FAILURE MAP
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FA-74341 / Experiment statistics / Open access

Sample ratio mismatch check: Chi-square terms divide by the observed count · case 01

The SRM statistic is inflated for under-filled arms and deflated for over-filled ones.

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

ROOT CAUSE

Each term is (o - e)^2 / o instead of dividing by the expected count.

VERIFIED REPAIR

Divide each squared deviation by the expected count.

Unsuccessful approach: Dividing by the total shrinks every term and hides real mismatches.

Case contract

counts and weights are per-arm lists. Expected count = total * w / sum(weights). chi2 sums (observed - expected)^2 / expected over positive-weight arms; any unit in a zero-weight arm is an immediate mismatch [None, True]. df = number of positive-weight arms - 1; mismatch iff chi2 exceeds the alpha = 0.001 critical value (10.828, 13.816, 16.266, 18.467, 20.515 for df 1..5). No units or df < 1 -> [0.0, False]. Return [round(chi2, 6), mismatch].

Why this case matters

SRM checks are the first gate on any experiment readout; a broken check hides assignment bugs.

1 / The failure

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

N = 1
observations = []
def solve(counts, weights):
    CRIT = {1: 10.828, 2: 13.816, 3: 16.266, 4: 18.467, 5: 20.515}
    total = sum(counts)
    wsum = sum(weights)
    if total == 0:
        return [0.0, False]
    chi2 = 0.0
    for o, w in zip(counts, weights):
        if w == 0:
            if o > 0:
                return [None, True]
            continue
        e = total * w / wsum
        chi2 += (o - e) ** 2 / o
    df = sum(1 for w in weights if w > 0) - 1
    if df < 1:
        return [0.0, False]
    return [round(chi2, 6), chi2 > CRIT[df]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('balanced split within noise', [[5040, 4960], [50, 50]], [0.64, False]),
  ('unequal design weights are respected', [[2000, 1000], [2, 1]], [0.0, False]),
  ('ratio weights not in percent', [[510, 490], [1, 1]], [0.4, False]),
  ('clear mismatch at alpha 0.001', [[5200, 4800], [1, 1]], [16.0, True]),
  ('moderate imbalance below the strict threshold', [[5100, 4900], [1, 1]], [4.0, False]),
  ('three arms uneven', [[3100, 3300, 3600], [1, 1, 1]], [38.0, True]),
  ('arm count sample 1', [[493, 477], [3, 3]], [0.263918, False]),
  ('arm count sample 2', [[45, 53, 73, 18], [1, 50, 2, 50]], [2400.801481, True])],
 [('unequal design weights are respected', [[2000, 1000], [2, 1]], [0.0, False]),
  ('ratio weights not in percent', [[510, 490], [1, 1]], [0.4, False]),
  ('clear mismatch at alpha 0.001', [[5200, 4800], [1, 1]], [16.0, True]),
  ('moderate imbalance below the strict threshold', [[5100, 4900], [1, 1]], [4.0, False]),
