Merge branch 'master' of raven.am28.uni-tuebingen.de:scientificComputing
This commit is contained in:
commit
7bab4e9baa
16
statistics/assignments/Makefile
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16
statistics/assignments/Makefile
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all:
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|
for number in 001 002 003 004 005 006 007 007 009 010 011 012 013 014 015 016 017 ; do \
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|
echo $$number ; \
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|
sed "s/000/$$number/g" day1.tex > tmp.tex; \
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|
pdflatex tmp.tex; \
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|
mv tmp.pdf day1_$$number.pdf; \
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||||||
|
cp ../data/example$$number.csv ./ ;\
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|
rm tmp.* ; \
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||||||
|
zip example$$number.zip example$$number.csv day1_$$number.pdf ; \
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|
rm example$$number.csv ;\
|
||||||
|
rm day1_$$number.pdf ; \
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||||||
|
done
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||||||
|
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||||||
|
clean:
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||||||
|
rm *.zip
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||||||
|
rm -rf auto
|
||||||
72
statistics/assignments/day1.tex
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72
statistics/assignments/day1.tex
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|
\documentclass[addpoints,10pt]{exam}
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|
\usepackage{url}
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|
\usepackage{color}
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|
\usepackage{hyperref}
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|
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|
\pagestyle{headandfoot}
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|
\runningheadrule
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|
\firstpageheadrule
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|
\firstpageheader{Scientific Computing}{afternoon assignment day 01}{10/20/2014}
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|
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
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|
\firstpagefooter{}{}{}
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|
\runningfooter{}{}{}
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|
\pointsinmargin
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|
\bracketedpoints
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|
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|
%\printanswers
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|
\shadedsolutions
|
||||||
|
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
\sffamily
|
||||||
|
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
|
||||||
|
\begin{questions}
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|
\question To publish scientific results, you will usually need to
|
||||||
|
use statistical methods. Some journals provide you with a brief
|
||||||
|
description of how they expect you to apply statistical methods. One
|
||||||
|
example can be found in the author guidelines of the journal
|
||||||
|
Nature.
|
||||||
|
|
||||||
|
Assume you collected the following dataset. You can download it from
|
||||||
|
Ilias as {\tt example000.csv}. Here is the description of the dataset:
|
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|
|
||||||
|
\begin{quotation}
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|
\tt
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|
\input{../examples/example000.tex}
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|
\end{quotation}
|
||||||
|
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||||||
|
\begin{parts}
|
||||||
|
\part Download the dataset and write a script that loads it into
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||||||
|
matlab.
|
||||||
|
|
||||||
|
\part Think about the type of your data (I might ask you that
|
||||||
|
tomorrow).
|
||||||
|
|
||||||
|
\part Produce a plot that displays the data in an appropriate
|
||||||
|
way. Make sure to respect all elements of good plotting we
|
||||||
|
discussed today.
|
||||||
|
|
||||||
|
\part Download the statistical checklist from nature. Produce {\bf
|
||||||
|
one} slide that contains the plot and a concise summary of your
|
||||||
|
data which respects the requirements made by nature (assume you
|
||||||
|
are producing a figure legend for the figure in nature). It is
|
||||||
|
good style to avoid expressions like ``the plot shows'' or
|
||||||
|
similar.
|
||||||
|
|
||||||
|
\part Upload your code, the data, and the slide as a zip to
|
||||||
|
Ilias. Deadline is 19h00. Structure the zip such that you can
|
||||||
|
present you program in front of the class. Several students will
|
||||||
|
be asked to present their slide and their code tomorrow morning.
|
||||||
|
|
||||||
|
\end{parts}
|
||||||
|
|
||||||
|
\end{questions}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\end{document}
|
||||||
46
statistics/assignments/day2.tex
Normal file
46
statistics/assignments/day2.tex
Normal file
@ -0,0 +1,46 @@
|
|||||||
|
\documentclass[addpoints,10pt]{exam}
|
||||||
|
\usepackage{url}
|
||||||
|
\usepackage{color}
|
||||||
|
\usepackage{hyperref}
|
||||||
|
|
||||||
|
\pagestyle{headandfoot}
|
||||||
|
\runningheadrule
|
||||||
|
\firstpageheadrule
|
||||||
|
|
||||||
|
\firstpageheader{Scientific Computing}{afternoon assignment day 02}{10/21/2014}
|
||||||
|
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
|
||||||
|
\firstpagefooter{}{}{}
|
||||||
|
\runningfooter{}{}{}
|
||||||
|
\pointsinmargin
|
||||||
|
\bracketedpoints
|
||||||
|
|
||||||
|
%\printanswers
|
||||||
|
\shadedsolutions
|
||||||
|
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
\sffamily
|
||||||
|
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
|
||||||
|
\begin{questions}
|
||||||
|
\question Download example002 from yesterday (brain weights).
|
||||||
|
\begin{parts}
|
||||||
|
\part Simulate a null distribution via permutation.
|
||||||
|
\part Determine whether you can reject ``means are equal'' on a
|
||||||
|
5\% significance level using the simulated null distribution.
|
||||||
|
\part Check whether the means are different with a two sample
|
||||||
|
t-test in matlab ({\tt ttest2}).
|
||||||
|
\part Plot the data appropriately and generate a single slide that
|
||||||
|
contains the plot and short discussion of the test that respects
|
||||||
|
the nature statistical checklist (ignore all question whether the
|
||||||
|
assumptions of the test are satisfied).
|
||||||
|
\part Upload the slide and the code to Ilias. Deadline is 19h00.
|
||||||
|
\end{parts}
|
||||||
|
\end{questions}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\end{document}
|
||||||
43
statistics/data/example001.csv
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43
statistics/data/example001.csv
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|
MAO,Diagnosis
|
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|
6.8,I
|
||||||
|
4.1,I
|
||||||
|
7.3,I
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||||||
|
14.2,I
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||||||
|
18.8,I
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||||||
|
9.9,I
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||||||
|
7.4,I
|
||||||
|
11.9,I
|
||||||
|
5.2,I
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||||||
|
7.8,I
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||||||
|
7.8,I
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||||||
|
8.7,I
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||||||
|
12.7,I
|
||||||
|
14.5,I
|
||||||
|
10.7,I
|
||||||
|
8.4,I
|
||||||
|
9.7,I
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||||||
|
10.6,I
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||||||
|
7.8,II
|
||||||
|
4.4,II
|
||||||
|
11.4,II
|
||||||
|
3.1,II
|
||||||
|
4.3,II
|
||||||
|
10.1,II
|
||||||
|
1.5,II
|
||||||
|
7.4,II
|
||||||
|
5.2,II
|
||||||
|
10,II
|
||||||
|
3.7,II
|
||||||
|
5.5,II
|
||||||
|
8.5,II
|
||||||
|
7.7,II
|
||||||
|
6.8,II
|
||||||
|
3.1,II
|
||||||
|
6.4,III
|
||||||
|
10.8,III
|
||||||
|
1.1,III
|
||||||
|
2.9,III
|
||||||
|
4.5,III
|
||||||
|
5.8,III
|
||||||
|
9.4,III
|
||||||
|
6.8,III
|
||||||
|
186
statistics/data/example002.csv
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186
statistics/data/example002.csv
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|
Weight,Sex
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1607,m
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1157,m
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1248,m
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1310,m
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1398,m
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1237,m
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1232,m
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1343,m
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1380,m
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1274,m
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1245,m
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1286,m
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1508,m
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1105,m
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1123,m
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1198,m
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1300,m
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1249,m
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1185,m
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915,m
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1345,m
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1107,m
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1357,m
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1227,m
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1205,m
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1435,m
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1289,m
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1093,m
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1211,m
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1260,m
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1193,m
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1330,m
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1130,m
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1357,m
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1193,m
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1232,m
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1321,m
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1260,m
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1380,m
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1230,m
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1136,m
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1029,m
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1223,m
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1240,m
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1264,m
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1020,m
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1415,m
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1410,m
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1275,m
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1230,m
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1085,m
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1048,m
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1181,m
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1103,m
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1165,m
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1547,m
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1173,m
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1660,m
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1307,m
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1535,m
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1315,m
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1257,m
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1424,m
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1309,m
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1170,m
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1412,m
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1270,m
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1230,m
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1233,m
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1561,m
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1193,m
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1272,m
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1355,m
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1137,m
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1354,m
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1110,m
