{
  "schemaVersion": 1,
  "runtime": {
    "R": "R version 4.6.1 (2026-06-24 ucrt)",
    "survey": "4.5",
    "jsonlite": "2.0.0"
  },
  "design": "Independent respondents within two fixed group strata; sampling weights treated as fixed; no clusters, FPC, replicate weights or calibration variance. Design formed on the chosen contributing population. Conditional valid-case estimates do not adjust nonresponse bias.",
  "inference": "svymean + svyby(covmat=TRUE) + svycontrast; Taylor linearization variance; two-sided t reference using degf(design), pointwise 95% t interval. This declared teaching reference is not a claim of Q/Displayr numerical parity.",
  "scenarios": {
    "unweighted/answered/exclude": {
      "groups": [
        {
          "group": "A",
          "rawN": 6,
          "weightSum": 6,
          "weightSquares": 6,
          "positiveWeight": 4,
          "proportion": 0.66666666666666663,
          "effectiveN": 6
        },
        {
          "group": "B",
          "rawN": 6,
          "weightSum": 6,
          "weightSquares": 6,
          "positiveWeight": 2,
          "proportion": 0.33333333333333331,
          "effectiveN": 6
        }
      ],
      "survey": {
        "difference": 0.33333333333333331,
        "standardError": 0.29814239699997191,
        "degreesFreedom": 10,
        "pValue": 0.28969161205100841,
        "normalPValue": 0.26355247728297271,
        "interval": [-0.33096932484662006, 0.99763599151328664]
      },
      "kishFormula": {
        "standardError": 0.27216552697590868,
        "z": 1.2247448713915889,
        "pValue": 0.22067136191984679
      }
    },
    "unweighted/answered/category": {
      "groups": [
        {
          "group": "A",
          "rawN": 7,
          "weightSum": 7,
          "weightSquares": 7,
          "positiveWeight": 4,
          "proportion": 0.5714285714285714,
          "effectiveN": 7
        },
        {
          "group": "B",
          "rawN": 7,
          "weightSum": 7,
          "weightSquares": 7,
          "positiveWeight": 2,
          "proportion": 0.2857142857142857,
          "effectiveN": 7
        }
      ],
      "survey": {
        "difference": 0.2857142857142857,
        "standardError": 0.27355060221609662,
        "degreesFreedom": 12,
        "pValue": 0.31685435697756981,
        "normalPValue": 0.29626987148428635,
        "interval": [-0.31030127595734214, 0.88172984738591353]
      },
      "kishFormula": {
        "standardError": 0.25325864583654811,
        "z": 1.1281521496355322,
        "pValue": 0.25925566826756868
      }
    },
    "unweighted/everyone/exclude": {
      "groups": [
        {
          "group": "A",
          "rawN": 8,
          "weightSum": 8,
          "weightSquares": 8,
          "positiveWeight": 4,
          "proportion": 0.5,
          "effectiveN": 8
        },
        {
          "group": "B",
          "rawN": 8,
          "weightSum": 8,
          "weightSquares": 8,
          "positiveWeight": 2,
          "proportion": 0.25,
          "effectiveN": 8
        }
      ],
      "survey": {
        "difference": 0.25,
        "standardError": 0.25,
        "degreesFreedom": 14,
        "pValue": 0.33428194339465733,
        "normalPValue": 0.31731050786291409,
        "interval": [-0.28619667197945098, 0.78619667197945098]
      },
      "kishFormula": {
        "standardError": 0.23385358667337133,
        "z": 1.0690449676496976,
        "pValue": 0.28504940740261264
      }
    },
    "unweighted/everyone/category": {
      "groups": [
        {
          "group": "A",
          "rawN": 8,
          "weightSum": 8,
          "weightSquares": 8,
          "positiveWeight": 4,
          "proportion": 0.5,
          "effectiveN": 8
        },
        {
          "group": "B",
          "rawN": 8,
          "weightSum": 8,
          "weightSquares": 8,
          "positiveWeight": 2,
          "proportion": 0.25,
          "effectiveN": 8
        }
      ],
      "survey": {
        "difference": 0.25,
        "standardError": 0.25,
        "degreesFreedom": 14,
        "pValue": 0.33428194339465733,
