[Tex/LaTex] beamer block inside an itemize environment with overlays

beameritemizeoverlaysrendering

I have a frame like this, there is a block inside the itemize environment, and there is an overlay :

\begin{frame}   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \frametitle{Comparing two Gaussian means: equality}

\begin{itemize}

\item<1-> Assume for instance that each measurement is $\approx 1000$ 

\item<1-> Would you mind if $\mu_1=1000$ and $\mu_2=1000.1$ ?

\item<1->[] 
\begin{alertblock}{Significant difference does not mean important difference}
  "The mean of the Gaussian distribution is well estimated whenever $n \geq 30$ 
  "Significant difference" is a shortcut for \emph{significantly different from $0$}. 
  The presence of a significant difference shows that there is a strong evidence that 
  $\boxed{\mu_1 \neq \mu_2}$ 
\end{alertblock}

\vspace{-13pt}
\item<1->[] 
\begin{columns}[T]
\column{.5\linewidth}
\begin{itemize}
\item<1-> Whether $\mu_1=\mu_2$ or  $\mu_1 \neq \mu_2$  is \emph{not} the question of interest
\item<2-> xx
\end{itemize}
\column{.5\linewidth}
\only<2->{\begin{figure}
...
\end{figure}
}
\end{columns}
\end{itemize}

\end{frame}

You can see the rendering here. The problem is that the two slides are not well superposed, and I have done many unsuccessful attempts to solve that.

enter image description here

Best Answer

That's exactly the purpose of the overlay area environment; in my example I used a dummy-image at the bottom:

\documentclass{beamer}
\usetheme{Boadilla}
\begin{document}

\begin{frame}   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frametitle{Comparing two Gaussian means: equality}

\begin{overlayarea}{\textwidth}{\textheight}
\begin{itemize}
\item<1-> Assume for instance that each measurement is $\approx 1000$ 
\item<1-> Would you mind if $\mu_1=1000$ and $\mu_2=1000.1$ ?
\item<1->[] 
\begin{alertblock}{Significant difference does not mean important difference}
  "The mean of the Gaussian distribution is well estimated whenever $n \geq 30$ 
  "Significant difference" is a shortcut for \emph{significantly different from $0$}. 
  The presence of a significant difference shows that there is a strong evidence that 
  $\boxed{\mu_1 \neq \mu_2}$ 
\end{alertblock}
\vspace{-13pt}
\item<1->[] 
\begin{columns}[T]
\column{.5\linewidth}
\begin{itemize}
\item<1-> Whether $\mu_1=\mu_2$ or  $\mu_1 \neq \mu_2$  is \emph{not} the question of interest
\item<2-> xx
\end{itemize}
\column{.5\linewidth}
\only<2->{\begin{figure}
\includegraphics[height=2cm]{example-image-a}
\end{figure}
}
\end{columns}
\end{itemize}
\end{overlayarea}
\end{frame}

\end{document}

enter image description here

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