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[project power analysis] update assignment

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Jan Grewe 2019-01-14 12:11:44 +01:00
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projects/project_power_analysis/power_analysis.tex
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@ -8,7 +8,7 @@
\begin{document}
\input{../instructions.tex}
In a scientific study 3 different substances are tested on 3 groups of
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.
@ -22,7 +22,7 @@ groups.
\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. Give both \emph{type I} and \emph{type II} errors.
\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}
@ -37,8 +37,8 @@ groups.
\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 groups size relative to the size of the experimental groups.
\part{} How large are the false positive results for $d=0.0$.
\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}