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"minimum": 6.3,
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"maximum": 53.0,
"iqr_linear": 16.85
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"late_count": 6,
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"late_fraction": 0.2,
"priority_count": 15,
"satisfaction_respondents": 27,
"satisfaction_missing": 3,
"satisfaction_missing_fraction": 0.1,
"respondent_mean_rating": 3.814814814814815,
"rating_counts_among_respondents": {
"1": 0,
"2": 3,
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},
"7": {
"n": 30,
"actual_minutes": {
"n": 30,
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"median": 63.45,
"sample_sd": 19.58262072560153,
"minimum": 18.1,
"q1_linear": 54.7,
"q3_linear": 76.575,
"maximum": 106.9,
"iqr_linear": 21.875
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"distance_km": {
"n": 30,
"sum": 851.5,
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"minimum": 6.7,
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},
"8": {
"n": 30,
"actual_minutes": {
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"median": 60.9,
"sample_sd": 24.866757803906822,
"minimum": 22.1,
"q1_linear": 46.8,
"q3_linear": 75.425,
"maximum": 124.5,
"iqr_linear": 28.625
},
"distance_km": {
"n": 30,
"sum": 796.6,
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"median": 24.35,
"sample_sd": 12.60478106700495,
"minimum": 6.0,
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"q3_linear": 34.75,
"maximum": 53.7,
"iqr_linear": 17.175
},
"late_count": 6,
"late_denominator": 30,
"late_fraction": 0.2,
"priority_count": 15,
"satisfaction_respondents": 23,
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"satisfaction_missing_fraction": 0.23333333333333334,
"respondent_mean_rating": 4.217391304347826,
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"3": 4,
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}
},
"by_late_status": {
"on_time": {
"n": 189,
"actual_minutes": {
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"sum": 11103.6,
"mean": 58.74920634920635,
"median": 59.5,
"sample_sd": 24.589101155661705,
"minimum": 6.7,
"q1_linear": 39.8,
"q3_linear": 76.3,
"maximum": 116.2,
"iqr_linear": 36.5
},
"distance_km": {
"n": 189,
"sum": 5210.1,
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"q3_linear": 35.2,
"maximum": 54.8,
"iqr_linear": 18.300000000000004
},
"late_count": 0,
"late_denominator": 189,
"late_fraction": 0.0,
"priority_count": 89,
"satisfaction_respondents": 168,
"satisfaction_missing": 21,
"satisfaction_missing_fraction": 0.1111111111111111,
"respondent_mean_rating": 4.333333333333333,
"rating_counts_among_respondents": {
"1": 0,
"2": 0,
"3": 19,
"4": 74,
"5": 75
}
},
"late": {
"n": 51,
"actual_minutes": {
"n": 51,
"sum": 3967.0,
"mean": 77.7843137254902,
"median": 72.9,
"sample_sd": 26.882591932691458,
"minimum": 35.4,
"q1_linear": 58.1,
"q3_linear": 90.25,
"maximum": 136.8,
"iqr_linear": 32.15
},
"distance_km": {
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"q3_linear": 35.85,
"maximum": 54.6,
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"late_count": 51,
"late_denominator": 51,
"late_fraction": 1.0,
"priority_count": 31,
"satisfaction_respondents": 31,
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"respondent_mean_rating": 3.064516129032258,
"rating_counts_among_respondents": {
"1": 1,
"2": 7,
"3": 12,
"4": 11,
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}
}
},
"observational_distance_time": {
"n": 240,
"pearson_r": 0.9226341940210205,
"slope_minutes_per_km": 1.805826695975647,
"intercept_minutes": 12.66216030301274,
"r_squared": 0.8512538559768181,
"rmse_minutes_denominator_n": 10.092739332289451,
"observed_distance_min_km": 5.2,
"observed_distance_max_km": 54.8,
"fitted_minutes_at_20_km": 48.77869422252568,
"fitted_minutes_at_40_km": 84.89522814203862,
"interpretation": "Association within this fictional observational snapshot, not a causal effect.",
"checks_before_inference": [
"Inspect scatterplot for approximate linearity and influential observations.",
"Inspect residuals for changing spread and systematic patterns.",
"Shipments share week conditions; independent errors are not established.",
"Service mix and unmeasured operational factors may confound relationships.",
"Do not extrapolate beyond observed distances or infer real-world performance."
