{
  "method": "Wilcoxon signed-rank on teacher-forced species token log-probabilities",
  "description": "Teacher-force through '### [Name] is a' prefix, then extract log P(species_token). Species token is the discriminative one requiring multi-hop reasoning. Comparison: m5 vs m6.",
  "comparison": "m5_vs_m6",
  "bonferroni_k": 5,
  "adjusted_alpha": 0.01,
  "results": {
    "prosqa_id": {
      "n": 500,
      "n_ties": 0,
      "n_nonzero": 500,
      "median_diff": -0.00013814407611789647,
      "mean_diff": -0.016247838157780962,
      "std_diff": 1.1177613567572349,
      "wilcoxon_stat": 41957.0,
      "p_value": 1.6143744744439177e-10,
      "p_bonferroni": 8.071872372219589e-10,
      "effect_size_r": 0.28595531145037273,
      "z_score": 6.394155149301574,
      "m5_median_lp": -0.00021824839495820925,
      "m6_median_lp": -0.0005059154354967177,
      "m5_mean_lp": -0.1827606344706453,
      "m6_mean_lp": -0.19900847262842628,
      "m5_prob_median": 0.9997817754194902,
      "m6_prob_median": 0.9994942125181384,
      "direction": "m5>m6"
    },
    "7hop": {
      "n": 1000,
      "n_ties": 0,
      "n_nonzero": 1000,
      "median_diff": 0.0001795582447812194,
      "mean_diff": 0.48284089019898646,
      "std_diff": 2.0365023730650087,
      "wilcoxon_stat": 209203.0,
      "p_value": 7.0192524328014474e-06,
      "p_bonferroni": 3.5096262164007236e-05,
      "effect_size_r": 0.1420844201182813,
      "z_score": 4.493103875980196,
      "m5_median_lp": -0.03740513697266579,
      "m6_median_lp": -0.03395153023302555,
      "m5_mean_lp": -1.109607256290728,
      "m6_mean_lp": -0.6267663660917415,
      "m5_prob_median": 0.9632857935932256,
      "m6_prob_median": 0.966618355268511,
      "direction": "m6>m5"
    },
    "8hop": {
      "n": 1000,
      "n_ties": 0,
      "n_nonzero": 1000,
      "median_diff": 0.0002561149522080086,
      "mean_diff": 0.3832407745273106,
      "std_diff": 2.227865684000055,
      "wilcoxon_stat": 215715.0,
      "p_value": 0.00015664918728829126,
      "p_bonferroni": 0.0007832459364414563,
      "effect_size_r": 0.119543095689937,
      "z_score": 3.7802846092765865,
      "m5_median_lp": -0.04081503301858902,
      "m6_median_lp": -0.03081549145281315,
      "m5_mean_lp": -1.0956443890799654,
      "m6_mean_lp": -0.7124036145526548,
      "m5_prob_median": 0.9600066830648615,
      "m6_prob_median": 0.9696544661086867,
      "direction": "m6>m5"
    },
    "dag": {
      "n": 1000,
      "n_ties": 0,
      "n_nonzero": 1000,
      "median_diff": 0.0026662750460673124,
      "mean_diff": 0.4216908030509094,
      "std_diff": 2.3045800471066755,
      "wilcoxon_stat": 210880.0,
      "p_value": 1.6359787033524354e-05,
      "p_bonferroni": 8.179893516762177e-05,
      "effect_size_r": 0.13627947523708756,
      "z_score": 4.3095354008171185,
      "m5_median_lp": -0.34515656530857086,
      "m6_median_lp": -0.2986634820699692,
      "m5_mean_lp": -1.6330430318220843,
      "m6_mean_lp": -1.2113522287711749,
      "m5_prob_median": 0.7081094794093652,
      "m6_prob_median": 0.7418089994658733,
      "direction": "m6>m5"
    },
    "dense": {
      "n": 1000,
      "n_ties": 0,
      "n_nonzero": 1000,
      "median_diff": -0.003164976616972126,
      "mean_diff": 0.11263441988590966,
      "std_diff": 2.239913360245438,
      "wilcoxon_stat": 244040.0,
      "p_value": 0.49665541423174153,
      "p_bonferroni": 1.0,
      "effect_size_r": 0.021495949738946255,
      "z_score": 0.6797616164357204,
      "m5_median_lp": -0.10577894374728203,
      "m6_median_lp": -0.16426319628953934,
      "m5_mean_lp": -1.1116475733733295,
      "m6_mean_lp": -0.9990131534874199,
      "m5_prob_median": 0.8996234934954318,
      "m6_prob_median": 0.8485186655238433,
      "direction": "m5>m6"
    }
  }
}