the extend to which two features of the world occur together
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positive correlation
two features of the world occur together
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negative correlation
two features of the world move in opposite directions
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covariance
measures the direction of the correlation
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correlation coefficient
strength of a linear relationship between two variables
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regression coefficient
how much Y changes on average when x changes by one unit
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description
no assumptions, tells correlations
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prediction
data must be representative, no causal story
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unbiasedness
would prediction be right on average if we made 1000 predictions
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causal inference
how does changing a feature of the world change some other feature, need random assignment, research and design
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counterfactual dependence
X causes Y if and only if Y occurs when X occurs and Y would not have occurred if X did not occur
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causal effect
if Y1 - Y0 does not equal 0, X has a _________ on Y
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the fundamental problem of causal inference
we never observe Y1 - Y0 for a person about only one is observable
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causation
correlation does not imply causation
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bias
causal inference problem
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noise
statistical inference problem
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confounding
something that influences both groups, common cause, reverse causation
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estimate
what we see in data, correlation
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estimand
what we are interesting in seeing, causal effect
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estimator
the procedure we use to generate our estimate
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unbiasedness
estimator is unbiased if by repeated our estimation procedure over and over again an infinite number of times the average value of estimates would equal estimated
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bias
E\[Y0|T = 1\] - E\[YO|T = 0\]
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apples to apples
YO and Y1 needs to be good substitutions and we need no difference on average between treatment and control groups
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selection
people choose to be in studies they care about
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common cause
behaviors are linked, natural causes, noise
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common shocks
behaviors across units are linked
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non-random treatment
treatments are linked to characteristics that also affect outcomes
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reverse causation
occurs when you believe that X causes Y, but in reality Y actually causes X