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So clearly in our example,
whether or not you're in a hospital
correlated with whether or not you died,
but the truth is, the example omitted
and important variable,
the sickness, the disease itself.
And in fact, the sickness did cause you to die,
and also effected your decision of whether you go to a hospital or not.
So if you draw acts of causation,
you find sickness causes death,
and sickness causes you to go to the hospital,
and if anything at all,
once you knew you were sick,
being in the hospital negatively correlated
with you dying;
that is, being in a hospital made it less likely
for you to pass away
given that you were sick.
In statistics, we call this a confounding variable.
It's very tempting to just omit this from your data,
and if you do, you might find correlations;
in this case, a positive correlation between the hospital and death,
that have nothing to do with the way things are being caused,
and as a result, those correlations don't relate at all
to what you should do.
So let's study another example.