changed title

statistics/Makefile

@@ -0,0 +1,24 @@
+DOTSOURCES = $(wildcard figs/*.dot)
+
+
+
+all: $(DOTSOURCES:dot=pdf) 
+	python figs/generate.py
+	python figs/generate03.py
+	python figs/generateTPlots.py
+	pdflatex talk*.tex
+	pdflatex talk*.tex
+	pdflatex talk*.tex
+
+
+figs/prob%.pdf : figs/prob%.dot
+	dot -Tpdf -o $@ $<
+
+figs/test%.pdf : figs/test%.dot
+	dot -Tpdf -o $@ $<
+
+figs/fig%.pdf : figs/fig%.dot
+	dot -Tpdf -o $@ $<
+
+clean:
+	rm -rf *.dvi *.pdf *.aux *.out *.log auto *.nav *.snm *.toc *.vrb

statistics/beamercolorthemetuebingen.sty

@@ -0,0 +1 @@
+../latex/beamercolorthemetuebingen.sty

statistics/certificate.lyx

@@ -0,0 +1,218 @@
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
+\begin_document
+\begin_header
+\textclass g-brief2
+\begin_preamble
+\fenstermarken % prints address window marks
+\faltmarken % prints folding marks
+%\lochermarke % prints puncher marks 
+\trennlinien % prints striplines
+%\unserzeichen % prints "our ref" instead of "my ref"
+\end_preamble
+\use_default_options false
+\maintain_unincluded_children false
+\language english
+\language_package default
+\inputencoding auto
+\fontencoding global
+\font_roman palatino
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize 12
+\spacing onehalf
+\use_hyperref false
+\papersize default
+\use_geometry false
+\use_amsmath 1
+\use_esint 1
+\use_mhchem 1
+\use_mathdots 1
+\cite_engine basic
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\secnumdepth 4
+\tocdepth 4
+\paragraph_separation skip
+\defskip medskip
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle empty
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+Note also the document preamble settings.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout NameRowA
+Dr.
+ rer.
+ nat.
+ Fabian Sinz
+\end_layout
+
+\begin_layout NameRowB
+
+\end_layout
+
+\begin_layout NameRowC
+
+\end_layout
+
+\begin_layout NameRowD
+
+\end_layout
+
+\begin_layout NameRowE
+
+\end_layout
+
+\begin_layout NameRowF
+
+\end_layout
+
+\begin_layout NameRowG
+
+\end_layout
+
+\begin_layout AddressRowA
+University Tübingen
+\end_layout
+
+\begin_layout AddressRowB
+
+\end_layout
+
+\begin_layout AddressRowC
+Auf der Morgenstelle 28
+\end_layout
+
+\begin_layout AddressRowD
+72076 Tübingen
+\end_layout
+
+\begin_layout InternetRowA
+http:/
+\begin_inset Formula $\!$
+\end_inset
+
+/www.epagoge.de
+\end_layout
+
+\begin_layout InternetRowB
+fabian.sinz@epagoge.de
+\end_layout
+
+\begin_layout ReturnAddress
+University Tübingen 
+\begin_inset Formula $\cdot$
+\end_inset
+
+ Auf der Morgenstelle 28 
+\begin_inset Formula $\cdot$
+\end_inset
+
+ 72076 Tübingen
+\end_layout
+
+\begin_layout Date
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+today
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Reference
+
+\end_layout
+
+\begin_layout Opening
+To whom it may concern,
+\end_layout
+
+\begin_layout Closing
+Best regards
+\end_layout
+
+\begin_layout Signature
+Dr.
+ Fabian Sinz
+\end_layout
+
+\begin_layout Encl.
+
+\end_layout
+
+\begin_layout Letter
+this letter certifies that 
+\emph on
+Lakshmi Channappa
+\emph default
+ attended the course 
+\emph on
+Statistics in a Nutshell
+\emph default
+ held at the Neurochip research group at the 
+\emph on
+Naturwissenschaftliches und Medizinisches Institut Reutlingen 
+\emph default
+in 2013
+\emph on
+.
+ 
+\emph default
+The course was organized in two lectures of four hours each and covered
+ topics such as basics of probability theory, errorbars and confidence intervals
+, statistical tests, p-values, multiple hypothesis testing, basics of study
+ design, and basics of ANOVA.
+ Small calculation and programming exercises were used to clarify selected
+ material.
+\end_layout
+
+\end_body
+\end_document

