{
  "analysis": "Executed artificial-data design sensitivity; no actual teacher outcomes",
  "seed": 20261015,
  "replicates_per_scenario": 10000,
  "two_sided_alpha": 0.05,
  "software": {
    "numpy": "2.3.5",
    "scipy": "1.17.0"
  },
  "assumptions": [
    "Independent normally distributed school-pair differences",
    "Complete follow-up, equal school weighting and fixed 20-minute weekday reduction",
    "No missingness, interference, unequal cohort penalty or quality-guardrail power included",
    "SD values are planning assumptions, not estimated from ATUS or local teacher records"
  ],
  "scenarios": [
    {
      "pairs": 16,
      "schools": 32,
      "assumed_sd_of_pair_differences_minutes": 30.0,
      "assumed_effect_minutes": -20.0,
      "power": 0.7068,
      "power_mcse": 0.004552293487902554,
      "null_rejection_rate": 0.0499,
      "approximate_mde_minutes": 22.298030843495177
    },
    {
      "pairs": 16,
      "schools": 32,
      "assumed_sd_of_pair_differences_minutes": 45.0,
      "assumed_effect_minutes": -20.0,
      "power": 0.39,
      "power_mcse": 0.0048774993593028795,
      "null_rejection_rate": 0.0508,
      "approximate_mde_minutes": 33.44704626524277
    },
    {
      "pairs": 16,
      "schools": 32,
      "assumed_sd_of_pair_differences_minutes": 60.0,
      "assumed_effect_minutes": -20.0,
      "power": 0.2427,
      "power_mcse": 0.004287151851754262,
      "null_rejection_rate": 0.0514,
      "approximate_mde_minutes": 44.59606168699035
    },
    {
      "pairs": 24,
      "schools": 48,
      "assumed_sd_of_pair_differences_minutes": 30.0,
      "assumed_effect_minutes": -20.0,
      "power": 0.8771,
      "power_mcse": 0.003283223872963889,
      "null_rejection_rate": 0.0495,
      "approximate_mde_minutes": 17.821745442492997
    },
    {
      "pairs": 24,
      "schools": 48,
      "assumed_sd_of_pair_differences_minutes": 45.0,
      "assumed_effect_minutes": -20.0,
      "power": 0.5488,
      "power_mcse": 0.004976128615701166,
      "null_rejection_rate": 0.0527,
      "approximate_mde_minutes": 26.7326181637395
    },
    {
      "pairs": 24,
      "schools": 48,
      "assumed_sd_of_pair_differences_minutes": 60.0,
      "assumed_effect_minutes": -20.0,
      "power": 0.3561,
      "power_mcse": 0.00478845267283702,
      "null_rejection_rate": 0.055,
      "approximate_mde_minutes": 35.643490884985994
    },
    {
      "pairs": 32,
      "schools": 64,
      "assumed_sd_of_pair_differences_minutes": 30.0,
      "assumed_effect_minutes": -20.0,
      "power": 0.953,
      "power_mcse": 0.002116388433156826,
      "null_rejection_rate": 0.051,
      "approximate_mde_minutes": 15.27952402288531
    },
    {
      "pairs": 32,
      "schools": 64,
      "assumed_sd_of_pair_differences_minutes": 45.0,
      "assumed_effect_minutes": -20.0,
      "power": 0.679,
      "power_mcse": 0.004668607929565301,
      "null_rejection_rate": 0.0516,
      "approximate_mde_minutes": 22.919286034327964
    },
    {
      "pairs": 32,
      "schools": 64,
      "assumed_sd_of_pair_differences_minutes": 60.0,
      "assumed_effect_minutes": -20.0,
      "power": 0.45,
      "power_mcse": 0.0049749371855331,
      "null_rejection_rate": 0.0487,
      "approximate_mde_minutes": 30.55904804577062
    }
  ]
}