46 lines
1.8 KiB
TeX
46 lines
1.8 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
|
|
|
|
\newcommand{\ptitle}{Power analysis}
|
|
\input{../header.tex}
|
|
\firstpagefooter{Supervisor: Peter Pilz}{phone: 29 74835}%
|
|
{email: peter.pilz@uni-tuebingen.de}
|
|
|
|
\begin{document}
|
|
\input{../instructions.tex}
|
|
|
|
In a scientific study three different substances are tested on three groups of
|
|
subjects, a forth group is not treated and serves as a control
|
|
group.
|
|
|
|
Simulate test results for the different groups using normally
|
|
distributed random numbers. The standard deviation is the same in all
|
|
groups. The effect size $d=\frac{\mu_1 - \mu_2}{\sigma}$ relative to
|
|
the control group is $0.0, 0.5,$ and $1.0$ for the three experimental
|
|
groups.
|
|
|
|
\begin{questions}
|
|
\question{} How large is the \emph{power} of the study if each group
|
|
consists of 10 subjects?
|
|
\begin{parts}
|
|
\part{} Execute a large number of experiments (10.000) and estimate how often statistically significant results are yielded with a t-test against control and with alpha=0.05. Give \emph{type II} error and power (1 - \emph{type II} error).
|
|
\end{parts}
|
|
\question{} What is the effect of different goup sizes?
|
|
\begin{parts}
|
|
\part{} Consider the following group sizes ($control:group1:group2:group3$):
|
|
\begin{itemize}
|
|
\item $4:12:12:12$
|
|
\item $7:11:11:11$
|
|
\item $13:9:9:9$
|
|
\item $16:8:8:8$
|
|
\item $19:7:7:7$
|
|
\item $22:6:6:6$
|
|
\item $25:5:5:5$
|
|
\item $28:4:4:4$
|
|
\end{itemize}
|
|
\part{} Plot the \emph{power} as a function of the size of the control group for $d={0.5, 1.0}$. Give the group size relative to the size of the experimental groups.
|
|
\part{} Plot the false positive results for d = 0.0 in relation to relative control group size.
|
|
\end{parts}
|
|
\question{} Can you recommend a group size for the control group?
|
|
\end{questions}
|
|
\end{document}
|