{
  "analysis": "Artificial paired-school change-score design sensitivity; no observed effects",
  "seed": 20261016,
  "replicatesPerScenario": 10000,
  "assumptions": {
    "initialStudentsPerSchool": 40,
    "meanRetainedTargetBeforeTruncation": 34,
    "retentionModel": "School-specific p ~ Beta(6.8,1.2); retained m ~ Binomial(40,p), lower-truncated by maximum(m,12)",
    "retainedSizeBounds": [
      12,
      40
    ],
    "baselineEndlineCorrelation": 0.6,
    "individualOutcomeSD": 1,
    "unattenuatedAssignedEffectSD": 0.3,
    "test": "Two-sided paired t test, alpha .05, pairs-1 df",
    "matching": "No extra residual correlation benefit assumed for matched schools",
    "exclusions": "No nonnormal bounds, informative attrition, whole-school dropout, measurement noninvariance, variable compliance or network interference modeled; comparison exposure is a scalar attenuation scenario, not a fitted spillover model."
  },
  "scenarios": [
    {
      "pairs": 24,
      "schools": 48,
      "outcomeICC": 0.05,
      "comparisonExposureFraction": 0.0,
      "assignedEffectSD": 0.3,
      "power": 0.976,
      "monteCarloSE": 0.0015304901175767199,
      "nullRejectionRate": 0.0528,
      "meanArtificialRetainedSize": 34.006595833333336,
      "retainedSizeCV": 0.15301253358786399,
      "retainedMinimum": 12,
      "retainedMaximum": 40
    },
    {
      "pairs": 24,
      "schools": 48,
      "outcomeICC": 0.05,
      "comparisonExposureFraction": 0.25,
      "assignedEffectSD": 0.22499999999999998,
      "power": 0.8446,
      "monteCarloSE": 0.0036228557796302075,
      "nullRejectionRate": 0.0489,
      "meanArtificialRetainedSize": 34.0045,
      "retainedSizeCV": 0.15289845687559042,
      "retainedMinimum": 12,
      "retainedMaximum": 40
    },
    {
      "pairs": 24,
      "schools": 48,
      "outcomeICC": 0.1,
      "comparisonExposureFraction": 0.0,
      "assignedEffectSD": 0.3,
      "power": 0.8738,
      "monteCarloSE": 0.003320746301661721,
      "nullRejectionRate": 0.0492,
      "meanArtificialRetainedSize": 33.99894166666667,
      "retainedSizeCV": 0.1533803679154877,
      "retainedMinimum": 12,
      "retainedMaximum": 40
    },
    {
      "pairs": 24,
      "schools": 48,
      "outcomeICC": 0.1,
      "comparisonExposureFraction": 0.25,
      "assignedEffectSD": 0.22499999999999998,
      "power": 0.6484,
      "monteCarloSE": 0.00477469831507709,
      "nullRejectionRate": 0.0506,
      "meanArtificialRetainedSize": 33.991391666666665,
      "retainedSizeCV": 0.15347634484846112,
      "retainedMinimum": 12,
      "retainedMaximum": 40
    },
    {
      "pairs": 32,
      "schools": 64,
      "outcomeICC": 0.05,
      "comparisonExposureFraction": 0.0,
      "assignedEffectSD": 0.3,
      "power": 0.9958,
      "monteCarloSE": 0.0006467116822819873,
      "nullRejectionRate": 0.049,
      "meanArtificialRetainedSize": 34.0008390625,
      "retainedSizeCV": 0.15315883462119548,
      "retainedMinimum": 12,
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    },
    {
      "pairs": 32,
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      "outcomeICC": 0.05,
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      "assignedEffectSD": 0.22499999999999998,
      "power": 0.9383,
      "monteCarloSE": 0.002406098709529598,
      "nullRejectionRate": 0.0461,
      "meanArtificialRetainedSize": 33.9983765625,
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      "assignedEffectSD": 0.3,
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      "nullRejectionRate": 0.0476,
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    {
      "pairs": 32,
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      "outcomeICC": 0.1,
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      "monteCarloSE": 0.004153232957588582,
      "nullRejectionRate": 0.0503,
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    {
      "pairs": 40,
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      "nullRejectionRate": 0.0463,
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      "nullRejectionRate": 0.0527,
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    {
      "pairs": 40,
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      "nullRejectionRate": 0.0482,
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    {
      "pairs": 40,
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      "nullRejectionRate": 0.0465,
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  ]
}