  ('traffic in a zero-weight arm is a mismatch', [[500, 500, 3], [1, 1, 0]], [None, True]),
  ('three arms uneven', [[3100, 3300, 3600], [1, 1, 1]], [38.0, True]),
  ('arm count sample 1', [[493, 477], [3, 3]], [0.263918, False]),
  ('arm count sample 6', [[32, 944, 99], [1, 50, 2]], [95.793172, True])],
 [('ratio weights not in percent', [[510, 490], [1, 1]], [0.4, False]),
  ('clear mismatch at alpha 0.001', [[5200, 4800], [1, 1]], [16.0, True]),
  ('moderate imbalance below the strict threshold', [[5100, 4900], [1, 1]], [4.0, False]),
  ('traffic in a zero-weight arm is a mismatch', [[500, 500, 3], [1, 1, 0]], [None, True]),
  ('drained arm does not loosen the threshold', [[5170, 4830, 0], [1, 1, 0]], [11.56, True]),
  ('arm count sample 9', [[495, 543], [1, 1]], [2.219653, False]),
  ('arm count sample 15', [[72, 0, 108], [3, 0, 50]], [397.488, True]),
  ('arm count sample 17', [[2, 967], [1, 50]], [15.514737, True])],
 [('clear mismatch at alpha 0.001', [[5200, 4800], [1, 1]], [16.0, True]),
  ('moderate imbalance below the strict threshold', [[5100, 4900], [1, 1]], [4.0, False]),
  ('traffic in a zero-weight arm is a mismatch', [[500, 500, 3], [1, 1, 0]], [None, True]),
  ('drained arm does not loosen the threshold', [[5170, 4830, 0], [1, 1, 0]], [11.56, True]),
  ('empty zero-weight arm is ignored', [[520, 480, 0], [1, 1, 0]], [1.6, False]),
  ('arm count sample 22', [[18, 19, 157], [3, 2, 50]], [27.553608, True]),
  ('arm count sample 23', [[99, 96], [2, 3]], [9.423077, False]),
  ('arm count sample 24', [[0, 0, 5018], [0, 0, 50]], [0.0, False])],
 [('moderate imbalance below the strict threshold', [[5100, 4900], [1, 1]], [4.0, False]),
  ('traffic in a zero-weight arm is a mismatch', [[500, 500, 3], [1, 1, 0]], [None, True]),
  ('drained arm does not loosen the threshold', [[5170, 4830, 0], [1, 1, 0]], [11.56, True]),
  ('empty zero-weight arm is ignored', [[520, 480, 0], [1, 1, 0]], [1.6, False]),
  ('no units yet', [[0, 0], [1, 1]], [0.0, False]),
  ('arm count sample 29', [[274, 203, 4530], [3, 2, 50]], [2.512849, False]),
  ('arm count sample 30', [[1029, 942, 3015], [1, 1, 3]], [4.252708, False]),
  ('arm count sample 39', [[0, 105, 375, 486], [0, 1, 3, 3]], [24.086957, True])]]
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
balanced split within noise[0.640041, False][0.64, False]Failed
unequal design weights are respected[0.0, False][0.0, False]Passed
ratio weights not in percent[0.40016, False][0.4, False]Failed
clear mismatch at alpha 0.001[16.025641, True][16.0, True]Failed
moderate imbalance below the strict threshold[4.001601, False][4.0, False]Failed
three arms uneven[37.652511, True][38.0, True]Failed
arm count sample 1[0.263989, False][0.263918, False]Failed
arm count sample 2[437.727679, True][2400.801481, True]Failed

