{
 "alpha": 0.025,
 "borderline": true,
 "correction": "westfall_young_min_p",
 "family_size": 6,
 "folds": "grouped by question: sorted ids shuffled with Random(20260724), fold = position mod 5",
 "group_key": "id",
 "grouped_version": "0.1",
 "groups_dropped_by_reason": {},
 "headline": "worst cell A*_G = 0.539 in length/_all (467 questions), family-adjusted p = 0.0466 over 6 cells",
 "k_band_breakdown_descriptive": {
  "alpha_first": {
   "10+": {
    "W": 0.5189,
    "n_groups": 57
   },
   "5": {
    "W": 0.4781,
    "n_groups": 262
   },
   "6-9": {
    "W": 0.4985,
    "n_groups": 148
   }
  },
  "alpha_last": {
   "10+": {
    "W": 0.5662,
    "n_groups": 57
   },
   "5": {
    "W": 0.4847,
    "n_groups": 262
   },
   "6-9": {
    "W": 0.5152,
    "n_groups": 148
   }
  },
  "length": {
   "10+": {
    "W": 0.4645,
    "n_groups": 57
   },
   "5": {
    "W": 0.4547,
    "n_groups": 262
   },
   "6-9": {
    "W": 0.4721,
    "n_groups": 148
   }
  },
  "lexicality": {
   "10+": {
    "W": 0.4732,
    "n_groups": 57
   },
   "5": {
    "W": 0.4957,
    "n_groups": 262
   },
   "6-9": {
    "W": 0.4286,
    "n_groups": 148
   }
  },
  "shape": {
   "10+": {
    "W": 0.4996,
    "n_groups": 57
   },
   "5": {
    "W": 0.5153,
    "n_groups": 262
   },
   "6-9": {
    "W": 0.5326,
    "n_groups": 148
   }
  },
  "words": {
   "10+": {
    "W": 0.449,
    "n_groups": 57
   },
   "5": {
    "W": 0.4823,
    "n_groups": 262
   },
   "6-9": {
    "W": 0.5196,
    "n_groups": 148
   }
  }
 },
 "min_cell_groups": 12,
 "mode": "grouped",
 "n_groups": 467,
 "n_groups_dropped": 0,
 "n_items": 3164,
 "n_items_in": 3164,
 "n_perm": 600,
 "n_perm_requested": 600,
 "n_separating_cells": 0,
 "null": "keyed position redrawn uniformly within each question (questions in sorted id order), every probe refit",
 "nulls": {
  "alpha_first": {
   "per_stratum": {
    "_all": {
     "adj_p": 0.9251,
     "astar_g": 0.51,
     "n_groups": 467,
     "raw_p": 0.3611,
     "separates": false,
     "threshold": 0.522
    }
   }
  },
  "alpha_last": {
   "per_stratum": {
    "_all": {
     "adj_p": 1.0,
     "astar_g": 0.504,
     "n_groups": 467,
     "raw_p": 0.7354,
     "separates": false,
     "threshold": 0.525
    }
   }
  },
  "length": {
   "per_stratum": {
    "_all": {
     "adj_p": 0.0466,
     "astar_g": 0.539,
     "n_groups": 467,
     "raw_p": 0.0083,
     "separates": false,
     "threshold": 0.528
    }
   }
  },
  "lexicality": {
   "per_stratum": {
    "_all": {
     "adj_p": 0.5441,
     "astar_g": 0.528,
     "n_groups": 467,
     "raw_p": 0.1281,
     "separates": false,
     "threshold": 0.536
    }
   }
  },
  "shape": {
   "per_stratum": {
    "_all": {
     "adj_p": 0.8353,
     "astar_g": 0.519,
     "n_groups": 467,
     "raw_p": 0.2612,
     "separates": false,
     "threshold": 0.531
    }
   }
  },
  "words": {
   "per_stratum": {
    "_all": {
     "adj_p": 1.0,
     "astar_g": 0.51,
     "n_groups": 467,
     "raw_p": 0.6206,
     "separates": false,
     "threshold": 0.534
    }
   }
  }
 },
 "option_count_distribution": {
  "10": 21,
  "11": 6,
  "12": 7,
  "13": 2,
  "14": 3,
  "15": 2,
  "16": 6,
  "17": 1,
  "18": 1,
  "19": 1,
  "20": 2,
  "21": 1,
  "22": 1,
  "26": 3,
  "5": 262,
  "6": 44,
  "7": 35,
  "8": 45,
  "9": 24
 },
 "p_floor": 0.001664,
 "paired_version": "0.1",
 "pinned_sha256": {
  "nulltest.py": "0e103dc41a3c208d2652646f2b8acc8b701ed7799402ca1ea0cb856de5ddf46c",
  "nulltest_paired.py": "2fbbebca77abd8b494272801fa3f957e1f910d7a10148a7c6ccc10116e4f37d3"
 },
 "probes": [
  "lexicality",
  "words",
  "length",
  "shape",
  "alpha_first",
  "alpha_last"
 ],
 "saturated": false,
 "scope": "SCOPE: this measures how much of the label signal is recoverable from SURFACE FORM alone by six model-free probes, two-sided, refit inside every permutation (labels shuffled within stratum) and family-wise corrected across all cells (Westfall-Young min-p). A PASS does NOT certify the benchmark is good: it cannot see circularity (labels drawn from the same store the system under test retrieves from), contamination, or mislabelling. It scores no model.",
 "statistic": "A*_G = max(W, 1-W); W = mean over questions of r_q = [#{wrong j: s_j > s_keyed} + ties/2]/(k_q-1)",
 "strata": [
  "_all"
 ],
 "stratum_key": null,
 "tool": "nulltest",
 "verdict": "PASS",
 "version": "1.4",
 "worst_cell": {
  "adj_p": 0.0466,
  "astar_g": 0.539,
  "n_groups": 467,
  "null": "length",
  "raw_p": 0.0083,
  "separates": false,
  "stratum": "_all",
  "threshold": 0.528
 }
}