        "normalPValue": 0.31731050786291409,
        "interval": [-0.28619667197945098, 0.78619667197945098]
      },
      "kishFormula": {
        "standardError": 0.23385358667337133,
        "z": 1.0690449676496976,
        "pValue": 0.28504940740261264
      }
    },
    "weighted/answered/exclude": {
      "groups": [
        {
          "group": "A",
          "rawN": 6,
          "weightSum": 8,
          "weightSquares": 12,
          "positiveWeight": 6,
          "proportion": 0.75,
          "effectiveN": 5.333333333333333
        },
        {
          "group": "B",
          "rawN": 6,
          "weightSum": 8,
          "weightSquares": 12,
          "positiveWeight": 3,
          "proportion": 0.375,
          "effectiveN": 5.333333333333333
        }
      ],
      "survey": {
        "difference": 0.375,
        "standardError": 0.29646353064078557,
        "degreesFreedom": 10,
        "pValue": 0.234584914438628,
        "normalPValue": 0.20590321073206835,
        "interval": [-0.2855619108177575, 1.0355619108177576]
      },
      "kishFormula": {
        "standardError": 0.28125,
        "z": 1.3333333333333333,
        "pValue": 0.1824224394517357
      }
    },
    "weighted/answered/category": {
      "groups": [
        {
          "group": "A",
          "rawN": 7,
          "weightSum": 10,
          "weightSquares": 16,
          "positiveWeight": 6,
          "proportion": 0.60000000000000009,
          "effectiveN": 6.25
        },
        {
          "group": "B",
          "rawN": 7,
          "weightSum": 10,
          "weightSquares": 16,
          "positiveWeight": 3,
          "proportion": 0.30000000000000004,
          "effectiveN": 6.25
        }
      ],
      "survey": {
        "difference": 0.30000000000000004,
        "standardError": 0.28982753492378882,
        "degreesFreedom": 12,
        "pValue": 0.32103277093213572,
        "normalPValue": 0.3006229881969068,
        "interval": [-0.33147995148277776, 0.93147995148277785]
      },
      "kishFormula": {
        "standardError": 0.26832815729997478,
        "z": 1.1180339887498949,
        "pValue": 0.26355247728297271
      }
    },
    "weighted/everyone/exclude": {
      "groups": [
        {
          "group": "A",
          "rawN": 8,
          "weightSum": 11,
          "weightSquares": 17,
          "positiveWeight": 6,
          "proportion": 0.54545454545454541,
          "effectiveN": 7.117647058823529
        },
        {
          "group": "B",
          "rawN": 8,
          "weightSum": 11,
          "weightSquares": 17,
          "positiveWeight": 3,
          "proportion": 0.27272727272727271,
          "effectiveN": 7.117647058823529
        }
      ],
      "survey": {
        "difference": 0.27272727272727271,
        "standardError": 0.26943380071963946,
        "degreesFreedom": 14,
        "pValue": 0.32860639129259206,
        "normalPValue": 0.31143111740214835,
        "interval": [-0.30515075633130839, 0.85060530178585381]
      },
      "kishFormula": {
        "standardError": 0.25040094888501019,
        "z": 1.0891622972743418,
        "pValue": 0.27608232187779724
      }
    },
    "weighted/everyone/category": {
      "groups": [
        {
          "group": "A",
          "rawN": 8,
          "weightSum": 11,
          "weightSquares": 17,
          "positiveWeight": 6,
          "proportion": 0.54545454545454541,
          "effectiveN": 7.117647058823529
        },
        {
          "group": "B",
          "rawN": 8,
          "weightSum": 11,
          "weightSquares": 17,
          "positiveWeight": 3,
          "proportion": 0.27272727272727271,
          "effectiveN": 7.117647058823529
        }
      ],
      "survey": {
        "difference": 0.27272727272727271,
        "standardError": 0.26943380071963946,
        "degreesFreedom": 14,
        "pValue": 0.32860639129259206,
        "normalPValue": 0.31143111740214835,
        "interval": [-0.30515075633130839, 0.85060530178585381]
      },
      "kishFormula": {
        "standardError": 0.25040094888501019,
