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# hw2.ass - Page 1 of 4 Stat209/Ed260 D Rogosa Assignment 2...

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Stat209/Ed260 D Rogosa 1/18/09 Assignment 2. Experiments and Observational Studies Formulation for causal inference 1. Neyman-Holland-Rubin formulation Create some counter-factual data (following Holland 1988 appendix) from Thursday lecture material (handout) consider a collection of 100 (experimental) units unit-level causal effect (T_tc(u) or rho(u)) is distributed over units as N(2,1) (mean 2, variance 1). Y(u,c) distributed over units N(10,1). potential outcomes: If you had {Y(u,c), Y(u,t)} for all 100 units make a statistical inference for effect of treatment-average causal (treatment) effect. (Inference is to the population from which the u are sampled). Compare result with specification of unit causal effect used in generating the artificial data. now back to reality. generate 100 values of an indicator variable G (group assignment), coin flip (Bernoulli trial has prob G = 1 equal to 1/2). If G=1 observe Y(u,t), if G = 0 observe Y(u,c) from above. Repeat statistical inference for effect of treatment (estimate of average causal effect) designating G=1 observations as the treatment group and G=0 observations as control. compare result with specification of unit causal effect Finally create a different dichotomous group indicator variable, call it say Gneq (representing non-random selection). Gneq is a Bernoulli trial outcome with probability Gneq=1

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hw2.ass - Page 1 of 4 Stat209/Ed260 D Rogosa Assignment 2...

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