{
  "step1_methods": {
    "methods": "π ratio CK/W5 (non-parametric), Weir & Cockerham Fst, empirical p-value",
    "justification": "π ratio extremely non-normal → parametric tests invalid",
    "data": "100-kb sliding windows, 50-kb step, Chr05",
    "pi_ratio_global": {
      "n": 3506,
      "mean": 1.38,
      "median": 1.19,
      "std": 0.63,
      "p95": 2.32,
      "p99": 3.58
    },
    "multi_threshold": {
      "min_vars_0": {
        "n_windows": 3506,
        "peak": 18.5,
        "pos_mb": 19.9,
        "n_vars": 918.0
      },
      "min_vars_10": {
        "n_windows": 3505,
        "peak": 18.5,
        "pos_mb": 19.9,
        "n_vars": 918.0
      },
      "min_vars_20": {
        "n_windows": 3505,
        "peak": 18.5,
        "pos_mb": 19.9,
        "n_vars": 918.0
      },
      "min_vars_30": {
        "n_windows": 3505,
        "peak": 18.5,
        "pos_mb": 19.9,
        "n_vars": 918.0
      },
      "min_vars_50": {
        "n_windows": 3498,
        "peak": 18.5,
        "pos_mb": 19.9,
        "n_vars": 918.0
      },
      "min_vars_100": {
        "n_windows": 3487,
        "peak": 18.5,
        "pos_mb": 19.9,
        "n_vars": 918.0
      }
    },
    "cdi": {
      "range": "19.75-20.35Mb",
      "windows": 12,
      "mean": 6.06,
      "median": 4.81,
      "peak": 18.5,
      "peak_mb": 19.9,
      "empirical_p": 0.0
    }
  },
  "step2_advanced": {
    "bootstrap_n": 10000,
    "cdi_mean_95ci": [
      4.38,
      8.57
    ],
    "cdi_median_95ci": [
      4.12,
      6.34
    ],
    "monte_carlo_p": 0.0,
    "cohens_d": 8.38,
    "interpretation": "large effect"
  },
  "step3_descriptive": {
    "descriptive": [
      {
        "variable": "π_W5",
        "n": 3506,
        "mean": 0.0018,
        "median": 0.0015,
        "std": 0.0014,
        "min": 0.0,
        "max": 0.0114,
        "skewness": 1.863,
        "kurtosis": 4.539,
        "cv_pct": 75.8
      },
      {
        "variable": "π_CK",
        "n": 3506,
        "mean": 0.0023,
        "median": 0.0019,
        "std": 0.0017,
        "min": 0.0,
        "max": 0.014,
        "skewness": 1.815,
        "kurtosis": 4.458,
        "cv_pct": 72.2
      },
      {
        "variable": "π_ratio (all Chr05)",
        "n": 3506,
        "mean": 1.3762,
        "median": 1.1913,
        "std": 0.6283,
        "min": 0.4509,
        "max": 18.5317,
        "skewness": 9.277,
        "kurtosis": 188.892,
        "cv_pct": 45.7
      },
      {
        "variable": "π_ratio (CDI)",
        "n": 12,
        "mean": 6.0615,
        "median": 4.8067,
        "std": 3.963,
        "min": 3.1019,
        "max": 18.5317,
        "skewness": 2.502,
        "kurtosis": 5.234,
        "cv_pct": 65.4
      },
      {
        "variable": "π_ratio (background)",
        "n": 3494,
        "mean": 1.3601,
        "median": 1.1906,
        "std": 0.5163,
        "min": 0.4509,
        "max": 11.473,
        "skewness": 4.909,
        "kurtosis": 57.418,
        "cv_pct": 38.0
      },
      {
        "variable": "Fst Weighted (all Chr05)",
        "n": 3506,
        "mean": 0.0138,
        "median": 0.0057,
        "std": 0.0195,
        "min": -0.0128,
        "max": 0.1536,
        "skewness": 2.057,
        "kurtosis": 5.604,
        "cv_pct": 141.6
      },
      {
        "variable": "Fst Weighted (CDI)",
        "n": 12,
        "mean": 0.0415,
        "median": 0.0359,
        "std": 0.0114,
        "min": 0.0278,
        "max": 0.0659,
        "skewness": 0.67,
        "kurtosis": -0.724,
        "cv_pct": 27.6
      }
    ],
    "cdi_outlier_enrichment": {
      "pct_above_p95": 100.0,
      "pct_above_p99": 83.3
    }
  },
  "step4_diagnostics": {
    "normality": {
      "Shapiro-Wilk": "W=0.535, p<0.001",
      "Jarque-Bera": "JB=5262574, p<0.001",
      "Kolmogorov-Smirnov": "D=0.2132, p<0.001",
      "Anderson-Darling": "A²=339.5 > crit(5%)=0.75 → REJECT",
      "conclusion": "π ratio IS NOT normal — all 5 tests reject. Non-parametric methods required."
    },
    "variance_homogeneity": {
      "Levene": "W=3.84, p=0.0627 → unequal",
      "conclusion": "Unequal variances — Welch or non-parametric methods"
    },
    "mann_whitney_cdi_vs_bg": "U=41799, p=1.33e-09",
    "spearman_pi_vs_nvars": "ρ=0.3193, p=0.0000",
    "fst_cdi_enrichment": "Fold=3.0×, p=1.36e-06"
  }
}