Causal Diagrams and Causal Models
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ABCDEFGHIJKLMNOPQRST
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OEI#
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YYY1119
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YYN16104
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YNY11121
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YNN60032
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NYY18102
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NYN132111
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NNY29120
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NNN155033
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OEITotal
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8837616743659462422742
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!O!E!I
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334366255306363280
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P(O) P(E)P(I)
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0.20905422220.39607136270.1406578954
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P(E|O)P(E|!O)E and O have some negative correlation. They must share either a causal relationship or a common causal factor.
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0.19488322620.4492472321
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P(O|E)P(O|!E)
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0.10286318350.2786969362
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P(O|I)P(O|!I)There is no correlation between O and I, so they can not share a common cause or cause each other.
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0.20584575020.2095793878
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P(I|O)P(I|!O)
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0.138499140.1412284742
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P(I|E)P(I|!E)Again we can infer negative correlation, which means they must share either a causal relationship or a common causal factor.
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0.11479610120.1576187007
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P(E|I)P(E|!I)
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0.32324846120.4079910813
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(1) O and I can not share a common cause, nor can they cause one another.
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(2) E and O must have a common cause or causal relation.
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(3) E and I must have a common cause or causal relation.
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(4) E can not cause O and I, given (1)
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(5) O and I must therefore cause E to satisfy (2) and (3)
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(6) To satisfy (1), O and I must be independent causes of E, which leaves only this graph: {(O->E), (I->E)}
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