statistics/environments.tex

@@ -0,0 +1,123 @@
+
+%%% Local Variables: 
+%%% mode: latex
+%%% TeX-master: t
+%%% End: 
+\definecolor{crimson}{HTML}{DC143C}
+\definecolor{cornflowerblue}{HTML}{6495ED}
+\definecolor{dodgerblue}{HTML}{1E90FF}
+\definecolor{deepskyblue}{HTML}{00BFFF}
+\definecolor{gainsboro}{HTML}{DCDCDC}
+\definecolor{ghostwhite}{HTML}{F8F8F8}
+\definecolor{lightgray}{HTML}{D3D3D3}
+
+\newenvironment<>{emphasize}[1]{%
+  \begin{actionenv}#2%
+      \def\insertblocktitle{#1}%
+      \par%
+      \mode<presentation>{%
+        \setbeamercolor{block title}{fg=black,bg=orange!100}
+       \setbeamercolor{block body}{fg=black,bg=cornflowerblue!70}
+       % \setbeamercolor{itemize item}{fg=orange!20!black}
+       % \setbeamertemplate{itemize item}[triangle]
+       \setbeamerfont{block title}{series=\bfseries}
+       % \setbeamerfont{block body}{family=\ttfamily}
+     }%
+      \usebeamertemplate{block begin}}
+    {\par\usebeamertemplate{block end}\end{actionenv}}
+
+\newenvironment<>{solution}[1]{%
+  \begin{actionenv}#2%
+      \def\insertblocktitle{#1}%
+      \par%
+      \mode<presentation>{%
+        \setbeamercolor{block title}{fg=black,bg=dodgerblue!100}
+       \setbeamercolor{block body}{fg=black,bg=lightgray!70}
+       % \setbeamercolor{itemize item}{fg=orange!20!black}
+       % \setbeamertemplate{itemize item}[triangle]
+       \setbeamerfont{block title}{series=\bfseries}
+       % \setbeamerfont{block body}{family=\ttfamily}
+     }%
+      \usebeamertemplate{block begin}}
+    {\par\usebeamertemplate{block end}\end{actionenv}}
+
+\newenvironment<>{question}[1]{%
+  \begin{actionenv}#2%
+      \def\insertblocktitle{#1}%
+      \par%
+      \mode<presentation>{%
+        \setbeamercolor{block title}{fg=black,bg=dodgerblue!100}
+       \setbeamercolor{block body}{fg=black,bg=lightgray!70}
+       % \setbeamercolor{itemize item}{fg=orange!20!black}
+       % \setbeamertemplate{itemize item}[triangle]
+       \setbeamerfont{block title}{series=\bfseries}
+       % \setbeamerfont{block body}{family=\ttfamily}
+     }%
+      \usebeamertemplate{block begin}}
+    {\par\usebeamertemplate{block end}\end{actionenv}}
+
+\renewenvironment<>{definition}[1]{%
+  \begin{actionenv}#2%
+      \def\insertblocktitle{#1}%
+      \par%
+      \mode<presentation>{%
+        \setbeamercolor{block title}{fg=black,bg=dodgerblue!100}
+       \setbeamercolor{block body}{fg=black,bg=lightgray!70}
+       % \setbeamercolor{itemize item}{fg=orange!20!black}
+       % \setbeamertemplate{itemize item}[triangle]
+       \setbeamerfont{block title}{series=\bfseries}
+       % \setbeamerfont{block body}{family=\ttfamily}
+     }%
+      \usebeamertemplate{block begin}}
+    {\par\usebeamertemplate{block end}\end{actionenv}}
+
+
+\newenvironment<>{description}[1]{%
+  \begin{actionenv}#2%
+      \def\insertblocktitle{#1}%
+      \par%
+      \mode<presentation>{%
+        \setbeamercolor{block title}{fg=white,bg=gray}
+       \setbeamercolor{block body}{fg=black,bg=gray!30}
+       % \setbeamercolor{itemize item}{fg=orange!20!black}
+       % \setbeamertemplate{itemize item}[triangle]
+       \setbeamerfont{block title}{family=\sffamily, series=\bfseries}
+       \setbeamerfont{block body}{family=\ttfamily}
+     }%
+      \usebeamertemplate{block begin}}
+    {\par\usebeamertemplate{block end}\end{actionenv}}
+
+\newenvironment<>{task}[1]{%
+  \begin{actionenv}#2%
+      \def\insertblocktitle{#1}%
+      \par%
+      \mode<presentation>{%
+        \setbeamercolor{block title}{fg=black,bg=dodgerblue!100}
+       \setbeamercolor{block body}{fg=black,bg=deepskyblue!80}
+       % \setbeamercolor{itemize item}{fg=orange!20!black}
+       % \setbeamertemplate{itemize item}[triangle]
+       \setbeamerfont{block title}{series=\bfseries}
+       % \setbeamerfont{block body}{family=\ttfamily}
+     }%
+      \usebeamertemplate{block begin}}
+    {\par\usebeamertemplate{block end}\end{actionenv}}
+
+\newenvironment<>{summary}[1]{%
+  \begin{actionenv}#2%
+      \def\insertblocktitle{#1}%
+      \par%
+      \mode<presentation>{%
+        \setbeamercolor{block title}{fg=black,bg=blue!40}
+       \setbeamercolor{block body}{fg=black,bg=blue!20}
+       % \setbeamercolor{itemize item}{fg=orange!20!black}
+       % \setbeamertemplate{itemize item}[triangle]
+       \setbeamerfont{block title}{series=\bfseries}
+       % \setbeamerfont{block body}{family=\ttfamily}
+     }%
+      \usebeamertemplate{block begin}}
+    {\par\usebeamertemplate{block end}\end{actionenv}}
+%%%%%%%%%%%%%%%%%%% PROGRESSBAR %%%%%%%%%%%%%%%%%%%%%%%%%%
+\definecolor{pbblue}{HTML}{0A75A8}% filling color for the progress bar
+\definecolor{pbgray}{HTML}{575757}% background color for the progress bar
+\definecolor{pbgreen}{HTML}{57EE57}% green color for the progress bar
+