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1265,m
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1407,m
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1227,m
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1330,m
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1222,m
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1305,m
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1475,m
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1177,m
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1337,m
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1145,m
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1070,m
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1305,m
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1085,m
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1303,m
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1532,m
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1238,m
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1233,m
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1280,m
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1245,m
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1459,m
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1157,m
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1302,m
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1385,m
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1342,m
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1303,m
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1115,m
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1365,m
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1227,m
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1353,m
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1125,f
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1027,f
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1112,f
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983,f
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1090,f
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1247,f
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1045,f
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983,f
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972,f
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1045,f
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937,f
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1245,f
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1200,f
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1270,f
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1200,f
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1145,f
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1090,f
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1343,f
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1010,f
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1038,f
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1000,f
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1085,f
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1006,f
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958,f
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1068,f
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1107,f
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1317,f
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952,f
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1056,f
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1203,f
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1183,f
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1392,f
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1130,f
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1284,f
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996,f
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1228,f
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1087,f
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1035,f
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1170,f
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1064,f
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1250,f
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1129,f
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1088,f
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1037,f
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1117,f
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1095,f
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1027,f
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1027,f
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1190,f
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1037,f
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1120,f
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1024,f
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1135,f
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1177,f
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1096,f
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1114,f
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52
statistics/data/example003.csv
Executable file
52
statistics/data/example003.csv
Executable file
@ -0,0 +1,52 @@
|
|||||||
|
singtime
|
||||||
|
4.3
|
||||||
|
24.1
|
||||||
|
6.6
|
||||||
|
7.3
|
||||||
|
4
|
||||||
|
2.6
|
||||||
|
4
|
||||||
|
3.9
|
||||||
|
9.4
|
||||||
|
6.2
|
||||||
|
1.6
|
||||||
|
6.5
|
||||||
|
0.2
|
||||||
|
2.7
|
||||||
|
17.4
|
||||||
|
5.6
|
||||||
|
2
|
||||||
|
3.8
|
||||||
|
1.2
|
||||||
|
0.7
|
||||||
|
1.6
|
||||||
|
2.3
|
||||||
|
3.7
|
||||||
|
0.8
|
||||||
|
0.5
|
||||||
|
4.5
|
||||||
|
11.5
|
||||||
|
3.5
|
||||||
|
0.8
|
||||||
|
5.2
|
||||||
|
2
|
||||||
|
0.7
|
||||||
|
1.7
|
||||||
|
5
|
||||||
|
2.8
|
||||||
|
1.5
|
||||||
|
3.9
|
||||||
|
3.7
|
||||||
|
4.5
|
||||||
|
1.8
|
||||||
|
1.2
|
||||||
|
0.7
|
||||||
|
0.7
|
||||||
|
4.2
|
||||||
|
4.7
|
||||||
|
2.2
|
||||||
|
1.4
|
||||||
|
14.1
|
||||||
|
8.6
|
||||||
|
3.7
|
||||||
|
3.5
|
||||||
|
29
statistics/data/example004.csv
Executable file
29
statistics/data/example004.csv
Executable file
@ -0,0 +1,29 @@
|
|||||||
|
Pulse
|
||||||
|
97
|
||||||
|
111
|
||||||
|
93
|
||||||
|
98
|
||||||
|
107
|
||||||
|
77
|
||||||
|
121
|
||||||
|
88
|
||||||
|
96
|
||||||
|
123
|
||||||
|
119
|
||||||
|
91
|
||||||
|
99
|
||||||
|
95
|
||||||
|
99
|
||||||
|
102
|
||||||
|
77
|
||||||
|
85
|
||||||
|
104
|
||||||
|
106
|
||||||
|
114
|
||||||
|
85
|
||||||
|
112
|
||||||
|
102
|
||||||
|
104
|
||||||
|
94
|
||||||
|
104
|
||||||
|
98
|
||||||
|
37
statistics/data/example005.csv
Executable file
37
statistics/data/example005.csv
Executable file
@ -0,0 +1,37 @@
|
|||||||
|
Branches
|
||||||
|
23
|
||||||
|
30
|
||||||
|
54
|
||||||
|
28
|
||||||
|
31
|
||||||
|
29
|
||||||
|
34
|
||||||
|
35
|
||||||
|
30
|
||||||
|
27
|
||||||
|
21
|
||||||
|
43
|
||||||
|
51
|
||||||
|
35
|
||||||
|
51
|
||||||
|
49
|
||||||
|
35
|
||||||
|
24
|
||||||
|
26
|
||||||
|
29
|
||||||
|
21
|
||||||
|
29
|
||||||
|
37
|
||||||
|
27
|
||||||
|
28
|
||||||
|
33
|
||||||
|
33
|
||||||
|
23
|
||||||
|
37
|
||||||
|
27
|
||||||
|
40
|
||||||
|
48
|
||||||
|
41
|
||||||
|
20
|
||||||
|
30
|
||||||
|
57
|
||||||
|
32
statistics/data/example006.csv
Executable file
32
statistics/data/example006.csv
Executable file
@ -0,0 +1,32 @@
|
|||||||
|
Glucose
|
||||||
|
81
|
||||||
|
85
|
||||||
|
93
|
||||||
|
93
|
||||||
|
99
|
||||||
|
76
|
||||||
|
75
|
||||||
|
84
|
||||||
|
78
|
||||||
|
84
|
||||||
|
81
|
||||||
|
82
|
||||||
|
89
|
||||||
|
81
|
||||||
|
96
|
||||||
|
82
|
||||||
|
74
|
||||||
|
70
|
||||||
|
84
|
||||||
|
86
|
||||||
|
80
|
||||||
|
70
|
||||||
|
131
|
||||||
|
75
|
||||||
|
88
|
||||||
|
102
|
||||||
|
115
|
||||||
|
89
|
||||||
|
82
|
||||||
|
79
|
||||||
|
106
|
||||||
|
24
statistics/data/example007.csv
Executable file
24
statistics/data/example007.csv
Executable file
@ -0,0 +1,24 @@
|
|||||||
|
NerveCells
|
||||||
|
35
|
||||||
|
19
|
||||||
|
33
|
||||||
|
34
|
||||||
|
17
|
||||||
|
26
|
||||||
|
16
|
||||||
|
40
|
||||||
|
28
|
||||||
|
30
|
||||||
|
23
|
||||||
|
12
|
||||||
|
27
|
||||||
|
33
|
||||||
|
22
|
||||||
|
31
|
||||||
|
28
|
||||||
|
28
|
||||||
|
35
|
||||||
|
23
|
||||||
|
23
|
||||||
|
19
|
||||||
|
29
|
||||||
|
21
statistics/data/example008.csv
Executable file
21
statistics/data/example008.csv
Executable file
@ -0,0 +1,21 @@
|
|||||||
|
RateChange,Treatment
|
||||||
|
28,Caffeine
|
||||||
|
11,Caffeine
|
||||||
|
-3,Caffeine
|
||||||
|
14,Caffeine
|
||||||
|
-2,Caffeine
|
||||||
|
-4,Caffeine
|
||||||
|
18,Caffeine
|
||||||
|
2,Caffeine
|
||||||
|
2,Caffeine
|
||||||
|
26,Decaf
|
||||||
|
1,Decaf
|
||||||
|
0,Decaf
|
||||||
|
-4,Decaf
|
||||||
|
-4,Decaf
|
||||||
|
14,Decaf
|
||||||
|
16,Decaf
|
||||||
|
8,Decaf
|
||||||
|
0,Decaf
|
||||||
|
18,Decaf
|
||||||
|
-10,Decaf
|
||||||
|
12
statistics/data/example009.csv
Executable file
12
statistics/data/example009.csv
Executable file
@ -0,0 +1,12 @@
|
|||||||
|
NEConcentration,Treatment
|
||||||
|
543,Toluene
|
||||||
|
523,Toluene
|
||||||
|
431,Toluene
|
||||||
|
635,Toluene
|
||||||
|
564,Toluene
|
||||||
|
549,Toluene
|
||||||
|
535,Control
|
||||||
|
385,Control
|
||||||
|
502,Control
|
||||||
|
412,Control
|
||||||
|
387,Control
|
||||||
|
13
statistics/data/example010.csv
Executable file
13
statistics/data/example010.csv
Executable file
@ -0,0 +1,13 @@
|
|||||||
|
Dopamine,Group
|
||||||
|
3420,toluene
|
||||||
|
2314,toluene
|
||||||
|
1911,toluene
|
||||||
|
2464,toluene
|
||||||
|
2781,toluene
|
||||||
|
2803,toluene
|
||||||
|
1820,control
|
||||||
|
1843,control
|
||||||
|
1397,control
|
||||||
|
1803,control
|
||||||
|
2539,control
|
||||||
|
1990,control
|
||||||
|
10
statistics/data/example011.csv
Executable file
10
statistics/data/example011.csv
Executable file
@ -0,0 +1,10 @@
|
|||||||
|
Animal,Site I,Site II
|
||||||
|
1,50.6,38
|
||||||
|
2,39.2,18.6
|
||||||
|
3,35.2,23.2
|
||||||
|
4,17,19
|
||||||
|
5,11.2,6.6
|
||||||
|
6,14.2,16.4
|
||||||
|
7,24.2,14.4
|
||||||
|
8,37.4,37.6
|
||||||
|
9,35.2,24.4
|
||||||
|
10
statistics/data/example012.csv
Executable file
10
statistics/data/example012.csv
Executable file
@ -0,0 +1,10 @@
|
|||||||
|
Subject,mCPP,Placebo
|
||||||
|
1,1.1,0
|
||||||
|
2,1.3,-0.3
|
||||||
|
3,1,0.6
|
||||||
|
4,1.7,0.3
|
||||||
|
5,1.4,-0.7
|
||||||
|
6,0.1,-0.2
|
||||||
|
7,0.5,0.6
|
||||||
|
8,1.6,0.9
|
||||||
|
9,-0.5,-2
|
||||||
|
9
statistics/data/example013.csv
Executable file
9
statistics/data/example013.csv
Executable file
@ -0,0 +1,9 @@
|
|||||||
|
Animal,Control,Regenerating
|
||||||
|
1,16.3,11.5
|
||||||
|
2,4.8,3.6
|
||||||
|
3,10.9,12.5
|
||||||
|
4,14.2,6.3
|
||||||
|
5,16.3,15.2
|
||||||
|
6,9.9,8.1
|
||||||
|
7,29.2,16.6
|
||||||
|
8,22.4,13.1
|
||||||
|
16
statistics/data/example014.csv
Executable file
16
statistics/data/example014.csv
Executable file
@ -0,0 +1,16 @@
|
|||||||
|
BodyTempDrop,AlcoholDose
|
||||||
|
0.2,1.5
|
||||||
|
1.9,1.5
|
||||||
|
-0.1,1.5
|
||||||
|
0.5,1.5
|
||||||
|
0.8,1.5
|
||||||
|
4,3
|
||||||
|
3.2,3
|
||||||
|
2.3,3
|
||||||
|
2.9,3
|
||||||
|
3.8,3
|
||||||
|
3.3,6
|
||||||
|
5.1,6
|
||||||
|
5.3,6
|
||||||
|
6.7,6
|
||||||
|
5.9,6
|
||||||
|
18
statistics/data/example015.csv
Executable file
18
statistics/data/example015.csv
Executable file
@ -0,0 +1,18 @@
|
|||||||
|
PeakFlow,Height
|
||||||
|
733,174
|
||||||
|
572,183
|
||||||
|
500,176
|
||||||
|
738,169
|
||||||
|
616,183
|
||||||
|
787,186
|
||||||
|
866,178
|
||||||
|
670,175
|
||||||
|
550,172
|
||||||
|
660,179
|
||||||
|
575,171
|
||||||
|
577,184
|
||||||
|
783,200
|
||||||
|
625,195
|
||||||
|
470,176
|
||||||
|
642,176
|
||||||
|
856,190
|
||||||
|
19
statistics/data/example016.csv
Executable file
19
statistics/data/example016.csv
Executable file
@ -0,0 +1,19 @@
|
|||||||
|
Patient,Before,After
|
||||||
|
1,98,75
|
||||||
|
2,100,60
|
||||||
|
3,82,25
|
||||||
|
4,100,55
|
||||||
|
5,93,78
|
||||||
|
6,119,102
|
||||||
|
7,70,58
|
||||||
|
8,78,70
|
||||||
|
9,104,90
|
||||||
|
10,70,50
|
||||||
|
11,60,65
|
||||||
|
12,88,45
|
||||||
|
13,45,36
|
||||||
|
14,159,144
|
||||||
|
15,65,27
|
||||||
|
16,98,90
|
||||||
|
17,66,16
|
||||||
|
18,67,53
|
||||||
|
21
statistics/data/example017.csv
Executable file
21
statistics/data/example017.csv
Executable file
@ -0,0 +1,21 @@
|
|||||||
|
LegStrength,UpperBodyStrength
|
||||||
|
55,low
|
||||||
|
70,low
|
||||||
|
45,low
|
||||||
|
246,low
|
||||||
|
240,low
|
||||||
|
96,low
|
||||||
|
225,low
|
||||||
|
40,middle
|
||||||
|
200,middle
|
||||||
|
250,middle
|
||||||
|
192,middle
|
||||||
|
117,middle
|
||||||
|
215,middle
|
||||||
|
181,high
|
||||||
|
85,high
|
||||||
|
416,high
|
||||||
|
228,high
|
||||||
|
257,high
|
||||||
|
316,high
|
||||||
|
134,high
|
||||||
|
6
statistics/examples/example001.tex
Normal file
6
statistics/examples/example001.tex
Normal file
@ -0,0 +1,6 @@
|
|||||||
|
MAO and Schizophrenia Monoamine oxidase (MAO) is an enzyme that is
|
||||||
|
thought to play a role in the regulation of behavior. To see whether
|
||||||
|
different categories of schizophrenic patients have different levels
|
||||||
|
of MAO activity, researchers collected blood specimens from 42
|
||||||
|
patients and measured the MAO activity in the platelets. Values are
|
||||||
|
expressed as nmol benzylaldehyde product per 108 platelets per hour.
