# POLS 2400 Study Guide - Fall 2019, Comprehensive Final Exam Notes - Linear Regression, Regression Analysis, Null Hypothesis

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Cause and Effect
Implies “if, then”
Counterfactuals
o If things had been the other way, we would have had the other outcome
o Fundamental Problem of Causal Inference
Counterfactuals cannot be observed, therefore results cannot be fully
known
Referring to a series of events that, by definition, did not happen
Entire theory of cause and effect based on counterfactuals
o Yi(1) Yi(0)
Ex. In study of black v white resumes
Yi(African American) Yi(White)
Holds idea that all other things are equal
Ceteris paribus
Trying to pick data tool that will best allow us to make causal
inferences
Basic requirements for causality
o Association or correlation
Things must be related
Necessary and sufficient conditions
Necessary= simple requirement (if x doesn’t happen, y doesn’t
happen)
Sufficient= if x happens, y happens
Proportional
The more of x, the more of y
o i.e. more cars on the road results in more traffic
Probabilistic/ likelihood
o Time order/ temporality
Causes must precede effects
o No alternative explanations
Statistical v theoretical relationship
i.e. ice cream sale and crime are statistically related b/c both
increase during the summer, but are not theoretically related b/c ice
cream sales don’t cause crime and vice versa
o Cause and effect are connected
Causal mechanisms
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Randomized Control Trials and Observational Studies
When looking at data from these studies…
o Methodology?
o Claims? What are the validity of those claims?
Randomized control trials
o Sample randomly assigned to groups w/ both groups being as alike as possible
Control and treatment groups
Measure difference/ change between treatment and control groups
o Goal: observe as close to the counterfactual as possible
o Looking at Sample Average Treatment Effect
o Can be statistically confident with a large enough sample
o Problems
Can be difficult to be neutral
i.e. thinking a mailer to get people to vote accidently favors one
candidate
Internal validity
o How good is the study?
o Does it satisfy causal assumptions?
o Can we say X caused Y for this study?
External validity
o How useful is this study?
o Does it apply to other samples?
o How confident can we be that X causes Y in general?
Observational studies
o Gather facts and data
o Can’t control treatment
Risk of missing confounding factors
o Statistical controls
Measure confounding effects to try and determine correlation
Include control variables in statistical analysis
Measure association w/ treatment and outcome
Thinking through alternative explanations
Natural experiments
o Don’t have control over the treatment, but can assume the assignment is random
o If the assignment is truly random, we can infer the causality holds
o Still have to account for confounders
Internal validity > observational, < RCT
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