statistics/figs/fig0.dot

@@ -0,0 +1,15 @@
+digraph G {
+	rankdir=TB;
+	node [fontsize=12, shape=rectangle, style=filled];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	data[label="type of data?"];
+	IR[label="data normal distributed\nor n large?"];
+	ordinal[label="?"];
+	nominal[label="?"];
+			 
+	data->IR[label="interval/ratio"]
+	data->nominal[label="nominal/discrete"]
+	data->ordinal[label="ordinal"]
+}

statistics/figs/fig01.dot

@@ -0,0 +1,94 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled, nodesep=0.95,ranksep=0.95];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	subgraph cluster_IR {
+		label = "interval/ ratio";
+		bgcolor=lightblue;
+		
+		IR[label="data normal distributed\nor n large?"];
+		
+		normal[label="1, 2, or >2 groups?"];
+		notnormal[label="transform into\nnormal?"];
+		trulynotnormal[label="1, 2, or >2 groups?"];
+
+		IR->normal[label="normal"];
+		IR->notnormal[label="not normal"];
+		notnormal->normal[label="yes"];
+		notnormal->trulynotnormal[label="no"];
+
+		onesamp[label="one-sample\nt-test"];
+		normal->onesamp[label="1 group"];
+
+		ttest[label="t-test"];
+		twosamp->ttest[label="independent"];
+
+
+		twosamp[label="paired or\nindependent?"];
+		pairedttest[label="paired\nt-test"];
+		normal->twosamp[label="2 groups"];
+		twosamp->pairedttest[label="paired"];
+
+		twosampNN[label="paired or\nindependent?"];
+
+		trulynotnormal->twosampNN[label="2 groups"];
+
+		signrank[label="Wilcoxon signed\nrank test"];
+
+		trulynotnormal->signrank[label="1 group\n(fix other\ngroup to\n one value)"];
+
+		
+	}
+
+	trulynotnormal->signtest[label="1 group\n(fix other\ngroup to\n one value)"];
+
+	twosampNN->signrank[label="paired"];
+	twosampNN->indepTwosampNN[label="independent"];
+
+	data->ordinal[label="ordinal"];
+
+	subgraph cluster_O {
+		label = "ordinal";
+		bgcolor=lightblue;
+		indepTwosampNN[label="Wilcoxon-Mann-Whitney\ntest"];
+	
+
+	
+		twosampOrd[label="paired or\nindependent?"];
+		ordinal->twosampOrd[label="2 groups"];
+		twosampOrd->indepTwosampNN[label="independent"];
+
+		signtest[label="sign test"];
+		ordinal[label="1, 2, or >2 groups?"];
+		ordinal->signtest[label="1 group\n(fix other\ngroup to\n one value)"];
+	}
+
+	
+	subgraph cluster_ND {
+		label = "nominal/discrete";
+		bgcolor=lightblue;
+		nd_test_type[label="1, 2, or >2 variables",color="green"];
+
+	}
+
+	
+	
+
+
+	data[label="type of data?"];
+	
+	data->IR[label="interval/ratio"];
+	data->nd_test_type[label="nominal/discrete",color="red"];
+
+
+
+	twosampNN->signtest[label="paired"];
+	twosampOrd->signtest[label="paired"];
+
+
+}
+	
+

