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remove broken equation tag
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malisi committed Apr 5, 2023
1 parent bf2301a commit cfa5117
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9 changes: 4 additions & 5 deletions hypothesistesting/hypothesistesting.Rmd
Original file line number Diff line number Diff line change
Expand Up @@ -234,10 +234,10 @@ can link the unobserved counterfactual outcomes to an observed outcome ($Y_i$)
using treatment assignment ($Z_i$) like so:

\begin{equation}
Y_i = Z_i y_{i,1} + (1 - Z_i) y_{i,0} (\#eq:identity)
Y_i = Z_i y_{i,1} + (1 - Z_i) y_{i,0}
\end{equation}

\@ref(eq:identity) says that our observed outcome, $Y_i$ (here, amount of
The above equation says that our observed outcome, $Y_i$ (here, amount of
taxes paid by person $i$), is $y_{i,1}$ when the person is assigned to the
treatment group ($Z_i=1$), and $y_{i,0}$ when the person is assigned to the
control group.
Expand All @@ -248,9 +248,8 @@ payments of every single person such that $H_0: y_{i,1} = y_{i,0} + \tau_i$ whe
$\tau_i=5$ for all $i$.

Let us entertain this model for the sake of argument. What would this
hypothesis imply for what we observe? We have the equation relating observed
to unobserved in \@ref(eq:identity) so, this model or hypothesis would
imply that:
hypothesis imply for what we observe? The above equation relates observed
to unobserved so, this model or hypothesis would imply that:

$$ \begin{aligned} Y_i & = Z_i ( y_{i,0} + \tau_i ) + ( 1 - Z_i) y_{i,0} \\
& = Z_i y_{i,0} + Z_i \tau_i + y_{i,0} - Z_i y_{i,0} \\
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662 changes: 332 additions & 330 deletions hypothesistesting/hypothesistesting.html

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