SHA-256 / b295e0b248ecb6c16247f0962ea2b7e26247b0f1450b266e6fdbbfbbcce835dc

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(counts, weights):
    CRIT = {1: 10.828, 2: 13.816, 3: 16.266, 4: 18.467, 5: 20.515}
    total = sum(counts)
    wsum = sum(weights)
    if total == 0:
        return [0.0, False]
    chi2 = 0.0
    for o, w in zip(counts, weights):
        if w == 0:
            if o > 0:
                return [None, True]
            continue
        e = total * w / wsum
        chi2 += (o - e) ** 2 / total
    df = sum(1 for w in weights if w > 0) - 1
    if df < 1:
        return [0.0, False]
    return [round(chi2, 6), chi2 > CRIT[df]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('balanced split within noise', [[5040, 4960], [50, 50]], [0.64, False]),
  ('unequal design weights are respected', [[2000, 1000], [2, 1]], [0.0, False]),
  ('ratio weights not in percent', [[510, 490], [1, 1]], [0.4, False]),
  ('clear mismatch at alpha 0.001', [[5200, 4800], [1, 1]], [16.0, True]),
  ('moderate imbalance below the strict threshold', [[5100, 4900], [1, 1]], [4.0, False]),
  ('three arms uneven', [[3100, 3300, 3600], [1, 1, 1]], [38.0, True]),
  ('arm count sample 1', [[493, 477], [3, 3]], [0.263918, False]),
  ('arm count sample 2', [[45, 53, 73, 18], [1, 50, 2, 50]], [2400.801481, True])],
 [('unequal design weights are respected', [[2000, 1000], [2, 1]], [0.0, False]),
  ('ratio weights not in percent', [[510, 490], [1, 1]], [0.4, False]),
  ('clear mismatch at alpha 0.001', [[5200, 4800], [1, 1]], [16.0, True]),
  ('moderate imbalance below the strict threshold', [[5100, 4900], [1, 1]], [4.0, False]),
  ('traffic in a zero-weight arm is a mismatch', [[500, 500, 3], [1, 1, 0]], [None, True]),
  ('three arms uneven', [[3100, 3300, 3600], [1, 1, 1]], [38.0, True]),
  ('arm count sample 1', [[493, 477], [3, 3]], [0.263918, False]),
  ('arm count sample 6', [[32, 944, 99], [1, 50, 2]], [95.793172, True])],
 [('ratio weights not in percent', [[510, 490], [1, 1]], [0.4, False]),
  ('clear mismatch at alpha 0.001', [[5200, 4800], [1, 1]], [16.0, True]),
  ('moderate imbalance below the strict threshold', [[5100, 4900], [1, 1]], [4.0, False]),
  ('traffic in a zero-weight arm is a mismatch', [[500, 500, 3], [1, 1, 0]], [None, True]),
  ('drained arm does not loosen the threshold', [[5170, 4830, 0], [1, 1, 0]], [11.56, True]),
  ('arm count sample 9', [[495, 543], [1, 1]], [2.219653, False]),
  ('arm count sample 15', [[72, 0, 108], [3, 0, 50]], [397.488, True]),
  ('arm count sample 17', [[2, 967], [1, 50]], [15.514737, True])],
 [('clear mismatch at alpha 0.001', [[5200, 4800], [1, 1]], [16.0, True]),
  ('moderate imbalance below the strict threshold', [[5100, 4900], [1, 1]], [4.0, False]),
  ('traffic in a zero-weight arm is a mismatch', [[500, 500, 3], [1, 1, 0]], [None, True]),
  ('drained arm does not loosen the threshold', [[5170, 4830, 0], [1, 1, 0]], [11.56, True]),
  ('empty zero-weight arm is ignored', [[520, 480, 0], [1, 1, 0]], [1.6, False]),
  ('arm count sample 22', [[18, 19, 157], [3, 2, 50]], [27.553608, True]),
  ('arm count sample 23', [[99, 96], [2, 3]], [9.423077, False]),
  ('arm count sample 24', [[0, 0, 5018], [0, 0, 50]], [0.0, False])],
 [('moderate imbalance below the strict threshold', [[5100, 4900], [1, 1]], [4.0, False]),
  ('traffic in a zero-weight arm is a mismatch', [[500, 500, 3], [1, 1, 0]], [None, True]),
  ('drained arm does not loosen the threshold', [[5170, 4830, 0], [1, 1, 0]], [11.56, True]),
  ('empty zero-weight arm is ignored', [[520, 480, 0], [1, 1, 0]], [1.6, False]),
  ('no units yet', [[0, 0], [1, 1]], [0.0, False]),
  ('arm count sample 29', [[274, 203, 4530], [3, 2, 50]], [2.512849, False]),
  ('arm count sample 30', [[1029, 942, 3015], [1, 1, 3]], [4.252708, False]),
  ('arm count sample 39', [[0, 105, 375, 486], [0, 1, 3, 3]], [24.086957, True])]]
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
balanced split within noise[0.32, False][0.64, False]Failed
unequal design weights are respected[0.0, False][0.0, False]Passed
ratio weights not in percent[0.2, False][0.4, False]Failed
clear mismatch at alpha 0.001[8.0, False][16.0, True]Failed
moderate imbalance below the strict threshold[2.0, False][4.0, False]Failed
three arms uneven[12.666667, False][38.0, True]Failed
arm count sample 1[0.131959, False][0.263918, False]Failed
arm count sample 2[72.010385, True][2400.801481, True]Failed