|
||||||
3
statistics/examples/example002.tex
Normal file
3
statistics/examples/example002.tex
Normal file
@ -0,0 +1,3 @@
|
|||||||
|
Brain Weight: In 1888, P. Topinard published data on the brain weights
|
||||||
|
of hundreds of French men and women. Brain weights are given in
|
||||||
|
gram.
|
||||||
4
statistics/examples/example003.tex
Normal file
4
statistics/examples/example003.tex
Normal file
@ -0,0 +1,4 @@
|
|||||||
|
Cricket Singing Times Male Mormon crickets (Anabrus simplex) sing to attract mates.
|
||||||
|
A field researcher measured the duration of 51 unsuccessful songs--that is, the time
|
||||||
|
until the singing male gave up and left his perch. The data is given
|
||||||
|
in minutes.
|
||||||
3
statistics/examples/example004.tex
Normal file
3
statistics/examples/example004.tex
Normal file
@ -0,0 +1,3 @@
|
|||||||
|
Pulse after Exercise: A group of 28 adults did some moderate exercise
|
||||||
|
for five minutes and then measured their pulses. Data is given in
|
||||||
|
beats/minute.
|
||||||
5
statistics/examples/example005.tex
Normal file
5
statistics/examples/example005.tex
Normal file
@ -0,0 +1,5 @@
|
|||||||
|
A dendritic tree is a branched structure that emanates from the body
|
||||||
|
of a nerve cell. As part of a study of brain development, 36 nerve
|
||||||
|
cells were taken from the brains of newborn guinea pigs. The
|
||||||
|
investigators counted the number of dendritic branch segments
|
||||||
|
emanating from each nerve cell.
|
||||||
4
statistics/examples/example006.tex
Normal file
4
statistics/examples/example006.tex
Normal file
@ -0,0 +1,4 @@
|
|||||||
|
For each of 31 healthy dogs, a veterinarian measured the glucose
|
||||||
|
concentration in the anterior chamber of the right eye and also in the
|
||||||
|
blood serum. The following data are the anterior chamber glucose
|
||||||
|
measurements, expressed as a percentage of the blood glucose.
|
||||||
5
statistics/examples/example007.tex
Normal file
5
statistics/examples/example007.tex
Normal file
@ -0,0 +1,5 @@
|
|||||||
|
A veterinary anatomist investigated the spatial arrangement of the
|
||||||
|
nerve cells in the intestine of a pony. He removed a block of tissue
|
||||||
|
from the intestinal wall, cut the block into many equal sections, and
|
||||||
|
counted the number of nerve cells in each of 23 randomly selected
|
||||||
|
sections.
|
||||||
8
statistics/examples/example008.tex
Normal file
8
statistics/examples/example008.tex
Normal file
@ -0,0 +1,8 @@
|
|||||||
|
Researchers were interested in the short-term effect that caffeine has
|
||||||
|
on heart rate. They enlisted a group of volunteers and measured each
|
||||||
|
person's resting heart rate. Then they had each subject drink 6 ounces
|
||||||
|
of coffee. Nine of the subjects were given coffee containing caffeine
|
||||||
|
and 11 were given decaffeinated coffee. After 10 minutes each person's
|
||||||
|
heart rate was measured again. The data in the table contains the
|
||||||
|
change in heart rate; a positive number means that heart rate went up
|
||||||
|
and a negative number means that heart rate went down.
|
||||||
9
statistics/examples/example009.tex
Normal file
9
statistics/examples/example009.tex
Normal file
@ -0,0 +1,9 @@
|
|||||||
|
Toluene and the Brain Abuse of substances containing toluene (for
|
||||||
|
example, glue) can produce various neurological symptoms. In an
|
||||||
|
investigation of the mechanism of these toxic effects, researchers
|
||||||
|
measured the concentrations of various chemicals in the brains of rats
|
||||||
|
that had been exposed to a toluene-laden atmosphere, and also in
|
||||||
|
unexposed control rats. The concentrations of the brain chemical
|
||||||
|
norepinephrine (NE) in the medulla region of the brain, for six
|
||||||
|
toluene-exposed rats and five control rats, are given in accompanying
|
||||||
|
data file in ng/g.
|
||||||
3
statistics/examples/example010.tex
Normal file
3
statistics/examples/example010.tex
Normal file
@ -0,0 +1,3 @@
|
|||||||
|
In a pharmacological study, researchers measured the concentration of
|
||||||
|
the brain chemical dopamine in six rats exposed to toluene and six
|
||||||
|
control rats. Number are specified in ng/g.
|
||||||
6
statistics/examples/example011.tex
Normal file
6
statistics/examples/example011.tex
Normal file
@ -0,0 +1,6 @@
|
|||||||
|
Nerve Cell Density For each of nine horses, a veterinary anatomist
|
||||||
|
measured the density of nerve cells at specified sites in the
|
||||||
|
intestine. The results for site I (midregion of jejunum) and site II
|
||||||
|
(mesenteric region of jejunum) are given in the accompanying dataset.
|
||||||
|
Each density value is the average of counts of nerve cells in five
|
||||||
|
equal sections of tissue.
|
||||||
6
statistics/examples/example012.tex
Normal file
6
statistics/examples/example012.tex
Normal file
@ -0,0 +1,6 @@
|
|||||||
|
Hunger Rating During a weight loss study each of nine subjects was
|
||||||
|
given either the active drug m-chlorophenylpiperazine (mCPP) for two
|
||||||
|
weeks and then a placebo for another two weeks, or else was given the
|
||||||
|
placebo for the first two weeks and then mCPP for the second two
|
||||||
|
weeks. As part of the study the subjects were asked to rate how hungry
|
||||||
|
they were at the end of each two-week period.
|
||||||
10
statistics/examples/example013.tex
Normal file
10
statistics/examples/example013.tex
Normal file
@ -0,0 +1,10 @@
|
|||||||
|
Certain types of nerve cells have the ability to regenerate a part of
|
||||||
|
the cell that has been amputated. In an early study of this process,
|
||||||
|
measurements were made on the nerves in the spinal cord in rhesus
|
||||||
|
monkeys. Nerves emanating from the left side of the cord were cut,
|
||||||
|
while nerves from the right side were kept intact. During the
|
||||||
|
regeneration process, the content of creatine phosphate (CP) was
|
||||||
|
measured in the left and the right portion of the spinal cord. The
|
||||||
|
following table shows the data for the right (control) side (Y1), and
|
||||||
|
for the left (regenerating) side (Y2). The units of measurement are mg
|
||||||
|
CP per 100 gm tissue.
|
||||||
9
statistics/examples/example014.tex
Normal file
9
statistics/examples/example014.tex
Normal file
@ -0,0 +1,9 @@
|
|||||||
|
In an investigation of the physiological effects of alcohol
|
||||||
|
(ethanol), 15 mice were randomly allocated to three treatment groups,
|
||||||
|
each to receive a different oral dose of alcohol. The dosage levels
|
||||||
|
were 1.5, 3.0, and 6.0 g alcohol/kg body weight. The body temperature
|
||||||
|
of each mouse was measured immediately before the alcohol was given
|
||||||
|
and again 20 minutes afterward. The accompanying data shows the drop
|
||||||
|
(before minus after) in body temperature for each mouse. (The negative
|
||||||
|
value - 0.1 refers to a mouse whose temperature rose rather than
|
||||||
|
fell.)