]
},
"inference_warning": "Descriptive snapshot, not a probability sample. Shared weeks and different route/service mixes preclude naive independent-row causal hub tests.",
"satisfaction_warning": "Ratings are ordinal and response is selectively missing. The respondent mean is a coding-based summary of respondents, not all customers. Missing ratings are never zero or imputed."
},
"trial": {
"control": {
"n": 20,
"sum": 479.79,
"mean": 23.9895,
"median": 24.450000000000003,
"sample_sd": 4.1253548172758485,
"minimum": 16.19,
"q1_linear": 21.245,
"q3_linear": 25.875,
"maximum": 34.04,
"iqr_linear": 4.629999999999999
},
"checklist": {
"n": 20,
"sum": 415.76,
"mean": 20.788,
"median": 20.75,
"sample_sd": 4.147730641409132,
"minimum": 9.77,
"q1_linear": 17.9575,
"q3_linear": 23.5325,
"maximum": 27.5,
"iqr_linear": 5.574999999999999
},
"control_mean_t_interval_95": {
"confidence_level": 0.95,
"mean": 23.9895,
"n": 20,
"df": 19,
"standard_error": 0.9224573802735021,
"critical_t": 2.0930240544083087,
"margin": 1.9307254860789125,
"low": 22.058774513921087,
"high": 25.920225486078913
},
"welch_checklist_minus_control": {
"first_n": 20,
"second_n": 20,
"difference": -3.2014999999999993,
"standard_error": 1.308094450758531,
"t_statistic": -2.4474532386736523,
"df": 37.99888814645343,
"two_sided_p": 0.019120112692739923,
"confidence_level": 0.95,
"ci_low": -5.849601316500556,
"ci_high": -0.5533986834994424,
"null_difference": 0.0,
"alternative": "two-sided",
"direction": "checklist minus control, minutes; negative means shorter",
"absolute_difference_minutes": -3.2014999999999993,
"absolute_magnitude_minutes": 3.2014999999999993,
"relative_difference_fraction_of_control": -0.13345421955438835,
"relative_difference_percent_of_control": -13.345421955438836,
"relative_ci_note": "No confidence interval for the relative change is computed; the Welch interval is in minutes."
},
"design": "40 independent simulated people from one fictional teaching process, one task each, balanced random assignment. Not a representative sample of any real workforce.",
"generating_model": "Duration = 24 + independent Normal(0,4.2) person error - 3 if assigned checklist; rounded to 0.01 minute. Each simulated person's two potential outcomes differ by -3 before rounding; only the assigned outcome is observed. No rerolls.",
"inference_scope": "Randomization illustrates causal identification within this simulated experiment. t methods assume independent errors and approximately normal within-group outcomes; equal population variances are not required by Welch. No claim about real people or shipment delivery performance.",
"p_value_warning": "The p-value is not the probability that the null is true, that chance caused the result, or that a future rollout will succeed.",
"ci_warning": "95% describes the long-run coverage of the method under its assumptions, not a 95% probability for a fixed unknown parameter after this interval is observed. Non-significance would not establish equivalence."
},
"probability_toy": {
"note": "Separate stipulated 1,000-shipment toy, not estimates from the CSV.",
"total": 1000,
"late": 100,
"on_time": 900,
"flagged_late": 80,
"unflagged_late": 20,
"flagged_on_time": 90,
"unflagged_on_time": 810,
"base_late_probability": 0.1,
"p_flag_given_late": 0.8,
"p_flag_given_on_time": 0.1,
"p_flag": 0.17,
"p_late_given_flag": 0.47058823529411764,
"p_late_or_flag": 0.19
}
}
