{
  "seed": 20261012,
  "repeats": 20000,
  "ci_coverage": [
    {
      "n": 20,
      "p": 0.05,
      "repeats": 20000,
      "wald": {
        "empirical_coverage": 0.634,
        "exact_binomial_coverage": 0.6389401372568057,
        "monte_carlo_se": 0.0034062002289941794
      },
      "wilson": {
        "empirical_coverage": 0.9255,
        "exact_binomial_coverage": 0.9245163262115039,
        "monte_carlo_se": 0.0018567410966529503
      }
    },
    {
      "n": 100,
      "p": 0.3,
      "repeats": 20000,
      "wald": {
        "empirical_coverage": 0.95,
        "exact_binomial_coverage": 0.9501801708754681,
        "monte_carlo_se": 0.0015411035007422448
      },
      "wilson": {
        "empirical_coverage": 0.9361,
        "exact_binomial_coverage": 0.9371897486104614,
        "monte_carlo_se": 0.0017294043772351213
      }
    }
  ],
  "all_null_independent_uniform_pvalues_20_tests": {
    "unadjusted": {
      "empirical_fwer": 0.64365,
      "theoretical_fwer_under_independence": 0.6415140775914581,
      "monte_carlo_se": 0.003386478093093177
    },
    "bonferroni": {
      "empirical_fwer": 0.05245,
      "theoretical_fwer_under_independence": 0.04883012474683324,
      "monte_carlo_se": 0.0015763723782786856
    }
  },
  "note": "Uniform independent null p-values are an idealized model, not a universal description of tests."
}