals alpha over remaining',
   [[0.0125, 0.5, 0.9, 0.9], 0.05],
   [[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]),
  ('adjusted values cap at one', [[0.4, 0.6], 0.05], [[False, False], [0.8, 0.8]]),
  ('original order is preserved', [[0.3, 0.001, 0.02], 0.05], [[False, True, True], [0.3, 0.003, 0.04]]),
  ('holm rejects more than bonferroni', [[0.01, 0.02], 0.05], [[True, True], [0.02, 0.02]]),
  ('single metric', [[0.05], 0.05], [[True], [0.05]]),
  ('metric p-value sample 21',
   [[0.0167, 0.6, 0.2, 0.02, 0.01], 0.05],
   [[False, False, False, False, True], [0.0668, 0.6, 0.4, 0.0668, 0.05]]),
  ('metric p-value sample 48',
   [[0.02, 0.2, 0.0167, 0.2, 0.025], 0.05],
   [[False, False, False, False, False], [0.0835, 0.4, 0.0835, 0.4, 0.0835]])]]
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 fixtureActualExpectedOutcome
all three pass their step thresholds[[True, True, True], [0.03, 0.04, 0.03]][[True, True, True], [0.03, 0.04, 0.03]]Passed
step-down stops at first non-rejection[[False, False, False], [0.06, 0.06, 0.06]][[False, False, False], [0.06, 0.06, 0.06]]Passed
boundary p equals alpha over remaining[[True, False, False, False], [0.05, 1.0, 1.0, 1.0]][[True, False, False, False], [0.05, 1.0, 1.0, 1.0]]Passed
adjusted values are monotone[[True, True, False], [0.03, 0.03, 0.5]][[True, True, False], [0.03, 0.03, 0.5]]Passed
adjusted values cap at one[[False, False], [0.8, 0.8]][[False, False], [0.8, 0.8]]Passed
metric p-value sample 1[[False, False, False, False], [0.08, 0.08, 0.1, 0.6]][[False, False, False, False], [0.08, 0.08, 0.1, 0.6]]Passed
metric p-value sample 2[[True, True, True], [0.0375, 0.0375, 0.0375]][[True, True, True], [0.0375, 0.0375, 0.0375]]Passed
metric p-value sample 3[[True], [0.025]][[True], [0.025]]Passed

SHA-256 / f6c95938ea32dcd32f9de19630d1b6cea8218fe1ac376cf798b16c1e028e3fcd

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 2026-09-29T14:48:57.270741+00:00.

Case digest / 643615471dbe490ebb1ed1fd84e0d630c6440263b3376e878dae4924ba4468c5