SHA-256 / 2bb6209f88768e26e23f241f12049d477634f73ba44d5f383d74c6ef206c8999

3 / The verified repair

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

N = 1
observations = []
def solve(counts, weights):
    CRIT = {1: 10.828, 2: 13.816, 3: 16.266, 4: 18.467, 5: 20.515}
    total = sum(counts)
    wsum = sum(weights)
    if total == 0:
        return [0.0, False]
    chi2 = 0.0
    for o, w in zip(counts, weights):
        if w == 0:
            if o > 0:
                return [None, True]
            continue
        e = total * w / wsum
        chi2 += (o - e) ** 2 / e
    df = sum(1 for w in weights if w > 0) - 1
    if df < 1:
        return [0.0, False]
    return [round(chi2, 6), chi2 > CRIT[df]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('balanced split within noise', [[5040, 4960], [50, 50]], [0.64, False]),
  ('unequal design weights are respected', [[2000, 1000], [2, 1]], [0.0, False]),
  ('ratio weights not in percent', [[510, 490], [1, 1]], [0.4, False]),
  ('clear mismatch at alpha 0.001', [[5200, 4800], [1, 1]], [16.0, True]),
  ('moderate imbalance below the strict threshold', [[5100, 4900], [1, 1]], [4.0, False]),
  ('three arms uneven', [[3100, 3300, 3600], [1, 1, 1]], [38.0, True]),
  ('arm count sample 1', [[493, 477], [3, 3]], [0.263918, False]),
  ('arm count sample 2', [[45, 53, 73, 18], [1, 50, 2, 50]], [2400.801481, True])],
 [('unequal design weights are respected', [[2000, 1000], [2, 1]], [0.0, False]),
  ('ratio weights not in percent', [[510, 490], [1, 1]], [0.4, False]),
  ('clear mismatch at alpha 0.001', [[5200, 4800], [1, 1]], [16.0, True]),
  ('moderate imbalance below the strict threshold', [[5100, 4900], [1, 1]], [4.0, False]),
  ('traffic in a zero-weight arm is a mismatch', [[500, 500, 3], [1, 1, 0]], [None, True]),
  ('three arms uneven', [[3100, 3300, 3600], [1, 1, 1]], [38.0, True]),
  ('arm count sample 1', [[493, 477], [3, 3]], [0.263918, False]),
  ('arm count sample 6', [[32, 944, 99], [1, 50, 2]], [95.793172, True])],
 [('ratio weights not in percent', [[510, 490], [1, 1]], [0.4, False]),
  ('clear mismatch at alpha 0.001', [[5200, 4800], [1, 1]], [16.0, True]),
  ('moderate imbalance below the strict threshold', [[5100, 4900], [1, 1]], [4.0, False]),
  ('traffic in a zero-weight arm is a mismatch', [[500, 500, 3], [1, 1, 0]], [None, True]),
  ('drained arm does not loosen the threshold', [[5170, 4830, 0], [1, 1, 0]], [11.56, True]),
  ('arm count sample 9', [[495, 543], [1, 1]], [2.219653, False]),
  ('arm count sample 15', [[72, 0, 108], [3, 0, 50]], [397.488, True]),
  ('arm count sample 17', [[2, 967], [1, 50]], [15.514737, True])],
 [('clear mismatch at alpha 0.001', [[5200, 4800], [1, 1]], [16.0, True]),
  ('moderate imbalance below the strict threshold', [[5100, 4900], [1, 1]], [4.0, False]),
  ('traffic in a zero-weight arm is a mismatch', [[500, 500, 3], [1, 1, 0]], [None, True]),
  ('drained arm does not loosen the threshold', [[5170, 4830, 0], [1, 1, 0]], [11.56, True]),
  ('empty zero-weight arm is ignored', [[520, 480, 0], [1, 1, 0]], [1.6, False]),
  ('arm count sample 22', [[18, 19, 157], [3, 2, 50]], [27.553608, True]),
  ('arm count sample 23', [[99, 96], [2, 3]], [9.423077, False]),
  ('arm count sample 24', [[0, 0, 5018], [0, 0, 50]], [0.0, False])],
 [('moderate imbalance below the strict threshold', [[5100, 4900], [1, 1]], [4.0, False]),
  ('traffic in a zero-weight arm is a mismatch', [[500, 500, 3], [1, 1, 0]], [None, True]),
  ('drained arm does not loosen the threshold', [[5170, 4830, 0], [1, 1, 0]], [11.56, True]),
  ('empty zero-weight arm is ignored', [[520, 480, 0], [1, 1, 0]], [1.6, False]),
  ('no units yet', [[0, 0], [1, 1]], [0.0, False]),
  ('arm count sample 29', [[274, 203, 4530], [3, 2, 50]], [2.512849, False]),
  ('arm count sample 30', [[1029, 942, 3015], [1, 1, 3]], [4.252708, False]),
  ('arm count sample 39', [[0, 105, 375, 486], [0, 1, 3, 3]], [24.086957, True])]]
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
balanced split within noise[0.64, False][0.64, False]Passed
unequal design weights are respected[0.0, False][0.0, False]Passed
ratio weights not in percent[0.4, False][0.4, False]Passed
clear mismatch at alpha 0.001[16.0, True][16.0, True]Passed
moderate imbalance below the strict threshold[4.0, False][4.0, False]Passed
three arms uneven[38.0, True][38.0, True]Passed
arm count sample 1[0.263918, False][0.263918, False]Passed
arm count sample 2[2400.801481, True][2400.801481, True]Passed

SHA-256 / d8a2244a07ed38aa1e564fc27f13a390125e05c8b22ef60a10633ea3772286c3

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 2026-09-29T14:48:55.877255+00:00.

Case digest / f40ddc19ea550177bef2ed51b70ddf3e684354855408c53b1c3597cce0a61b33