in your standard statistics class you're gonna talk about
a lot of topics that fall under this idea of statistical inference.
This is stuff like sampling, hypothesis test, competence intervals,
p values, standard errors, t test, statistical significance, the
normal distribution, priors and posterior etc.
In these modules, we're basically gonna completely ignore all of
this stuff.
The reason we have to worry about this is that what we wanna do
is compute some number in the population like the average treatment
effect for every single person but in practice, we don't
observe every single person so we just can't compute that number.
So what we're gonna do instead is compute it for the people we do
observe and then hope that we're not too far off from the true number
that's out there if we observed everybody else.
So what's statistical inference is about, is about computing statistics,
using the data we have to learn about the data that we don't
have but we physically could have gotten.
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So we wanna know about the average treatment effect, that's the
average for everybody.
We may not observe everybody, so we're gonna compute the average
for just the people we do observe and hope that it's close to the
true average for everybody.
But we could have feasibly gone out and gathered more data.
That's what statistics is about
and all of these topics are about quantifying how close we are to
the truth, if we were to get more data.
So in principle if we had a very, very large amount of data, none
of this is important, you just throw it all away.
Now Causal Inference, the topic of these
modules is about something a little different.
It's about how can we use the data we have to learn about something
which is literally impossible to get data on, that is counterfactual.
Once somebody is treated we see that they're treated, we see what
their outcome is we will never,
ever ever see what their outcome is when they're not treated.
That's data that's impossible to get.
So in causal inference no matter how much data you have there's
always potentially gonna be a problem about learning what we wanna
learn.
That's again the fundamental problem of causal inference.
So that's the main difference between causal inference and statistical
inference.
Statistical inference problems are gonna go away as you get more
and more data.
Causal inference problems not necessarily.
Now causal inference is often called identification analysis because
the goal of it is to say when we have some
data, what can we learn from the data what can we identify
from the data? So the average treatment effect is it's just a number
out there, well with a particular data set our prediction of way
of gathering data will we be able to learn that the average treatment
effect?
Can we identify it?
That's what causal analysis won't answer.
So the techniques we'll study later on are often called identification
strategies because they are going to be ways for showing that you
can actually learn numbers like this like the average treatment
effect from real data.
So in practice however we're usually going to have not an enormous
amount of data.
So usually we will have to worry about stuff like this statistical
inference.
So we're usually going to use first two causal analysis to see whether
we can actually identify something like the average treatment effect
from the data can we actually learn it?
data good enough for that?
Second we're not gonna have a huge amount of data so we're gonna
have to do some statistical inference to estimate the average treatment
effect.
And then finally we're gonna say well we don't have all the data
we could have possibility gotten so our estimate is not going to be
the true average treatment.
It's gonna be a little off.
So how do we quantify the uncertainty and how far away we are?
So those are gonna be the tools that statistical inference uses.
But in these modules were gonna focus on the very first step.
If you had a lot of data would you even be able to learn something
like the average treatment effect?
That's the goal of causal inference.
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