demo-mini

[{"question_id": 1, "desc_id": "simpson_hospital-confounding-ate-modelNone-spec0-q0", "given_info": "For patients who are young and pay a low hospital bill, the probability of recovery is 3%. For patients who are young and pay a high hospital bill, the probability of recovery is 15%. For patients who are old and pay a low hospital bill, the probability of recovery is 93%. For patients who are old and pay a high hospital bill, the probability of recovery is 7%. The overall probability of old age is 13%.", "question": "Will high hospital bill increase the chance of recovery?", "answer": "no", "meta": {"story_id": "simpson_hospital", "graph_id": "confounding", "treated": true, "result": true, "polarity": true, "groundtruth": -0.006379550539189899, "query_type": "ate", "rung": 2, "formal_form": "E[Y | do(X = 1)] - E[Y | do(X = 0)]", "given_info": {"p(Y | V1, X)": [[0.02868900837194475, 0.14792608457745604], [0.9282110229603693, 0.07042057615419703]], "p(V1)": [0.12857020276920017]}, "estimand": "\\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]", "treatment": "X", "outcome": "Y", "model": {"story_id": "simpson_hospital", "graph_id": "confounding", "spec_id": 0, "spec": {"V1": [0.12857020276919962], "X": [0.49927786244011496, 0.6014983576233575], "Y": [0.028689008371944547, 0.14792608457745593, 0.9282110229603695, 0.07042057615419683]}, "seed": 11, "builder": "random", "simpson": true, "equation_type": "bernoulli", "background": "Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and recovery. Hospital costs has a direct effect on recovery.", "variable_mapping": {"V1name": "age", "V11": "old age", "V10": "youth", "Xname": "hospital costs", "X1": "high hospital bill", "X0": "low hospital bill", "Yname": "recovery", "Y1": "recovery", "Y0": "non-recovery"}, "structure": "V1->X,V1->Y,X->Y", "params": {"p(V1)": [0.12857020276919962], "p(X | V1)": [0.49927786244011496, 0.6014983576233575], "p(Y | V1, X)": [[0.028689008371944547, 0.14792608457745593], [0.9282110229603695, 0.07042057615419683]]}}}, "reasoning": {"step0": "Let V1 = age; X = hospital costs; Y = recovery.", "step1": "V1->X,V1->Y,X->Y", "step2": "E[Y | do(X = 1)] - E[Y | do(X = 0)]", "step3": "\\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]", "step4": "P(Y=1 | V1=0, X=0) = 0.03\nP(Y=1 | V1=0, X=1) = 0.15\nP(Y=1 | V1=1, X=0) = 0.93\nP(Y=1 | V1=1, X=1) = 0.07\nP(V1=1) = 0.13", "step5": "0.87 * (0.15 - 0.03) + 0.13 * (0.07 - 0.93) = -0.01", "end": "-0.01 < 0"}}, {"question_id": 2, "desc_id": "simpson_hospital-confounding-ate-modelNone-spec0-q1", "given_info": "For patients who are young and pay a low hospital bill, the probability of recovery is 3%. For patients who are young and pay a high hospital bill, the probability of recovery is 15%. For patients who are old and pay a low hospital bill, the probability of recovery is 93%. For patients who are old and pay a high hospital bill, the probability of recovery is 7%. The overall probability of old age is 13%.", "question": "Will high hospital bill decrease the chance of recovery?", "answer": "yes", "meta": {"story_id": "simpson_hospital", "graph_id": "confounding", "treated": true, "result": true, "polarity": false, "groundtruth": -0.006379550539189899, "query_type": "ate", "rung": 2, "formal_form": "E[Y | do(X = 1)] - E[Y | do(X = 0)]", "given_info": {"p(Y | V1, X)": [[0.02868900837194475, 0.14792608457745604], [0.9282110229603693, 0.07042057615419703]], "p(V1)": [0.12857020276920017]}, "estimand": "\\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]", "treatment": "X", "outcome": "Y", "model": {"story_id": "simpson_hospital", "graph_id": "confounding", "spec_id": 0, "spec": {"V1": [0.12857020276919962], "X": [0.49927786244011496, 0.6014983576233575], "Y": [0.028689008371944547, 0.14792608457745593, 0.9282110229603695, 0.07042057615419683]}, "seed": 11, "builder": "random", "simpson": true, "equation_type": "bernoulli", "background": "Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and recovery. Hospital costs has a direct effect on recovery.", "variable_mapping": {"V1name": "age", "V11": "old age", "V10": "youth", "Xname": "hospital costs", "X1": "high hospital bill", "X0": "low hospital bill", "Yname": "recovery", "Y1": "recovery", "Y0": "non-recovery"}, "structure": "V1->X,V1->Y,X->Y", "params": {"p(V1)": [0.12857020276919962], "p(X | V1)": [0.49927786244011496, 0.6014983576233575], "p(Y | V1, X)": [[0.028689008371944547, 0.14792608457745593], [0.9282110229603695, 0.07042057615419683]]}}}, "reasoning": {"step0": "Let V1 = age; X = hospital costs; Y = recovery.", "step1": "V1->X,V1->Y,X->Y", "step2": "E[Y | do(X = 1)] - E[Y | do(X = 0)]", "step3": "\\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]", "step4": "P(Y=1 | V1=0, X=0) = 0.03\nP(Y=1 | V1=0, X=1) = 0.15\nP(Y=1 | V1=1, X=0) = 0.93\nP(Y=1 | V1=1, X=1) = 0.07\nP(V1=1) = 0.13", "step5": "0.87 * (0.15 - 0.03) + 0.13 * (0.07 - 0.93) = -0.01", "end": "-0.01 < 0"}}, {"question_id": 3, "desc_id": "simpson_hospital-confounding-ate-modelNone-spec0-q2", "given_info": "For patients who are young and pay a low hospital bill, the probability of recovery is 3%. For patients who are young and pay a high hospital bill, the probability of recovery is 15%. For patients who are old and pay a low hospital bill, the probability of recovery is 93%. For patients who are old and pay a high hospital bill, the probability of recovery is 7%. The overall probability of old age is 13%.", "question": "Will low hospital bill increase the chance of recovery?", "answer": "yes", "meta": {"story_id": "simpson_hospital", "graph_id": "confounding", "treated": false, "result": true, "polarity": true, "groundtruth": 0.006379550539189899, "query_type": "ate", "rung": 2, "formal_form": "E[Y | do(X = 1)] - E[Y | do(X = 0)]", "given_info": {"p(Y | V1, X)": [[0.02868900837194475, 0.14792608457745604], [0.9282110229603693, 0.07042057615419703]], "p(V1)": [0.12857020276920017]}, "estimand": "\\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]", "treatment": "X", "outcome": "Y", "model": {"story_id": "simpson_hospital", "graph_id": "confounding", "spec_id": 0, "spec": {"V1": [0.12857020276919962], "X": [0.49927786244011496, 0.6014983576233575], "Y": [0.028689008371944547, 0.14792608457745593, 0.9282110229603695, 0.07042057615419683]}, "seed": 11, "builder": "random", "simpson": true, "equation_type": "bernoulli", "background": "Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and recovery. Hospital costs has a direct effect on recovery.", "variable_mapping": {"V1name": "age", "V11": "old age", "V10": "youth", "Xname": "hospital costs", "X1": "high hospital bill", "X0": "low hospital bill", "Yname": "recovery", "Y1": "recovery", "Y0": "non-recovery"}, "structure": "V1->X,V1->Y,X->Y", "params": {"p(V1)": [0.12857020276919962], "p(X | V1)": [0.49927786244011496, 0.6014983576233575], "p(Y | V1, X)": [[0.028689008371944547, 0.14792608457745593], [0.9282110229603695, 0.07042057615419683]]}}}, "reasoning": {"step0": "Let V1 = age; X = hospital costs; Y = recovery.", "step1": "V1->X,V1->Y,X->Y", "step2": "E[Y | do(X = 1)] - E[Y | do(X = 0)]", "step3": "\\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]", "step4": "P(Y=1 | V1=0, X=0) = 0.03\nP(Y=1 | V1=0, X=1) = 0.15\nP(Y=1 | V1=1, X=0) = 0.93\nP(Y=1 | V1=1, X=1) = 0.07\nP(V1=1) = 0.13", "step5": "0.87 * (0.15 - 0.03) + 0.13 * (0.07 - 0.93) = 0.01", "end": "0.01 > 0"}}, {"question_id": 4, "desc_id": "simpson_hospital-confounding-ate-modelNone-spec0-q3", "given_info": "For patients who are young and pay a low hospital bill, the probability of recovery is 3%. For patients who are young and pay a high hospital bill, the probability of recovery is 15%. For patients who are old and pay a low hospital bill, the probability of recovery is 93%. For patients who are old and pay a high hospital bill, the probability of recovery is 7%. The overall probability of old age is 13%.", "question": "Will low hospital bill decrease the chance of recovery?", "answer": "no", "meta": {"story_id": "simpson_hospital", "graph_id": "confounding", "treated": false, "result": true, "polarity": false, "groundtruth": 0.006379550539189899, "query_type": "ate", "rung": 2, "formal_form": "E[Y | do(X = 1)] - E[Y | do(X = 0)]", "given_info": {"p(Y | V1, X)": [[0.02868900837194475, 0.14792608457745604], [0.9282110229603693, 0.07042057615419703]], "p(V1)": [0.12857020276920017]}, "estimand": "\\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]", "treatment": "X", "outcome": "Y", "model": {"story_id": "simpson_hospital", "graph_id": "confounding", "spec_id": 0, "spec": {"V1": [0.12857020276919962], "X": [0.49927786244011496, 0.6014983576233575], "Y": [0.028689008371944547, 0.14792608457745593, 0.9282110229603695, 0.07042057615419683]}, "seed": 11, "builder": "random", "simpson": true, "equation_type": "bernoulli", "background": "Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and recovery. Hospital costs has a direct effect on recovery.", "variable_mapping": {"V1name": "age", "V11": "old age", "V10": "youth", "Xname": "hospital costs", "X1": "high hospital bill", "X0": "low hospital bill", "Yname": "recovery", "Y1": "recovery", "Y0": "non-recovery"}, "structure": "V1->X,V1->Y,X->Y", "params": {"p(V1)": [0.12857020276919962], "p(X | V1)": [0.49927786244011496, 0.6014983576233575], "p(Y | V1, X)": [[0.028689008371944547, 0.14792608457745593], [0.9282110229603695, 0.07042057615419683]]}}}, "reasoning": {"step0": "Let V1 = age; X = hospital costs; Y = recovery.", "step1": "V1->X,V1->Y,X->Y", "step2": "E[Y | do(X = 1)] - E[Y | do(X = 0)]", "step3": "\\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]", "step4": "P(Y=1 | V1=0, X=0) = 0.03\nP(Y=1 | V1=0, X=1) = 0.15\nP(Y=1 | V1=1, X=0) = 0.93\nP(Y=1 | V1=1, X=1) = 0.07\nP(V1=1) = 0.13", "step5": "0.87 * (0.15 - 0.03) + 0.13 * (0.07 - 0.93) = 0.01", "end": "0.01 > 0"}}]