|
||||||
5
statistics/examples/example015.tex
Normal file
5
statistics/examples/example015.tex
Normal file
@ -0,0 +1,5 @@
|
|||||||
|
The peak flow rate of a person is the fastest rate
|
||||||
|
at which the person can expel air after taking a deep breath.
|
||||||
|
Peak flow rate is measured in units of liters per minute and
|
||||||
|
gives an indication of the person's respiratory health. Flow is given
|
||||||
|
in l/min, height in cm.
|
||||||
6
statistics/examples/example016.tex
Normal file
6
statistics/examples/example016.tex
Normal file
@ -0,0 +1,6 @@
|
|||||||
|
An experiment was conducted to study the effect of tamoxifen on
|
||||||
|
patients with cervical cancer. One of the measurements made, both
|
||||||
|
before and again after tamoxifen was given, was microvessel density
|
||||||
|
(MVD). MVD, which is measured as number of vessels per mm$^2$, is a
|
||||||
|
measurement that relates to the formation of blood vessels that feed a
|
||||||
|
tumor and allow it to grow and spread.
|
||||||
5
statistics/examples/example017.tex
Normal file
5
statistics/examples/example017.tex
Normal file
@ -0,0 +1,5 @@
|
|||||||
|
A group of female college students were divided into three groups
|
||||||
|
according to upper body strength. Their leg strength was tested by
|
||||||
|
measuring how many consecutive times they could leg press 246 pounds
|
||||||
|
before exhaustion. (The subjects were allowed only one second of rest
|
||||||
|
between consecutive lifts.)
|
||||||
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62
statistics/lecture_statistics.tex → statistics/lecture_statistics01.tex
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62
statistics/lecture_statistics.tex → statistics/lecture_statistics01.tex
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@ -22,14 +22,19 @@
|
|||||||
% \useoutertheme{miniframes}
|
% \useoutertheme{miniframes}
|
||||||
}
|
}
|
||||||
|
|
||||||
\AtBeginSection[]
|
\AtBeginSubsection[]
|
||||||
{
|
{
|
||||||
\begin{frame}<beamer>
|
\begin{frame}<beamer>
|
||||||
\begin{center}
|
\begin{center}
|
||||||
\Huge \insertsectionhead
|
\Huge \insertsectionhead
|
||||||
\end{center}
|
\end{center}
|
||||||
|
\tableofcontents[
|
||||||
|
currentsubsection,
|
||||||
|
hideothersubsections,
|
||||||
|
sectionstyle=show/hide,
|
||||||
|
subsectionstyle=show/shaded,
|
||||||
|
]
|
||||||
% \frametitle{\insertsectionhead}
|
% \frametitle{\insertsectionhead}
|
||||||
% \tableofcontents[currentsection,hideothersubsections]
|
|
||||||
\end{frame}
|
\end{frame}
|
||||||
}
|
}
|
||||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
|
||||||
@ -84,25 +89,7 @@ Bernstein Center T\"ubingen}
|
|||||||
|
|
||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
\begin{frame}
|
|
||||||
\frametitle{plan}
|
|
||||||
\setcounter{tocdepth}{1}
|
|
||||||
\tableofcontents
|
|
||||||
|
|
||||||
\end{frame}
|
|
||||||
\begin{frame}
|
|
||||||
\frametitle{information}
|
|
||||||
\begin{itemize}
|
|
||||||
\item Samuels, M. L., Wittmer, J. A., \& Schaffner,
|
|
||||||
A. A. (2010). Statistics for the Life Sciences (4th ed.,
|
|
||||||
p. 668). Prentice Hall.
|
|
||||||
\item Zar, J. H. (1999). Biostatistical Analysis. (D. Lynch,
|
|
||||||
Ed.)Prentice Hall New Jersey (4th ed., Vol. 4th, p. 663). Prentice
|
|
||||||
Hall. doi:10.1037/0012764
|
|
||||||
\item \url{http://stats.stackexchange.com}
|
|
||||||
\end{itemize}
|
|
||||||
\end{frame}
|
|
||||||
|
|
||||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
% errorbars (error bar paper)
|
% errorbars (error bar paper)
|
||||||
% confidence intervals (sources of error)
|
% confidence intervals (sources of error)
|
||||||
@ -170,7 +157,8 @@ Bernstein Center T\"ubingen}
|
|||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
\section[descriptive statistics, errorbars, and plots]{Day 1 -- descriptive statistics, errorbars, and plots}
|
\section{Day 1 -- descriptive statistics and plots}
|
||||||
|
|
||||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
\subsection{types of data}
|
\subsection{types of data}
|
||||||
|
|
||||||
@ -315,8 +303,8 @@ Bernstein Center T\"ubingen}
|
|||||||
\frametitle{exercise}
|
\frametitle{exercise}
|
||||||
\begin{task}{Spearman rank correlation}
|
\begin{task}{Spearman rank correlation}
|
||||||
\begin{enumerate}
|
\begin{enumerate}
|
||||||
\item Use {\tt randi} to generate two 100-dimensional vectors
|
\item Use {\tt randi} to generate two vectors
|
||||||
{\tt x,y} of random integers between $0$ and $10$.
|
{\tt x,y} with $100$ random integers between $0$ and $10$ each.
|
||||||
\item Find out how to compute the Spearman
|
\item Find out how to compute the Spearman
|
||||||
rank correlation $$\rho = 1- {\frac {6 \sum
|
rank correlation $$\rho = 1- {\frac {6 \sum
|
||||||
d_i^2}{n(n^2 - 1)}}$$ with Matlab. $d_i = x_i - y_i$ is the
|
d_i^2}{n(n^2 - 1)}}$$ with Matlab. $d_i = x_i - y_i$ is the
|
||||||
@ -358,7 +346,6 @@ correlation coefficient does not have that property.
|
|||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
\section{description of data and plotting}
|
|
||||||
\subsection{what makes a good plot}
|
\subsection{what makes a good plot}
|
||||||
%-------------------------------------------------------------
|
%-------------------------------------------------------------
|
||||||
\begin{frame}[fragile]
|
\begin{frame}[fragile]
|
||||||
@ -522,7 +509,7 @@ correlation coefficient does not have that property.
|
|||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
\subsection{nominal scale}
|
\subsection{plotting data}
|
||||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
|
||||||
%-------------------------------------------------------------
|
%-------------------------------------------------------------
|
||||||
@ -723,6 +710,23 @@ hold off
|
|||||||
\end{center}
|
\end{center}
|
||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
|
%-------------------------------------------------------------
|
||||||
|
\begin{frame}[fragile,fragile]
|
||||||
|
\frametitle{robust statistics}
|
||||||
|
\begin{task}{When is statistic called robust (leave-one-out)?}
|
||||||
|
\begin{itemize}
|
||||||
|
\item Generate an array with $20$ random numbers using {\tt
|
||||||
|
randn}.
|
||||||
|
\item Compute $20$ means: the $i^{th}$ mean is computed from the
|
||||||
|
data set {\em without} the $i^{th}$ example.
|
||||||
|
\item Repeat this with the median.
|
||||||
|
\item Make a bar plot that depicts the means of the computed means
|
||||||
|
and medians along with an appropriate measure of dispersion.
|
||||||
|
\item What can you observe? Do you understand why?
|
||||||
|
\end{itemize}
|
||||||
|
\end{task}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
%-------------------------------------------------------------
|
%-------------------------------------------------------------
|
||||||
\begin{frame}[fragile]
|
\begin{frame}[fragile]
|
||||||
\frametitle{plotting interval/ratio/absolute data}
|
\frametitle{plotting interval/ratio/absolute data}
|
||||||
@ -791,7 +795,13 @@ hold off
|
|||||||
ordinal vs. ordinal data (why not the bar chart?).
|
ordinal vs. ordinal data (why not the bar chart?).
|
||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
|
%-------------------------------------------------------------
|
||||||
|
\begin{frame}[fragile]
|
||||||
|
\begin{center}
|
||||||
|
\Huge
|
||||||
|
That's it.
