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Qtm 110 final review docx

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QTM 110 FINAL REVIEW Equations N μX= Bias= E [ Y 0|T =1 ]−E [Y 0∨T =0] 1 ∑X N i=1 i ' cov ( X ,Y )=E [ ( X−μ X )( Y −μY ) ] Baye s Rule P (A∧B) P ( A|B )= or P( B) P (B∨ A)P( A) P ( A|B )= P(B) corr ( X , Y )=cov (X , Y )/ σ X σ Y P ( A∧B )=P ( A|B ) P( B) Regression Coefficient β=cov ( X ,Y )/σ X Law of Total Probability √ 2 is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m σ X = E [ X −μ X ] 2 P ( A )=P ( A|B ) P ( B ) + P ( A| B ) P( B) Inferential Errors 1. Base Rate Fallacy a. Ignoring the base rate 2. Regression to the Mean a. Outcome is determined by randomness and partly deterministic factors 3. Selection on the Dependent Variable a. Only one group being compared 4. Multiple Testing a. Doing the same trials, or testing multiple hypothesis or different methods, until a positive result is found 5. Not Comparing Apples-to-Apples a. Y0 of treatment and control is not the same 6. Reverse Causality a. Consider the opposite Th Correlation Two variables are correlated if they co-vary together. Variables will never be perfectly correlated due to variation in data. Correlation does not imply causation! sh Covariance  A statistic used to summarize the extent of correlation between two variables o Measures the joint variability between two variables o Direction of correlation  cov ( X ,Y )=E [ ( X−μ X )( Y −μY ) ] , where μ X and μY are the means o First, solve ( X −μ X ) ( Y −μY ) for each observatio ...
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