\documentclass[11pt]{article}
\setlength{\oddsidemargin}{0.0truein}
\setlength{\evensidemargin}{0.0truein}
\setlength{\textwidth}{6.5truein}
\setlength{\topmargin}{0.0truein}
\setlength{\textheight}{9.0truein} \setlength{\headsep}{0.0truein}
\setlength{\headheight}{0.0truein} \setlength{\topskip}{10.0pt}
\setlength{\parskip}{5mm}
\usepackage{url}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}

\begin{center}
  \textbf{\textsc{STANFORD UNIVERSITY}}\\[5pt]
  \textbf{\textsc{DEPARTMENT OF STATISTICS}}\\[5pt]
  \Large{\textbf\textsc{{DEPARTMENTAL SEMINAR}}}
\end{center}
\begin{center}
  4:15 p.m., Tuesday, August 15, 2006\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
\end{center}


\begin{center}
  \textsl{Daniele De Martini} \\
Dipartimento di Scienze Economiche e Metodi Quantitativi (SEMEQ)\\
Universit\`a del Piemonte Orientale\\
\end{center}
\begin{center}
  \textbf{On the Stability of Statistical Tests}
\end{center}


\noindent The application of statistical tests in various research
fields often generates problems, because the results obtained through
statistical hypothesis testing have been, and are, often confuted in
further studies, for example in the biomedical field.  Here, stemming
from the variability of statistical tests, we first introduce the
estimator of the reproducibility probability of the statistical
significance, i.e. the estimator of the power of the test. Then we
define rejection regions on the basis of the estimator of the
power. In many standard examples, the threshold for the power
estimator to define statistical tests turns out to be $1/2$, at least
approximately, in parametric as well as in nonparametric
frameworks. Moreover, we introduce the notion of stability, which is
based on the lower bound of the power.  Some numerical examples are
shown, and a brief discussion is given.

\end{document}