{
  "disclosure": "Illustrative analysis \u00b7 Sample data",
  "customer": "Fieldwork Events",
  "survey": "Post-event feedback",
  "question": "How would you rate the event?",
  "scale": [
    1,
    2,
    3,
    4,
    5
  ],
  "method": "Synthetic independent ratings, treated numerically on a 1\u20135 scale. Approximate 95% intervals use mean \u00b1 1.96 \u00d7 standard error. Sample variances use n \u2212 1. The difference interval uses the square root of the sum of the two mean variances. Two-sided normal-approximation p-value; one planned comparison. This is an illustrative method, not a reproduction of the production analysis engine. An association does not establish causation or rule out selection bias. Explanations are prewritten; no model is called.",
  "scenarios": [
    {
      "id": "meaningful",
      "label": "Meaningful difference",
      "headline": "Workshop attendees rated the event higher.",
      "explanation": "People who joined a workshop gave the event a higher average rating. The gap is large enough to stand out from sampling noise in this example.",
      "action": "Read the written feedback to understand what attendees valued.",
      "groups": [
        {
          "label": "Joined a workshop",
          "counts": [
            3,
            7,
            20,
            70,
            100
          ],
          "n": 200,
          "mean": 4.285,
          "standardError": 0.06315709853593171,
          "interval": [
            4.161212086869574,
            4.408787913130427
          ]
        },
        {
          "label": "Skipped workshops",
          "counts": [
            8,
            18,
            54,
            80,
            40
          ],
          "n": 200,
          "mean": 3.63,
          "standardError": 0.07274585760711723,
          "interval": [
            3.48741811909005,
            3.7725818809099496
          ]
        }
      ],
      "difference": 0.6550000000000002,
      "interval": [
        0.4661798734218067,
        0.8438201265781937
      ],
      "p": 1.0530151867587792e-11
    },
    {
      "id": "unclear",
      "label": "No clear difference",
      "headline": "These ratings are too close to call.",
      "explanation": "The two groups gave almost the same average rating. The uncertainty around the gap includes zero, so this sample does not support a difference.",
      "action": "Avoid ranking these groups. Keep collecting feedback.",
      "groups": [
        {
          "label": "Joined a workshop",
          "counts": [
            5,
            10,
            30,
            85,
            70
          ],
          "n": 200,
          "mean": 4.025,
          "standardError": 0.06815497415825615,
          "interval": [
            3.891416250649818,
            4.158583749350182
          ]
        },
        {
          "label": "Skipped workshops",
          "counts": [
            4,
            13,
            31,
            83,
            69
          ],
          "n": 200,
          "mean": 4.0,
          "standardError": 0.0687285827763985,
          "interval": [
            3.865291977758259,
            4.134708022241741
          ]
        }
      ],
      "difference": 0.025000000000000355,
      "interval": [
        -0.1647125967002021,
        0.21471259670020282
      ],
      "p": 0.796186628486452
    }
  ]
}