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new \entermde function for adding terms to both indices

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This commit is contained in:
Jan Benda
2019-12-06 08:45:10 +01:00
parent 16df08f9b2
commit 2a2e02b37e
6 changed files with 51 additions and 32 deletions
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5
bootstrap/lecture/bootstrap-chapter.tex
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@@ -18,8 +18,9 @@
\section{TODO}
\begin{itemize}
\item Proper introduction of confidence intervals
\item Proper introduction of statistical tests (significance, power, etc.)
\item This chapter easily covers two lectures:
\item 1. Bootstrapping with a proper introduction of of confidence intervals
\item 2. Permutation test with a proper introduction of statistical tests (dsitrubution of nullhypothesis significance, power, etc.)
\end{itemize}
\end{document}

37
bootstrap/lecture/bootstrap.tex
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@@ -33,7 +33,7 @@ population. Rather, we draw samples (\enterm{simple random sample}
then estimate a statistical measure of interest (e.g. the average
length of the pickles) within this sample and hope that it is a good
approximation of the unknown and immeasurable true average length of
the population (\endeterm{Populationsparameter}{population
the population (\entermde{Populationsparameter}{population
parameter}). We apply statistical methods to find out how precise
this approximation is.
@@ -71,17 +71,18 @@ distribution of average values around the true mean of the population
(\subfigref{bootstrapsamplingdistributionfig}{b}).
Alternatively, we can use \enterm{bootstrapping}
(\determ{Bootstrap-Verfahren}) to generate new samples from one set of
measurements (\endeterm{Resampling}{resampling}). From these
bootstrapped samples we compute the desired statistical measure and
estimate their distribution (\endeterm{Bootstrapverteilung}{bootstrap
distribution}, \subfigref{bootstrapsamplingdistributionfig}{c}).
Interestingly, this distribution is very similar to the sampling
distribution regarding its width. The only difference is that the
bootstrapped values are distributed around the measure of the original
sample and not the one of the statistical population. We can use the
bootstrap distribution to draw conclusion regarding the precision of
our estimation (e.g. standard errors and confidence intervals).
(\determ[Bootstrap!Verfahren]{Bootstrapverfahren}) to generate new
samples from one set of measurements
(\entermde{Resampling}{resampling}). From these bootstrapped samples
we compute the desired statistical measure and estimate their
distribution (\entermde{Bootstrap!Verteilung}{bootstrap distribution},
\subfigref{bootstrapsamplingdistributionfig}{c}). Interestingly, this
distribution is very similar to the sampling distribution regarding
its width. The only difference is that the bootstrapped values are
distributed around the measure of the original sample and not the one
of the statistical population. We can use the bootstrap distribution
to draw conclusion regarding the precision of our estimation (e.g.
standard errors and confidence intervals).
Bootstrapping methods create bootstrapped samples from a SRS by
resampling. The bootstrapped samples are used to estimate the sampling
@@ -140,8 +141,8 @@ distribution is the standard error of the mean.
\section{Permutation tests}
Statistical tests ask for the probability of a measured value to
originate from a null hypothesis. Is this probability smaller than the
desired \endeterm{Signifikanz}{significance level}, the
\endeterm{Nullhypothese}{null hypothesis} may be rejected.
desired \entermde{Signifikanz}{significance level}, the
\entermde{Nullhypothese}{null hypothesis} may be rejected.
Traditionally, such probabilities are taken from theoretical
distributions which are based on assumptions about the data. Thus the
@@ -166,15 +167,15 @@ while we conserve all other statistical properties of the data.
\end{figure}
A good example for the application of a
\endeterm{Permutationstest}{permutaion test} is the statistical
assessment of \endeterm[correlation]{Korrelation}{correlations}. Given
\entermde{Permutationstest}{permutaion test} is the statistical
assessment of \entermde[correlation]{Korrelation}{correlations}. Given
are measured pairs of data points $(x_i, y_i)$. By calculating the
\endeterm[correlation!correlation
\entermde[correlation!correlation
coefficient]{Korrelation!Korrelationskoeffizient}{correlation
coefficient} we can quantify how strongly $y$ depends on $x$. The
correlation coefficient alone, however, does not tell whether the
correlation is significantly different from a random correlation. The
\endeterm[]{Nullhypothese}{null hypothesis} for such a situation is that
\entermde{Nullhypothese}{null hypothesis} for such a situation is that
$y$ does not depend on $x$. In order to perform a permutation test, we
need to destroy the correlation by permuting the $(x_i, y_i)$ pairs,
i.e. we rearrange the $x_i$ and $y_i$ values in a random