|
||||||
|
\end{center}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
\end{document}
|
\end{document}
|
||||||
772
statistics/lecture_statistics02.tex
Normal file
772
statistics/lecture_statistics02.tex
Normal file
@ -0,0 +1,772 @@
|
|||||||
|
\documentclass{beamer}
|
||||||
|
\usepackage{xcolor}
|
||||||
|
\usepackage{listings}
|
||||||
|
\usepackage{pgf}
|
||||||
|
%\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade}
|
||||||
|
%\usepackage{multimedia}
|
||||||
|
\usepackage[latin1]{inputenc}
|
||||||
|
\usepackage{amsmath}
|
||||||
|
\usepackage{bm}
|
||||||
|
\usepackage[T1]{fontenc}
|
||||||
|
\usepackage{hyperref}
|
||||||
|
\usepackage{ulem}
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
\mode<presentation>
|
||||||
|
{
|
||||||
|
\usetheme{Singapore}
|
||||||
|
\setbeamercovered{opaque}
|
||||||
|
\usecolortheme{tuebingen}
|
||||||
|
\setbeamertemplate{navigation symbols}{}
|
||||||
|
\usefonttheme{default}
|
||||||
|
\useoutertheme{infolines}
|
||||||
|
% \useoutertheme{miniframes}
|
||||||
|
}
|
||||||
|
|
||||||
|
\AtBeginSubsection[]
|
||||||
|
{
|
||||||
|
\begin{frame}<beamer>
|
||||||
|
\begin{center}
|
||||||
|
\Huge \insertsectionhead
|
||||||
|
\end{center}
|
||||||
|
\tableofcontents[
|
||||||
|
currentsubsection,
|
||||||
|
hideothersubsections,
|
||||||
|
sectionstyle=show/hide,
|
||||||
|
subsectionstyle=show/shaded,
|
||||||
|
]
|
||||||
|
% \frametitle{\insertsectionhead}
|
||||||
|
\end{frame}
|
||||||
|
}
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
|
||||||
|
|
||||||
|
\setbeamertemplate{blocks}[rounded][shadow=true]
|
||||||
|
|
||||||
|
\title[]{Scientific Computing -- Statistics}
|
||||||
|
\author[Statistics]{Fabian Sinz\\Dept. Neuroethology,
|
||||||
|
University T\"ubingen\\
|
||||||
|
Bernstein Center T\"ubingen}
|
||||||
|
|
||||||
|
\institute[Scientific Computing]{}
|
||||||
|
\date{10/20/2014}
|
||||||
|
%\logo{\pgfuseimage{logo}}
|
||||||
|
|
||||||
|
\subject{Lectures}
|
||||||
|
|
||||||
|
%%%%%%%%%% configuration for code
|
||||||
|
\lstset{
|
||||||
|
basicstyle=\ttfamily,
|
||||||
|
numbers=left,
|
||||||
|
showstringspaces=false,
|
||||||
|
language=Matlab,
|
||||||
|
commentstyle=\itshape\color{darkgray},
|
||||||
|
keywordstyle=\color{blue},
|
||||||
|
stringstyle=\color{green},
|
||||||
|
backgroundcolor=\color{blue!10},
|
||||||
|
breaklines=true,
|
||||||
|
breakautoindent=true,
|
||||||
|
columns=flexible,
|
||||||
|
frame=single,
|
||||||
|
captionpos=b,
|
||||||
|
xleftmargin=1em,
|
||||||
|
xrightmargin=1em,
|
||||||
|
aboveskip=10pt
|
||||||
|
}
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
|
||||||
|
\newcommand{\mycite}[1]{
|
||||||
|
\begin{flushright}
|
||||||
|
\tiny \color{black!80} #1
|
||||||
|
\end{flushright}
|
||||||
|
}
|
||||||
|
|
||||||
|
\input{../latex/environments.tex}
|
||||||
|
\makeatother
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
|
||||||
|
\begin{frame}
|
||||||
|
\titlepage
|
||||||
|
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{information}
|
||||||
|
\begin{itemize}
|
||||||
|
\item Samuels, M. L., Wittmer, J. A., \& Schaffner,
|
||||||
|
A. A. (2010). Statistics for the Life Sciences (4th ed.,
|
||||||
|
p. 668). Prentice Hall.
|
||||||
|
\item Zar, J. H. (1999). Biostatistical Analysis. (D. Lynch,
|
||||||
|
Ed.)Prentice Hall New Jersey (4th ed., Vol. 4th, p. 663). Prentice
|
||||||
|
Hall. doi:10.1037/0012764
|
||||||
|
\item \url{http://stats.stackexchange.com}
|
||||||
|
\end{itemize}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
\section{Day 2 -- errorbars, confidence intervals, and tests}
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
\subsection{Types of evidence}
|
||||||
|
\begin{frame}
|
||||||
|
\scriptsize
|
||||||
|
\frametitle{Examples}
|
||||||
|
\begin{itemize}
|
||||||
|
\item Before new drugs are given to human subjects, it is common
|
||||||
|
practice to first test them in dogs or other animals. In part of
|
||||||
|
one study, a new investigational drug was given to eight male and
|
||||||
|
eight female dogs at doses of 8 mg/kg and 25 mg/kg. Within each
|
||||||
|
sex, the two doses were assigned at random to the eight dogs. Many
|
||||||
|
``endpoints'' were measured, such as cholesterol, sodium, glucose,
|
||||||
|
and so on, from blood samples, in order to screen for toxicity
|
||||||
|
problems in the dogs before starting studies on humans. One
|
||||||
|
endpoint was alkaline phosphatase level (or APL, measured in U/l).
|
||||||
|
For females, the effect of increasing the dose from 8 to 25 mg/kg
|
||||||
|
was positive, although small (the average APL increased from 133.5
|
||||||
|
to 143 U/l), but for males the effect of increasing the dose from
|
||||||
|
8 to 25 mg/kg was negative.\pause
|
||||||
|
\item On 15 July 1911, 65-year-old Mrs. Jane Decker was struck by
|
||||||
|
lightning while in her house. She had been deaf since birth, but
|
||||||
|
after being struck, she recovered her hearing, which led to a
|
||||||
|
headline in the New York Times, ``Lightning Cures Deafness.''
|
||||||
|
\pause
|
||||||
|
\item Some research has suggested that there is a genetic basis for
|
||||||
|
sexual orientation. One such study involved measuring the
|
||||||
|
midsagittal area of the anterior commissure (AC) of the brain for
|
||||||
|
30 homosexual men, 30 heterosexual men, and 30 heterosexual
|
||||||
|
women. The researchers found that the AC tends to be larger in
|
||||||
|
heterosexual women than in heterosexual men and that it is even
|
||||||
|
larger in homosexual men.
|
||||||
|
\end{itemize}
|
||||||
|
\mycite{Samuels, Wittmer, Schaffner 2010}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
|
\begin{frame}
|
||||||
|
\scriptsize
|
||||||
|
\frametitle{types of evidence}
|
||||||
|
\begin{center}
|
||||||
|
\Large
|
||||||
|
{\em experiment} \\ is better than\\ {\em observational study}\\ is
|
||||||
|
better than\\ {\em anecdotal evidence}
|
||||||
|
\end{center}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{What is inferential statistics?}
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{sources of error in an experiment}
|
||||||
|
\begin{task}{Think about it for 2 min}
|
||||||
|
If you repeat a scientific experiment, why do you not get the same
|
||||||
|
result every time you repeat it?
|
||||||
|
\end{task}
|
||||||
|
\pause
|
||||||
|
\begin{itemize}
|
||||||
|
\item sampling error (a finite subset of the population of interest
|
||||||
|
is selected in each experiment)
|
||||||
|
\item nonsampling errors (e.g. noise, uncontrolled factors)
|
||||||
|
\end{itemize}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
% ----------------------------------------------------------
|
||||||
|
\begin{frame}[fragile]
|
||||||
|
\frametitle{statisticians are lazy}
|
||||||
|
\Large
|
||||||
|
\only<1>{
|
||||||
|
\begin{center}
|
||||||
|
\includegraphics[width=.8\linewidth]{figs/2012-10-29_16-26-05_771.jpg}
|
||||||
|
\end{center}
|
||||||
|
\mycite{Larry Gonick, The Cartoon Guide to Statistics}
|
||||||
|
}\pause
|
||||||
|
\only<2>{
|
||||||
|
\begin{center}
|
||||||
|
\includegraphics[width=.8\linewidth]{figs/2012-10-29_16-41-39_523.jpg}
|
||||||
|
\end{center}
|
||||||
|
\mycite{Larry Gonick, The Cartoon Guide to Statistics}
|
||||||
|
}\pause
|
||||||
|
\only<3>{
|
||||||
|
\begin{center}
|
||||||
|
\includegraphics[width=.8\linewidth]{figs/2012-10-29_16-29-35_312.jpg}
|
||||||
|
\end{center}
|
||||||
|
\mycite{Larry Gonick, The Cartoon Guide to Statistics}
|
||||||
|
}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
% % ----------------------------------------------------------
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{illustrating examples}
|
||||||
|
\begin{question}{lung volume of smokers}
|
||||||
|
Assume you know the sampling distribution of the mean lung volume
|
||||||
|
of smokers. Would you believe that
|
||||||
|
the sample came from a group of smokers?
|
||||||
|
\begin{center}
|
||||||
|
\includegraphics[width=.6\linewidth]{figs/example01.png}
|
||||||
|
\end{center}
|
||||||
|
\end{question}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{illustrating examples}
|
||||||
|
\begin{question}{lung volume of smokers}
|
||||||
|
What about now? How would the sampling distribution change if I
|
||||||
|
change the population to (i) athletes, (ii) old people, (iii) all people?
|
||||||
|
\begin{center}
|
||||||
|
\includegraphics[width=.6\linewidth]{figs/example02.png}
|
||||||
|
\end{center}
|
||||||
|
\end{question}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{illustrating examples}
|
||||||
|
\begin{question}{Is this diet effective?}
|
||||||
|
\begin{center}
|
||||||
|
\includegraphics[width=.6\linewidth]{figs/example03.png}
|
||||||
|
\end{center}
|
||||||
|
\end{question}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{illustrating examples}
|
||||||
|
\begin{question}{Is this diet effective?}
|
||||||
|
What do you think now?
