{
  "analytic": "evaluation-intervals",
  "kind": "declared_analytical_or_constructed_example",
  "experimental_model_result": false,
  "panels": [
    {
      "kind": "line",
      "x": [
        20,
        100,
        500,
        2000
      ],
      "series": [
        {
          "label": "Wilson lower",
          "y": [
            0.4810232237710206,
            0.6041496156718804,
            0.6584314090816449,
            0.679548150789189
          ]
        },
        {
          "label": "Observed proportion",
          "y": [
            0.7,
            0.7,
            0.7,
            0.7
          ]
        },
        {
          "label": "Wilson upper",
          "y": [
            0.854524726031006,
            0.7810524613377188,
            0.7385187435059938,
            0.7196850021706058
          ]
        }
      ],
      "xlabel": "Independent items",
      "ylabel": "95% Wilson interval",
      "logx": true,
      "logy": false
    }
  ],
  "title": "The same proportion has different finite-sample precision",
  "assumptions": "Observed proportion 0.7; independent Bernoulli items, z=1.96; not a benchmark result. Cluster dependence requires another uncertainty calculation.",
  "worked": "观察比例均为0.7时，n=20的Wilson区间约[0.481,0.855]，n=500约[0.658,0.739]。相关题目会让这个独立模型过于乐观。",
  "source_ids": [
    "mmlu",
    "helm",
    "mmmu",
    "arxiv-2107.06499",
    "arxiv-2104.08758"
  ],
  "formula_source": "Article equations and this versioned script",
  "diagram_nodes": [
    "定义任务与目标总体",
    "固定题集 / 时间 / 去重",
    "版本化模型与解码预算",
    "逐题结果及判定依据",
    "配对统计与分层指标",
    "权重敏感性和适用边界"
  ]
}