        "z": 1.0891622972743418,
        "pValue": 0.27608232187779724
      }
    },
    "extreme/answered/exclude": {
      "groups": [
        {
          "group": "A",
          "rawN": 6,
          "weightSum": 39,
          "weightSquares": 1035,
          "positiveWeight": 6,
          "proportion": 0.15384615384615385,
          "effectiveN": 1.4695652173913043
        },
        {
          "group": "B",
          "rawN": 6,
          "weightSum": 38,
          "weightSquares": 1032,
          "positiveWeight": 33,
          "proportion": 0.86842105263157887,
          "effectiveN": 1.3992248062015504
        }
      ],
      "survey": {
        "difference": -0.71457489878542502,
        "standardError": 0.20957895763360618,
        "degreesFreedom": 10,
        "pValue": 0.0066630508455060239,
        "normalPValue": 0.00065064498968603682,
        "interval": [-1.1815459168476483, -0.24760388072320183]
      },
      "kishFormula": {
        "standardError": 0.41260885903257577,
        "z": -1.7318457496546598,
        "pValue": 0.083301030040257837
      }
    },
    "extreme/answered/category": {
      "groups": [
        {
          "group": "A",
          "rawN": 7,
          "weightSum": 41,
          "weightSquares": 1039,
          "positiveWeight": 6,
          "proportion": 0.14634146341463417,
          "effectiveN": 1.6179018286814244
        },
        {
          "group": "B",
          "rawN": 7,
          "weightSum": 40,
          "weightSquares": 1036,
          "positiveWeight": 33,
          "proportion": 0.82500000000000007,
          "effectiveN": 1.5444015444015444
        }
      ],
      "survey": {
        "difference": -0.6786585365853659,
        "standardError": 0.22068098876352721,
        "degreesFreedom": 12,
        "pValue": 0.009621712879771269,
        "normalPValue": 0.0021029637163843115,
        "interval": [-1.1594811061669885, -0.19783596700374334]
      },
      "kishFormula": {
        "standardError": 0.41315543155167139,
        "z": -1.6426228115567914,
        "pValue": 0.10046099803429749
      }
    },
    "extreme/everyone/exclude": {
      "groups": [
        {
          "group": "A",
          "rawN": 8,
          "weightSum": 42,
          "weightSquares": 1040,
          "positiveWeight": 6,
          "proportion": 0.14285714285714285,
          "effectiveN": 1.6961538461538461
        },
        {
          "group": "B",
          "rawN": 8,
          "weightSum": 41,
          "weightSquares": 1037,
          "positiveWeight": 33,
          "proportion": 0.80487804878048785,
          "effectiveN": 1.6210221793635486
        }
      ],
      "survey": {
        "difference": -0.66202090592334506,
        "standardError": 0.22404296180373853,
        "degreesFreedom": 14,
        "pValue": 0.010444433492606327,
        "normalPValue": 0.0031278689092107273,
        "interval": [-1.1425452679216805, -0.18149654392500963]
      },
      "kishFormula": {
        "standardError": 0.41118739078068334,
        "z": -1.6100223906828159,
        "pValue": 0.10739296828486221
      }
    },
    "extreme/everyone/category": {
      "groups": [
        {
          "group": "A",
          "rawN": 8,
          "weightSum": 42,
          "weightSquares": 1040,
          "positiveWeight": 6,
          "proportion": 0.14285714285714285,
          "effectiveN": 1.6961538461538461
        },
        {
          "group": "B",
          "rawN": 8,
          "weightSum": 41,
          "weightSquares": 1037,
          "positiveWeight": 33,
          "proportion": 0.80487804878048785,
          "effectiveN": 1.6210221793635486
        }
      ],
      "survey": {
        "difference": -0.66202090592334506,
        "standardError": 0.22404296180373853,
        "degreesFreedom": 14,
        "pValue": 0.010444433492606327,
        "normalPValue": 0.0031278689092107273,
        "interval": [-1.1425452679216805, -0.18149654392500963]
      },
      "kishFormula": {
        "standardError": 0.41118739078068334,
        "z": -1.6100223906828159,
        "pValue": 0.10739296828486221
      }
    }
  }
}