statistics/figs/fig02.dot

@@ -0,0 +1,96 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled, nodesep=0.95,ranksep=0.95];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	subgraph cluster_IR {
+		label = "interval/ ratio";
+		bgcolor=lightblue;
+		
+		IR[label="data normal distributed\nor n large?"];
+		
+		normal[label="1, 2, or >2 groups?"];
+		notnormal[label="transform into\nnormal?"];
+		trulynotnormal[label="1, 2, or >2 groups?"];
+
+		IR->normal[label="normal"];
+		IR->notnormal[label="not normal"];
+		notnormal->normal[label="yes"];
+		notnormal->trulynotnormal[label="no"];
+
+		onesamp[label="one-sample\nt-test"];
+		normal->onesamp[label="1 group"];
+
+		ttest[label="t-test"];
+		twosamp->ttest[label="independent"];
+
+
+		twosamp[label="paired or\nindependent?"];
+		pairedttest[label="paired\nt-test"];
+		normal->twosamp[label="2 groups"];
+		twosamp->pairedttest[label="paired"];
+
+		twosampNN[label="paired or\nindependent?"];
+
+		trulynotnormal->twosampNN[label="2 groups"];
+
+		signrank[label="Wilcoxon signed\nrank test"];
+
+		trulynotnormal->signrank[label="1 group\n(fix other\ngroup to\n one value)"];
+
+		
+	}
+
+	trulynotnormal->signtest[label="1 group\n(fix other\ngroup to\n one value)"];
+
+	twosampNN->signrank[label="paired"];
+	twosampNN->indepTwosampNN[label="independent"];
+
+	data->ordinal[label="ordinal"];
+
+	subgraph cluster_O {
+		label = "ordinal";
+		bgcolor=lightblue;
+		indepTwosampNN[label="Wilcoxon-Mann-Whitney\ntest"];
+	
+
+	
+		twosampOrd[label="paired or\nindependent?"];
+		ordinal->twosampOrd[label="2 groups"];
+		twosampOrd->indepTwosampNN[label="independent"];
+
+		signtest[label="sign test"];
+		ordinal[label="1, 2, or >2 groups?"];
+		ordinal->signtest[label="1 group\n(fix other\ngroup to\n one value)"];
+	}
+
+	
+	subgraph cluster_ND {
+		label = "nominal/discrete";
+		bgcolor=lightblue;
+		nd_test_type[label="1, 2, or >2 variables",color="green"];
+		onesampND[label="chi square for\ngoodness of fit"];
+
+		nd_test_type->onesampND[label="1 variable"];
+	}
+
+	
+	
+
+
+	data[label="type of data?"];
+	
+	data->IR[label="interval/ratio"];
+	data->nd_test_type[label="nominal/discrete",color="red"];
+
+
+
+	twosampNN->signtest[label="paired"];
+	twosampOrd->signtest[label="paired"];
+
+
+}
+	
+