|
||||||
|
\begin{center}
|
||||||
|
\includegraphics[width=.6\linewidth]{figs/example04.png}
|
||||||
|
\end{center}
|
||||||
|
\end{question}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
% ----------------------------------------------------------
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{the (imaginary) meta-study}
|
||||||
|
\begin{center}
|
||||||
|
\only<1>{
|
||||||
|
\framesubtitle{finite sampling introduces variation: the sampling distribution}
|
||||||
|
\includegraphics[width=.8\linewidth]{figs/samplingDistribution.png}
|
||||||
|
\mycite{Hesterberg et al., Bootstrap Methods and Permutation
|
||||||
|
Tests}
|
||||||
|
}\pause
|
||||||
|
\only<2>{
|
||||||
|
\framesubtitle{statistic vs. population parameter}
|
||||||
|
\includegraphics[width=.8\linewidth]{figs/statistic1.png}
|
||||||
|
\mycite{Hesterberg et al., Bootstrap Methods and Permutation
|
||||||
|
Tests}
|
||||||
|
}\pause
|
||||||
|
\only<3>{
|
||||||
|
\framesubtitle{statistic vs. population parameter}
|
||||||
|
\includegraphics[width=.8\linewidth]{figs/statistic2.png}
|
||||||
|
\mycite{Hesterberg et al., Bootstrap Methods and Permutation
|
||||||
|
Tests}
|
||||||
|
}\pause
|
||||||
|
\only<4>{
|
||||||
|
\framesubtitle{shat parts of this diagram do we have in real life?}
|
||||||
|
|
||||||
|
\includegraphics[width=.8\linewidth]{figs/samplingDistribution.png}
|
||||||
|
\mycite{Hesterberg et al., Bootstrap Methods and Permutation
|
||||||
|
Tests}
|
||||||
|
}\pause
|
||||||
|
\only<5>{
|
||||||
|
\framesubtitle{what parts of this diagram do we have in real life?}
|
||||||
|
|
||||||
|
\includegraphics[width=.8\linewidth]{figs/statistic3.png}
|
||||||
|
\mycite{Hesterberg et al., Bootstrap Methods and Permutation
|
||||||
|
Tests}
|
||||||
|
}\pause
|
||||||
|
\only<6->{
|
||||||
|
\framesubtitle{what statistics does }
|
||||||
|
\begin{minipage}{1.0\linewidth}
|
||||||
|
\begin{minipage}{0.5\linewidth}
|
||||||
|
\includegraphics[width=1.\linewidth]{figs/statistic4.png}
|
||||||
|
\mycite{Hesterberg et al., Bootstrap Methods and Permutation
|
||||||
|
Tests}
|
||||||
|
\end{minipage}
|
||||||
|
\begin{minipage}{0.5\linewidth}
|
||||||
|
\begin{itemize}
|
||||||
|
\item it assumes, derives, or simulates the sampling
|
||||||
|
distribution\pause
|
||||||
|
\item the sampling distribution makes only sense if you think
|
||||||
|
about it in terms of the meta study\pause
|
||||||
|
\item {\color{red} the sampling distribution is the key to
|
||||||
|
answering questions about the population from the value of
|
||||||
|
the statistic}
|
||||||
|
\end{itemize}
|
||||||
|
\end{minipage}
|
||||||
|
\end{minipage}
|
||||||
|
}
|
||||||
|
|
||||||
|
\end{center}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{summary}
|
||||||
|
\begin{itemize}
|
||||||
|
\item In statistics, we use finite samples from a population to reason
|
||||||
|
about features of the population. \pause
|
||||||
|
\item The particular feature of the population we are interested in is called
|
||||||
|
{\color{blue} population parameter}. We usually measure this
|
||||||
|
parameter in our finite sample as well
|
||||||
|
({\color{blue}statistic}).\pause
|
||||||
|
\item Because of variations due to finite sampling the statistic
|
||||||
|
almost never matches the population parameter. \pause
|
||||||
|
\item Using the {\color{blue}sampling distribution} of the statistic, we make
|
||||||
|
statements about the relation between our statistic and the
|
||||||
|
population parameter.
|
||||||
|
\end{itemize}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
\subsection{Errorbars}
|
||||||
|
% ----------------------------------------------------------
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{illustrating example}
|
||||||
|
|
||||||
|
As part of a study of the development of the thymus gland, researcher
|
||||||
|
weighed the glands of $50$ chick embyos after 14 days of
|
||||||
|
incubation. The following plot depicts the mean thymus gland weights in (mg):
|
||||||
|
\mycite{modified from SWS exercise 6.3.3.}
|
||||||
|
\pause
|
||||||
|
{\bf Which of the two bar plots is the correct way of displaying the
|
||||||
|
data?}
|
||||||
|
|
||||||
|
\begin{columns}
|
||||||
|
\begin{column}[l]{.5\linewidth}
|
||||||
|
\includegraphics[width=\linewidth]{figs/StandardErrorOrStandardDeviation.pdf}
|
||||||
|
\end{column}
|
||||||
|
\begin{column}[r]{.5\linewidth}
|
||||||
|
\pause That depends on what you want to say
|
||||||
|
\begin{itemize}
|
||||||
|
\item To give a measure of variability in the data: use the
|
||||||
|
{\color{blue} standard deviation $\hat\sigma =
|
||||||
|
\sqrt{\frac{1}{n-1}\sum_{i=1}^n (x_i - \hat\mu)^2}$}
|
||||||
|
\item To make a statement about the variability in the mean
|
||||||
|
estimation: use {\color{blue}standard error $\frac{\hat\sigma}{\sqrt{n}}$}
|
||||||
|
\end{itemize}
|
||||||
|
\end{column}
|
||||||
|
\end{columns}
|
||||||
|
|
||||||
|
%%%%%%%%%%%%%%% GO ON HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
% that depends: variability (descriptiv statistics, how variable is
|
||||||
|
% the mean -> inferential, makes only sense in the meta-study setting)
|
||||||
|
% first matlab exercise: simulate standard error
|
||||||
|
% recommend paper for eyeballing test results from standard errors
|
||||||
|
% from std of mean to confidence intervals
|
||||||
|
% introduce bootstrapping (matlab exercise), then t-statistic
|
||||||
|
% intervals
|
||||||
|
% end with standard error of the median (and the thing from wikipedia)
|
||||||
|
\end{frame}
|
||||||
|
%------------------------------------------------------------------------------
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{standard error}
|
||||||
|
\framesubtitle{bootstrapping}
|
||||||
|
|
||||||
|
\begin{task}{standard error vs. standard deviation}
|
||||||
|
|
||||||
|
\begin{itemize}
|
||||||
|
\item Download the dataset {\tt thymusglandweights.dat} from Ilias
|
||||||
|
\item Write a program that loads the data into matlab, extracts
|
||||||
|
the the first $80$ datapoints, and repeat the following steps
|
||||||
|
$m=500$ times:
|
||||||
|
\begin{enumerate}
|
||||||
|
\item draw $50$ data points from $x$ with replacement
|
||||||
|
\item compute their mean and store it
|
||||||
|
\end{enumerate}
|
||||||
|
Look at the standard deviation of the computed means.
|
||||||
|
\item Compare the result to the standard deviation of the original
|
||||||
|
$50$ data points and the standard error.
|
||||||
|
\end{itemize}
|
||||||
|
\end{task}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
\begin{frame}[fragile]
|
||||||
|
\frametitle{standard error}
|
||||||
|
\begin{lstlisting}
|
||||||
|
load thymusglandweights.dat
|
||||||
|
|
||||||
|
n = 80;
|
||||||
|
m = 500;
|
||||||
|
x = thymusglandweights(1:n);
|
||||||
|
|
||||||
|
|
||||||
|
mu = zeros(m,1);
|
||||||
|
for i = 1:m
|
||||||
|
mu(i) = mean(x(randi(n,n,1)));
|
||||||
|
end
|
||||||
|
disp(['bootstrap standard error: ', num2str(std(mu))]);
|
||||||
|
disp(['standard error: ', num2str(std(x)/sqrt(n))]);
|
||||||
|
\end{lstlisting}
|
||||||
|
\end{frame}
|
||||||
|
%------------------------------------------------------------------------------
|
||||||
|
\begin{frame}[fragile]
|
||||||
|
\frametitle{standard error}
|
||||||
|
\framesubtitle{bootstrapping}
|
||||||
|
\begin{itemize}
|
||||||
|
\item The sample standard error $\frac{\hat\sigma}{\sqrt{n}}$ is
|
||||||
|
{\color{blue}an estimate of the standard deviation of the means}
|
||||||
|
in repeated experiments which is computed form a single
|
||||||
|
experiment.
|
||||||
|
\item When you want to do statistical tests on the mean, it is
|
||||||
|
better to use the standard error, because one can eyeball
|
||||||
|
significance from it
|
||||||
|
\mycite{Cumming, G., Fidler, F., \& Vaux, D. L. (2007). Error bars
|
||||||
|
in experimental biology. The Journal of Cell Biology, 177(1),
|
||||||
|
7--11.}
|
||||||
|
\item {\color{blue}Bootstrapping} is a way to generate an estimate
|
||||||
|
of the {\color{blue}sampling distribution of any statistic}. Instead of
|
||||||
|
sampling from the true distribution, it samples from the
|
||||||
|
empirical distribution represented by your dataset.
|
||||||
|
\mycite{Efron, B., \& Tibshirani, R. J. (1994). An Introduction to the Bootstrap. Chapman and Hall/CRC}
|
||||||
|
\end{itemize}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
%------------------------------------------------------------------------------
|
||||||
|
\begin{frame}[fragile]
|
||||||
|
\frametitle{standard error of the median?}
|
||||||
|
{\bf What kind of errorbars should we use for the median?}
|
||||||
|
|
||||||
|
It depends again:
|
||||||
|
|
||||||
|
{\bf Descriptive statistics}
|
||||||
|
\begin{itemize}
|
||||||
|
\item As a {\color{blue}descriptive statistic} one could use the {\em median
|
||||||
|
absolute deviation}: the median of the absolute differences of
|
||||||
|
the datapoints from the median.
|
||||||
|
\item Alternatively, one could bootstrap a standard error of the
|
||||||
|
median.
|
||||||
|
\end{itemize}
|
||||||
|
\pause
|
||||||
|
{\bf Inferential statistics}
|
||||||
|
\begin{itemize}
|
||||||
|
\item For {\color{blue}inferential statistics} one should use
|
||||||
|
something that gives the reader {\color{blue}information about
|
||||||
|
significance}.
|
||||||
|
\item Here, {\color{blue} confidence intervals} are a better choice.
