{"abstract":"Equal averaging ignores unequal degrees of freedom.","category":"Statistics","checks":4,"contract":"Integer finite observations and equal lengths for paired samples. Counts and weights are nonnegative. Rational results use reduced Fraction strings. Empty or undefined statistics return None where shown. n1,n2>=2 and v1,v2 are nonnegative integer unbiased within-group sample variances; pool by degrees of freedom. Exact operational definition: str(Fraction((n1-1)*v1+(n2-1)*v2,n1+n2-2))","evaluation_group":"model-d3ef406cc0729bc7","failed_approach":"Sample sizes replace the degrees of freedom associated with sample variances.","family":"xn-pooled-sample-variance-rational","id":"FA-6336","implementations":{"attempt":{"sha256":"b41a0b31cd22b4bb5b53d478d6645106c95116ad04b90f7d40d7988155afb8ac","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(n1, v1, n2, v2):\n    return str(Fraction(n1*v1+n2*v2,n1+n2))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (2, 1, 4, 3)', solve(*(2, 1, 4, 3)), '5/2')\ncheck('fixture 2: (3, 2, 3, 4)', solve(*(3, 2, 3, 4)), '3')\ncheck('fixture 3: (2, 0, 2, 0)', solve(*(2, 0, 2, 0)), '0')\ncheck('fixture 4: (2, 4, 5, 1)', solve(*(2, 4, 5, 1)), '8/5')\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"04a79cef878ed1881f2da8f9ba312e79ab20f94c362ea7b95da0d15ac4b84cfc","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(n1, v1, n2, v2):\n    return str(Fraction(v1+v2,2))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (2, 1, 4, 3)', solve(*(2, 1, 4, 3)), '5/2')\ncheck('fixture 2: (3, 2, 3, 4)', solve(*(3, 2, 3, 4)), '3')\ncheck('fixture 3: (2, 0, 2, 0)', solve(*(2, 0, 2, 0)), '0')\ncheck('fixture 4: (2, 4, 5, 1)', solve(*(2, 4, 5, 1)), '8/5')\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"ac650dc1baea8a1b9158bb632b49c4ed78665ad46c02796e7a35531bba6cdd3d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(n1, v1, n2, v2):\n    return str(Fraction((n1-1)*v1+(n2-1)*v2,n1+n2-2))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (2, 1, 4, 3)', solve(*(2, 1, 4, 3)), '5/2')\ncheck('fixture 2: (3, 2, 3, 4)', solve(*(3, 2, 3, 4)), '3')\ncheck('fixture 3: (2, 0, 2, 0)', solve(*(2, 0, 2, 0)), '0')\ncheck('fixture 4: (2, 4, 5, 1)', solve(*(2, 4, 5, 1)), '8/5')\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":" 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.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"xn-pooled-sample-variance-rational","generated_at":"2026-09-29T14:38:00.556183+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Statistical estimators results depend on the stated convention.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return str(Fraction((n1-1)*v1+(n2-1)*v2,n1+n2-2))","root_cause":"Equal averaging ignores unequal degrees of freedom.","sha256":"a8fc110cb03832baef2fa0e1b456ac78c2827aca5ea0b039f87d06f68209c36a","title":"Pooled sample variance rational · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":83.044,"exit_code":1,"observations":[{"actual":"7/3","check":"fixture 1: (2, 1, 4, 3)","expected":"5/2","passed":false},{"actual":"3","check":"fixture 2: (3, 2, 3, 4)","expected":"3","passed":true},{"actual":"0","check":"fixture 3: (2, 0, 2, 0)","expected":"0","passed":true},{"actual":"13/7","check":"fixture 4: (2, 4, 5, 1)","expected":"8/5","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 1, 4, 3)\", \"actual\": \"7/3\", \"expected\": \"5/2\", \"passed\": false}, {\"check\": \"fixture 2: (3, 2, 3, 4)\", \"actual\": \"3\", \"expected\": \"3\", \"passed\": true}, {\"check\": \"fixture 3: (2, 0, 2, 0)\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"fixture 4: (2, 4, 5, 1)\", \"actual\": \"13/7\", \"expected\": \"8/5\", \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":45.963,"exit_code":1,"observations":[{"actual":"2","check":"fixture 1: (2, 1, 4, 3)","expected":"5/2","passed":false},{"actual":"3","check":"fixture 2: (3, 2, 3, 4)","expected":"3","passed":true},{"actual":"0","check":"fixture 3: (2, 0, 2, 0)","expected":"0","passed":true},{"actual":"5/2","check":"fixture 4: (2, 4, 5, 1)","expected":"8/5","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 1, 4, 3)\", \"actual\": \"2\", \"expected\": \"5/2\", \"passed\": false}, {\"check\": \"fixture 2: (3, 2, 3, 4)\", \"actual\": \"3\", \"expected\": \"3\", \"passed\": true}, {\"check\": \"fixture 3: (2, 0, 2, 0)\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"fixture 4: (2, 4, 5, 1)\", \"actual\": \"5/2\", \"expected\": \"8/5\", \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":52.85,"exit_code":0,"observations":[{"actual":"5/2","check":"fixture 1: (2, 1, 4, 3)","expected":"5/2","passed":true},{"actual":"3","check":"fixture 2: (3, 2, 3, 4)","expected":"3","passed":true},{"actual":"0","check":"fixture 3: (2, 0, 2, 0)","expected":"0","passed":true},{"actual":"8/5","check":"fixture 4: (2, 4, 5, 1)","expected":"8/5","passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 1, 4, 3)\", \"actual\": \"5/2\", \"expected\": \"5/2\", \"passed\": true}, {\"check\": \"fixture 2: (3, 2, 3, 4)\", \"actual\": \"3\", \"expected\": \"3\", \"passed\": true}, {\"check\": \"fixture 3: (2, 0, 2, 0)\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"fixture 4: (2, 4, 5, 1)\", \"actual\": \"8/5\", \"expected\": \"8/5\", \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}