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\footnotesize
\noindent Statistica Sinica {\bf 13}(2003), 163-177
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\centerline{\large\bf THE GEOMETRY OF TWO-STAGE TESTS}
\vspace{.25cm}
\centerline{Michael A. Proschan}
\vspace{.4cm}
\centerline{\it National Heart, Lung and Blood Institute, NIH}
%II Rockledge Center}
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\begin{quotation}
\noindent {\it Abstract:}
Sample size calculations require specification of the treatment effect, but what
if this is not known? Two-stage tests use the first stage to estimate the
treatment effect and modify the sample size accordingly. The purpose of this
paper is to unify the theory of two-stage testing based on treatment
effect. The conditional error function approach of Proschan and Hunsberger
(1995) is shown to be
a useful way to evaluate the properties of any two-stage test. The connection
between two-stage tests and positive quadrant tests is exploited to motivate
certain conditional error functions. \par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Double sampling, type I error rate, p-value, positive quadrant tests.
\end{quotation}\par
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