|
||||||
|
\end{itemize}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
% ----------------------------------------------------------
|
||||||
|
\subsection{confidence intervals \& bootstrapping}
|
||||||
|
%------------------------------------------------------------------------------
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{confidence intervals}
|
||||||
|
\begin{center}
|
||||||
|
\only<1>{
|
||||||
|
\vspace{.1cm}
|
||||||
|
\includegraphics[width=.6\linewidth]{figs/2012-10-29_14-55-39_181.jpg}
|
||||||
|
\mycite{Larry Gonick, The Cartoon Guide to Statistics}
|
||||||
|
|
||||||
|
}\pause
|
||||||
|
\only<2>{
|
||||||
|
\vspace{.1cm}
|
||||||
|
\includegraphics[width=.6\linewidth]{figs/2012-10-29_14-56-59_866.jpg}
|
||||||
|
\mycite{Larry Gonick, The Cartoon Guide to Statistics}
|
||||||
|
}\pause
|
||||||
|
\only<3>{
|
||||||
|
\vspace{.1cm}
|
||||||
|
\includegraphics[width=.4\linewidth]{figs/2012-10-29_14-58-18_054.jpg}
|
||||||
|
\mycite{Larry Gonick, The Cartoon Guide to Statistics}
|
||||||
|
}\pause
|
||||||
|
\only<4>{
|
||||||
|
\vspace{.1cm}
|
||||||
|
\includegraphics[width=.6\linewidth]{figs/2012-10-29_14-59-05_984.jpg}
|
||||||
|
\mycite{Larry Gonick, The Cartoon Guide to Statistics}
|
||||||
|
}\pause
|
||||||
|
\only<5>{
|
||||||
|
\vspace{.1cm}
|
||||||
|
\includegraphics[width=.6\linewidth]{figs/2012-10-29_15-04-38_517.jpg}
|
||||||
|
\mycite{Larry Gonick, The Cartoon Guide to Statistics}
|
||||||
|
}\pause
|
||||||
|
\only<6>{
|
||||||
|
\vspace{.1cm}
|
||||||
|
\includegraphics[width=.6\linewidth]{figs/2012-10-29_15-09-25_388.jpg}
|
||||||
|
\mycite{Larry Gonick, The Cartoon Guide to Statistics}
|
||||||
|
}
|
||||||
|
\end{center}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
% ----------------------------------------------------------
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{confidence intervals for the median}
|
||||||
|
\begin{definition}{Confidence interval}
|
||||||
|
A confidence $(1-\alpha)\cdot 100\%$ interval for a statistic
|
||||||
|
$\hat\theta$ is an interval $\hat\theta \pm a$ such that the
|
||||||
|
population parameter $\theta$ is contained in that interval
|
||||||
|
$(1-\alpha)\cdot 100\%$ of the experiments.
|
||||||
|
|
||||||
|
An alternative way to put it is that $(\hat\theta - \theta) \in
|
||||||
|
[-a,a]$ in $(1-\alpha)\cdot 100\%$ of the cases.
|
||||||
|
\end{definition}
|
||||||
|
|
||||||
|
|
||||||
|
\begin{columns}
|
||||||
|
\begin{column}[l]{.5\linewidth}
|
||||||
|
If we knew the sampling distribution of the median $\hat m$, could
|
||||||
|
we generate a e.g. a $95\%$ confidence interval?\pause
|
||||||
|
\vspace{.5cm}
|
||||||
|
|
||||||
|
Yes, we could choose the interval such that $\hat m - m$ in that
|
||||||
|
interval in $95\%$ of the cases.
|
||||||
|
\end{column}
|
||||||
|
\begin{column}[r]{.5\linewidth}
|
||||||
|
\only<1>{\includegraphics[width=\linewidth]{figs/samplingDistributionMedian00.pdf}}
|
||||||
|
\only<2>{\includegraphics[width=\linewidth]{figs/samplingDistributionMedian01.pdf}}
|
||||||
|
\end{column}
|
||||||
|
\end{columns}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
% ----------------------------------------------------------
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{confidence intervals for the mean via bootstrapping}
|
||||||
|
\framesubtitle{how to get the sampling distribution}
|
||||||
|
|
||||||
|
\begin{task}{bootstrapping a confidence interval for the mean}
|
||||||
|
\begin{itemize}
|
||||||
|
\item Use the same dataset as before.
|
||||||
|
\item Bootstrap $500$ means.
|
||||||
|
\item Plot their distribution.
|
||||||
|
\item Compute the $2.5\%$ and the $97.5\%$ percentile of the
|
||||||
|
$500$ means.
|
||||||
|
\item Mark them in the plot.
|
||||||
|
\end{itemize}
|
||||||
|
These two numbers give you $\hat m -a$ and $\hat m + a$ for
|
||||||
|
the $95\%$ confidence interval.
|
||||||
|
\end{task}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
\begin{frame}[fragile]
|
||||||
|
\frametitle{confidence intervals for the median}
|
||||||
|
\scriptsize
|
||||||
|
\begin{lstlisting}
|
||||||
|
load thymusglandweights.dat
|
||||||
|
n = 80;
|
||||||
|
x = thymusglandweights(1:n);
|
||||||
|
|
||||||
|
m = 500;
|
||||||
|
me = zeros(m,1);
|
||||||
|
for i = 1:m
|
||||||
|
me(i) = mean(x(randi(n,n,1)));
|
||||||
|
end
|
||||||
|
|
||||||
|
disp(['bootstrap quantiles: ' , num2str(quantile(me,0.025)), ' ' ,num2str(quantile(me,1-0.025))]);
|
||||||
|
|
||||||
|
\end{lstlisting}
|
||||||
|
\end{frame}
|
||||||
|
% ----------------------------------------------------------
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{confidence intervals}
|
||||||
|
\framesubtitle{Notice the theme!}
|
||||||
|
\begin{enumerate}
|
||||||
|
\item choose a statistic
|
||||||
|
\item get a the sampling distribution of the statistic (by theory or
|
||||||
|
simulation)
|
||||||
|
\item use that distribution to reason about the relation between the
|
||||||
|
true population parameter (e.g. $m$) and the sampled statistic
|
||||||
|
$\hat m$
|
||||||
|
\end{enumerate}
|
||||||
|
|
||||||
|
\begin{center}
|
||||||
|
\color{blue}
|
||||||
|
This is the scaffold of most statistical techniques. Try to find
|
||||||
|
it and it can help you understand them.
|
||||||
|
\end{center}
|
||||||
|
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% ----------------------------------------------------------
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{confidence interval for the mean}
|
||||||
|
\framesubtitle{Let's search the pattern in the normal way of computing
|
||||||
|
a confidence interval for the mean}
|
||||||
|
\begin{itemize}
|
||||||
|
\item If the $x_1,...,x_n\sim \mathcal N(\mu,\sigma)$ are Gaussian, then $\hat\mu$ is Gaussian as
|
||||||
|
well
|
||||||
|
\item What is the mean of $\hat\mu$? What is its standard deviation?\pause
|
||||||
|
\item[]{\color{gray} $\langle\hat\mu\rangle_{X_1,...,X_n} = \mu$ and
|
||||||
|
$\mbox{std}(\hat\mu) = \frac{\sigma}{\sqrt{n}}$}\pause
|
||||||
|
\item The problem is, that $\hat\mu \sim \mathcal N\left(\mu,
|
||||||
|
\frac{\sigma}{\sqrt{n}}\right)$ depends on unknown population
|
||||||
|
parameters.\pause
|
||||||
|
\item However, $$\frac{\hat\mu-\mu}{\hat\sigma/\sqrt{n}} \sim
|
||||||
|
\mbox{t-distribution with }n-1\mbox{ degrees of freedom}$$
|
||||||
|
\item Therefore,
|
||||||
|
\begin{align*}
|
||||||
|
P\left(t_{2.5\%}\le\frac{\hat{\mu}-\mu}{\hat{\sigma}/\sqrt{n}}\le t_{97.5\%}\right)&=P\left(t_{2.5\%}\frac{\hat{\sigma}}{\sqrt{n}}\le\hat{\mu}-\mu\le t_{97.5\%}\frac{\hat{\sigma}}{\sqrt{n}}\right)
|
||||||
|
\end{align*}
|
||||||
|
\end{itemize}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
% ----------------------------------------------------------
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{confidence interval for the mean}
|
||||||
|
\begin{task}{Bootstrapping a confidence interval for the mean}
|
||||||
|
Extend your script to contain the analytical confidence
|
||||||
|
interval using
|
||||||
|
\begin{align*}
|
||||||
|
P\left(t_{2.5\%}\le\frac{\hat{\mu}-\mu}{\hat{\sigma}/\sqrt{n}}\le t_{97.5\%}\right)&=P\left(t_{2.5\%}\frac{\hat{\sigma}}{\sqrt{n}}\le\hat{\mu}-\mu\le t_{97.5\%}\frac{\hat{\sigma}}{\sqrt{n}}\right)
|
||||||
|
\end{align*}
|
||||||
|
Hint: Use the function {\tt tinv(0.025, n-1)} to get the value of
|
||||||
|
$t_{2.5\%}$ and similar for $t_{97.5\%}$.
|
||||||
|
\end{task}
|
||||||
|
|
||||||
|
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
|
\begin{frame}[fragile]
|
||||||
|
\frametitle{solution}
|
||||||
|
\scriptsize
|
||||||
|
\begin{lstlisting}
|
||||||
|
load thymusglandweights.dat
|
||||||
|
n = 80;
|
||||||
|
x = thymusglandweights(1:n);
|
||||||
|
|
||||||
|
m = 500;
|
||||||
|
me = zeros(m,1);
|
||||||
|
for i = 1:m
|
||||||
|
me(i) = mean(x(randi(n,n,1)));
|
||||||
|
end
|
||||||
|
|
||||||
|
t025 = tinv(0.025, n-1);
|
||||||
|
t975 = tinv(0.975, n-1);
|
||||||
|
|
||||||
|
se = std(x)/sqrt(n);
|
||||||
|
|
||||||
|
disp(['bootstrap quantiles: ' , num2str(quantile(me,0.025)), ' ' ,num2str(quantile(me,1-0.025))]);
|
||||||
|
disp(['analytical CI: ' , num2str(mean(x)+t025*se), ' ' , num2str(mean(x)+t975*se)]);
|
||||||
|
|
||||||
|
\end{lstlisting}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
\subsection{statistical tests}
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{ingredients into a test}
|
||||||
|
|
||||||
|
\begin{itemize}
|
||||||
|
\item {\bf What is the goal of a test?}\pause
|
||||||
|
\item[] Check whether a measured
|
||||||
|
statistic looks different from what you would expect if there was no
|
||||||
|
effect.\pause
|
||||||
|
\item {\bf What are the ingredients into a test?}\pause
|
||||||
|
\item[] a test statistic (e.g. the mean, the median, ...) and a null
|
||||||
|
distribution\pause
|
||||||
|
\item {\bf What is a null distribution?}\pause
|
||||||
|
\item[] The sampling distribution of the statistic in case there is
|
||||||
|
no effect (i.e. the Null hypothesis is true).
