{
  "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: m3 vs m6.",
  "comparison": "m3_vs_m6",
  "bonferroni_k": 5,
  "adjusted_alpha": 0.01,
  "results": {
    "prosqa_id": {
      "n": 500,
      "n_ties": 0,
      "n_nonzero": 500,
      "median_diff": -0.00036554490657181304,
      "mean_diff": -0.0860310743720925,
      "std_diff": 1.2170259847022458,
      "wilcoxon_stat": 13588.0,
      "p_value": 5.51961631585719e-52,
      "p_bonferroni": 2.759808157928595e-51,
      "effect_size_r": 0.6784589997867199,
      "z_score": 15.17080443469621,
      "m3_median_lp": -1.9490528757160064e-05,
      "m6_median_lp": -0.0005059154354967177,
      "m3_mean_lp": -0.11297739825633377,
      "m6_mean_lp": -0.19900847262842628,
      "m3_prob_median": 0.999980509661182,
      "m6_prob_median": 0.9994942125181384,
      "direction": "m3>m6"
    },
    "7hop": {
      "n": 1000,
      "n_ties": 0,
      "n_nonzero": 1000,
      "median_diff": -0.00025782780085137347,
      "mean_diff": 0.7641824833154048,
      "std_diff": 2.6517137931258605,
      "wilcoxon_stat": 218786.0,
      "p_value": 0.0005729096557360483,
      "p_bonferroni": 0.0028645482786802414,
      "effect_size_r": 0.10891281201066103,
      "z_score": 3.444125523274317,
      "m3_median_lp": -0.026303233578801155,
      "m6_median_lp": -0.03395153023302555,
      "m3_mean_lp": -1.3909488494071465,
      "m6_mean_lp": -0.6267663660917415,
      "m3_prob_median": 0.974039683283398,
      "m6_prob_median": 0.966618355268511,
      "direction": "m3>m6"
    },
    "8hop": {
      "n": 1000,
      "n_ties": 0,
      "n_nonzero": 1000,
      "median_diff": -0.0003167157010466326,
      "mean_diff": 0.5979843548741289,
      "std_diff": 2.54137471092738,
      "wilcoxon_stat": 226686.0,
      "p_value": 0.009898001252072113,
      "p_bonferroni": 0.04949000626036057,
      "effect_size_r": 0.08156691781779862,
      "z_score": 2.5793724202401473,
      "m3_median_lp": -0.023225629702210426,
      "m6_median_lp": -0.03081549145281315,
      "m3_mean_lp": -1.310387969426784,
      "m6_mean_lp": -0.7124036145526548,
      "m3_prob_median": 0.977042009203823,
      "m6_prob_median": 0.9696544661086867,
      "direction": "m3>m6"
    },
    "dag": {
      "n": 1000,
      "n_ties": 0,
      "n_nonzero": 1000,
      "median_diff": -0.0005894981513847597,
      "mean_diff": 0.5916298918708122,
      "std_diff": 2.942288236114359,
      "wilcoxon_stat": 229183.0,
      "p_value": 0.021108131302877156,
      "p_bonferroni": 0.10554065651438578,
      "effect_size_r": 0.07292353834949769,
      "z_score": 2.3060447622304863,
      "m3_median_lp": -0.22532972693443298,
      "m6_median_lp": -0.2986634820699692,
      "m3_mean_lp": -1.802982120641987,
      "m6_mean_lp": -1.2113522287711749,
      "m3_prob_median": 0.7982529698569824,
      "m6_prob_median": 0.7418089994658733,
      "direction": "m3>m6"
    },
    "dense": {
      "n": 1000,
      "n_ties": 0,
      "n_nonzero": 1000,
      "median_diff": -0.00013662463516084244,
      "mean_diff": 0.6544579904913999,
      "std_diff": 2.796134035440923,
      "wilcoxon_stat": 216195.0,
      "p_value": 0.000193202514204543,
      "p_bonferroni": 0.000966012571022715,
      "effect_size_r": 0.1178815730048011,
      "z_score": 3.7277426485859038,
      "m3_median_lp": -0.1466745063662529,
      "m6_median_lp": -0.16426319628953934,
      "m3_mean_lp": -1.65347114397882,
      "m6_mean_lp": -0.9990131534874199,
      "m3_prob_median": 0.8635750198463003,
      "m6_prob_median": 0.8485186655238433,
      "direction": "m3>m6"
    }
  }
}