46 lines
1.7 KiB
TeX
46 lines
1.7 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
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\newcommand{\ptitle}{EOD waveform}
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\input{../header.tex}
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\firstpagefooter{Supervisor: Peter Pilz}{phone: 29 74835}%
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{email: peter.pilz@uni-tuebingen.de}
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\begin{document}
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\input{../instructions.tex}
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In a scientific study 3 different substances are tested on 3 groups of
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subjects, a forth group is not treated and serves as a control
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group.
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Simulate test results for the different groups using normally
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distributed random numbers. The standard deviation is the same in all
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groups. The effect size $d=\frac{\mu_1 - \mu_2}{\sigma}$ relative to
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the control group is $0.0, 0.5,$ and $1.0$ for the three experimental
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groups.
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\begin{questions}
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\question{} How large is the \emph{power} of the study if each group
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consists of 10 subjects?
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\begin{parts}
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\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.
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\end{parts}
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\question{} What is the effect of different goup sizes?
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\begin{parts}
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\part{} Consider the following group sizes ($control:group1:group2:group3$):
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\begin{itemize}
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\item $4:12:12:12$
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\item $7:11:11:11$
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\item $13:9:9:9$
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\item $16:8:8:8$
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\item $19:7:7:7$
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\item $22:6:6:6$
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\item $25:5:5:5$
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\item $28:4:4:4$
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\end{itemize}
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\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.
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\part{} How large are the false positive results for $d=0.0$.
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\end{parts}
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\question{} Can you recommend a group size for the control group?
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\end{questions}
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\end{document}
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