|
||||||
|
\end{itemize}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{how tests work}
|
||||||
|
\begin{enumerate}
|
||||||
|
\item Choose a statistic.
|
||||||
|
\item Get a null distribution.
|
||||||
|
\item Compare your actually measure value with the Null
|
||||||
|
distribution.
|
||||||
|
\end{enumerate}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{Example: one sample test}
|
||||||
|
\framesubtitle{step 2: get a Null distribution}
|
||||||
|
\scriptsize
|
||||||
|
Assume that the expected weight of a thymus gland from the
|
||||||
|
literature is 34.3g. We want to test whether the mean of our
|
||||||
|
thymus gland dataset is different from the expectation in the
|
||||||
|
literature. Comparing a statistic of a dataset against a fixed value
|
||||||
|
is called {\em one sample test}.
|
||||||
|
\pause
|
||||||
|
|
||||||
|
\begin{itemize}
|
||||||
|
\item {\bf How could we simulate the distribution of the data if the
|
||||||
|
mean was really 30g?}\pause
|
||||||
|
\item[] Bootstrapping.
|
||||||
|
\end{itemize}
|
||||||
|
|
||||||
|
\begin{task}{generating a null distribution}
|
||||||
|
\begin{itemize}
|
||||||
|
\item Write a matlab program that bootstraps 2000 means from the
|
||||||
|
thymus gland dataset.
|
||||||
|
\item How can we adjust the data that it has mean 34.3g (remember,
|
||||||
|
we want to simulate the null distribution)?
|
||||||
|
\item Plot a histogram of these 2000 means.
|
||||||
|
\item Also indicate the actual mean of the data.
|
||||||
|
\end{itemize}
|
||||||
|
\end{task}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{Example: one sample test}
|
||||||
|
\framesubtitle{step 3: compare the actual value to the Null distribution}
|
||||||
|
\begin{minipage}{1.0\linewidth}
|
||||||
|
\begin{minipage}{0.5\linewidth}
|
||||||
|
The question we want to answer in this step is:
|
||||||
|
\begin{center}
|
||||||
|
\color{blue} Does the actually measure value look like it came
|
||||||
|
from the Null distribution?
|
||||||
|
\end{center}
|
||||||
|
\end{minipage}
|
||||||
|
\begin{minipage}{0.5\linewidth}
|
||||||
|
\includegraphics[width=\linewidth]{figs/bootstraptest.png}
|
||||||
|
\end{minipage}
|
||||||
|
\end{minipage}
|
||||||
|
{\bf How could we do this in our bootstrapping example?}\pause
|
||||||
|
\begin{itemize}
|
||||||
|
\item Set a threshold. \pause How do we choose the threshold? \pause Via type I error.\pause
|
||||||
|
\item Specify the type I error if we used the actual measured value
|
||||||
|
as threshold (p-value). Why is that a reasonable strategy?
|
||||||
|
\end{itemize}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{Example: one sample test}
|
||||||
|
\framesubtitle{step 3: compare the actual value to the Null distribution}
|
||||||
|
\begin{task}{type I error and p-value}
|
||||||
|
Extend the script such that it
|
||||||
|
\begin{itemize}
|
||||||
|
\item computes the $5\%$ significance boundaries from the
|
||||||
|
distribution and plot it into the histogram.
|
||||||
|
\item computes a p-value.
|
||||||
|
\end{itemize}
|
||||||
|
\end{task}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{two sample test}
|
||||||
|
\framesubtitle{permutation test}
|
||||||
|
Brain Weight In 1888, P. Topinard published data on the brain
|
||||||
|
weights of hundreds of French men and women. Brain weights are given
|
||||||
|
in gram. The data can be downloaded from Ilias (example 002 from
|
||||||
|
yesterday).
|
||||||
|
|
||||||
|
\vspace{.5cm}
|
||||||
|
{\bf How could we determine (similar to bootstrapping) whether the
|
||||||
|
mean brain weight of males and females are different?}
|
||||||
|
\begin{itemize}
|
||||||
|
\item What do we use as a statistic?
|
||||||
|
\item[]<2-> The difference of the means of the two groups.
|
||||||
|
\item How do we simulate the null distribution?
|
||||||
|
\item[]<3-> Shuffle the labels ``male'' and ``female'', compute
|
||||||
|
difference in means of two groups, and repeat.
|
||||||
|
\end{itemize}
|
||||||
|
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
|
\begin{frame}
|
||||||
|
\begin{center}
|
||||||
|
\Huge That's it.
|
||||||
|
\end{center}
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
\end{document}
|
||||||
|
|
||||||
|
|
||||||
13
statistics/matlab/bootstrap_mean.m
Normal file
13
statistics/matlab/bootstrap_mean.m
Normal file
@ -0,0 +1,13 @@
|
|||||||
|
load thymusglandweights.dat
|
||||||
|
x = thymusglandweights(1:50);
|
||||||
|
|
||||||
|
m = 500;
|
||||||
|
n = length(x);
|
||||||
|
|
||||||
|
mu = zeros(m,1);
|
||||||
|
for i = 1:m
|
||||||
|
mu(i) = mean(x(randi(n,n,1)));
|
||||||
|
end
|
||||||
|
fprintf("bootstrap standard error: %.4f\n", std(mu));
|
||||||
|
fprintf("standard error: %.4f\n", std(x)/sqrt(n));
|
||||||
|
|
||||||
19
statistics/matlab/ci_mean.m
Normal file
19
statistics/matlab/ci_mean.m
Normal file
@ -0,0 +1,19 @@
|
|||||||
|
load thymusglandweights.dat
|
||||||
|
|
||||||
|
n = 80;
|
||||||
|
x = thymusglandweights(1:n);
|
||||||
|
|
||||||
|
m = 5000;
|
||||||
|
me = zeros(m,1);
|
||||||
|
for i = 1:m
|
||||||
|
me(i) = median(x(randi(n,n,1)));
|
||||||
|
end
|
||||||
|
|
||||||
|
t025 = tinv(0.025, n-1);
|
||||||
|
t975 = tinv(0.975, n-1);
|
||||||
|
|
||||||
|
se = std(x)/sqrt(n);
|
||||||
|
|
||||||
|
fprintf('bootstrap quantiles: %.4f, %.4f \n', quantile(me,0.025), quantile(me,0.975));
|
||||||
|
fprintf('analytical quantile: %.4f, %.4f \n', mean(x)+t025*se, mean(x)+t975*se);
|
||||||
|
|
||||||
17
statistics/matlab/ci_media.m
Normal file
17
statistics/matlab/ci_media.m
Normal file
@ -0,0 +1,17 @@
|
|||||||
|
load thymusglandweights.dat
|
||||||
|
x = thymusglandweights(1:50);
|
||||||
|
|
||||||
|
m = 500;
|
||||||
|
n = length(x);
|
||||||
|
x = sort(x);
|
||||||
|
me = zeros(m,1);
|
||||||
|
for i = 1:m
|
||||||
|
me(i) = median(x(randi(n,n,1)));
|
||||||
|
end
|
||||||
|
|
||||||
|
a1 = binoinv(0.025,n,.5)-1;
|
||||||
|
a2 = binoinv(1-0.025,n,.5);
|
||||||
|
|
||||||
|
fprintf('bootstrap quantiles: %.4f, %.4f \n', quantile(me,0.025), quantile(me,1-0.025));
|
||||||
|
fprintf('analytical quantile: %.4f, %.4f \n', x(a1),x(a2));
|
||||||
|
|
||||||
38
statistics/matlab/tests.m
Normal file
38
statistics/matlab/tests.m
Normal file
@ -0,0 +1,38 @@
|
|||||||
|
close all
|
||||||
|
clear all
|
||||||
|
load thymusglandweights.dat
|
||||||
|
|
||||||
|
literature_mean = 34.3;
|
||||||
|
|
||||||
|
x = thymusglandweights;
|
||||||
|
n = length(x);
|
||||||
|
y = x - mean(x) + literature_mean;
|
||||||
|
|
||||||
|
m = 2000;
|
||||||
|
me = zeros(m,1);
|
||||||
|
for i = 1:m
|
||||||
|
me(i) = median(y(randi(n,n,1)));
|
||||||
|
end
|
||||||
|
|
||||||
|
hist(me, 50);
|
||||||
|
hold on
|
||||||
|
mu = mean(x);
|
||||||
|
plot([mu,mu],[0,200],'--r','LineWidth',3);
|
||||||
|
xlabel('thymus gland weights [g]');
|
||||||
|
ylabel('frequency');
|
||||||
|
title('bootstrapped null distribution');
|
||||||
|
hold off
|
||||||
|
|
||||||
|
% 5% significance boundaries
|
||||||
|
low = quantile(me,0.025);
|
||||||
|
high = quantile(me,0.975);
|
||||||
|
disp(['the 5% boundaries are: ', num2str(low), ' ', num2str(high)]);
|
||||||
|
|
||||||
|
hold on
|
||||||
|
plot([low,low],[0,200],'--g','LineWidth',3);
|
||||||
|
plot([high,high],[0,200],'--g','LineWidth',3);
|
||||||
|
hold off
|
||||||
|
|
||||||
|
pval = mean(abs(me-literature_mean) > abs(mu - literature_mean))
|
||||||
|
|
||||||
|
legend('Null distribution','measured mean','5% significance boundaries')
|
||||||
10000
statistics/matlab/thymusglandweights.dat
Normal file
10000
statistics/matlab/thymusglandweights.dat
Normal file
File diff suppressed because it is too large
Load Diff
Reference in New Issue
Block a user