Exam 1

binary

variables take on only two distinct values

discrete

finite number of values

continuous

infinite number of values

correlation

the extend to which two features of the world occur together

positive correlation

two features of the world occur together

negative correlation

two features of the world move in opposite directions

covariance

measures the direction of the correlation

correlation coefficient

strength of a linear relationship between two variables

regression coefficient

how much Y changes on average when x changes by one unit

description

no assumptions, tells correlations

prediction

data must be representative, no causal story

unbiasedness

would prediction be right on average if we made 1000 predictions

causal inference

how does changing a feature of the world change some other feature, need random assignment, research and design

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

causal effect

if Y1 - Y0 does not equal 0, X has a _________ on Y

the fundamental problem of causal inference

we never observe Y1 - Y0 for a person about only one is observable

causation

correlation does not imply causation

bias

causal inference problem

noise

statistical inference problem

confounding

something that influences both groups, common cause, reverse causation

estimate

what we see in data, correlation

estimand

what we are interesting in seeing, causal effect

estimator

the procedure we use to generate our estimate

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

bias

E\[Y0|T = 1\] - E\[YO|T = 0\]

apples to apples

YO and Y1 needs to be good substitutions and we need no difference on average between treatment and control groups

selection

people choose to be in studies they care about

common cause

behaviors are linked, natural causes, noise

common shocks

behaviors across units are linked

non-random treatment

treatments are linked to characteristics that also affect outcomes

reverse causation

occurs when you believe that X causes Y, but in reality Y actually causes X

E\[Y1 - Y0\]

average treatment effect for population