statistics/figs/fig03.dot

@@ -0,0 +1,98 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled, nodesep=0.95,ranksep=0.95];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	subgraph cluster_IR {
+		label = "interval/ ratio";
+		bgcolor=lightblue;
+		
+		IR[label="data normal distributed\nor n large?"];
+		
+		normal[label="1, 2, or >2 groups?"];
+		notnormal[label="transform into\nnormal?"];
+		trulynotnormal[label="1, 2, or >2 groups?"];
+
+		IR->normal[label="normal"];
+		IR->notnormal[label="not normal"];
+		notnormal->normal[label="yes"];
+		notnormal->trulynotnormal[label="no"];
+
+		onesamp[label="one-sample\nt-test"];
+		normal->onesamp[label="1 group"];
+
+		ttest[label="t-test"];
+		twosamp->ttest[label="independent"];
+
+
+		twosamp[label="paired or\nindependent?"];
+		pairedttest[label="paired\nt-test"];
+		normal->twosamp[label="2 groups"];
+		twosamp->pairedttest[label="paired"];
+
+		twosampNN[label="paired or\nindependent?"];
+
+		trulynotnormal->twosampNN[label="2 groups"];
+
+		signrank[label="Wilcoxon signed\nrank test"];
+
+		trulynotnormal->signrank[label="1 group\n(fix other\ngroup to\n one value)"];
+
+		
+	}
+
+	trulynotnormal->signtest[label="1 group\n(fix other\ngroup to\n one value)"];
+
+	twosampNN->signrank[label="paired"];
+	twosampNN->indepTwosampNN[label="independent"];
+
+	data->ordinal[label="ordinal"];
+
+	subgraph cluster_O {
+		label = "ordinal";
+		bgcolor=lightblue;
+		indepTwosampNN[label="Wilcoxon-Mann-Whitney\ntest"];
+	
+
+	
+		twosampOrd[label="paired or\nindependent?"];
+		ordinal->twosampOrd[label="2 groups"];
+		twosampOrd->indepTwosampNN[label="independent"];
+
+		signtest[label="sign test"];
+		ordinal[label="1, 2, or >2 groups?"];
+		ordinal->signtest[label="1 group\n(fix other\ngroup to\n one value)"];
+	}
+
+	
+	subgraph cluster_ND {
+		label = "nominal/discrete";
+		bgcolor=lightblue;
+		nd_test_type[label="1, 2, or >2 variables",color="green"];
+		onesampND[label="chi square for\ngoodness of fit"];
+		twosampND[label="chi square for\nindependence"];
+
+		nd_test_type->onesampND[label="1 variable"];
+		nd_test_type->twosampND[label="2 variables"];
+	}
+
+	
+	
+
+
+	data[label="type of data?"];
+	
+	data->IR[label="interval/ratio"];
+	data->nd_test_type[label="nominal/discrete",color="red"];
+
+
+
+	twosampNN->signtest[label="paired"];
+	twosampOrd->signtest[label="paired"];
+
+
+}
+	
+

statistics/figs/fig04.dot

@@ -0,0 +1,99 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled, nodesep=0.95,ranksep=0.95];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	subgraph cluster_IR {
+		label = "interval/ ratio";
+		bgcolor=lightblue;
+		
+		IR[label="data normal distributed\nor n large?"];
+		
+		normal[label="1, 2, or >2 groups?"];
+		notnormal[label="transform into\nnormal?"];
+		trulynotnormal[label="1, 2, or >2 groups?"];
+
+		IR->normal[label="normal"];
+		IR->notnormal[label="not normal"];
+		notnormal->normal[label="yes"];
+		notnormal->trulynotnormal[label="no"];
+
+		onesamp[label="one-sample\nt-test"];
+		normal->onesamp[label="1 group"];
+
+		ttest[label="t-test"];
+		twosamp->ttest[label="independent"];
+
+
+		twosamp[label="paired or\nindependent?"];
+		pairedttest[label="paired\nt-test"];
+		normal->twosamp[label="2 groups"];
+		twosamp->pairedttest[label="paired"];
+
+		twosampNN[label="paired or\nindependent?"];
+
+		trulynotnormal->twosampNN[label="2 groups"];
+
+		signrank[label="Wilcoxon signed\nrank test"];
+
+		trulynotnormal->signrank[label="1 group\n(fix other\ngroup to\n one value)"];
+
+		
+	}
+
+	trulynotnormal->signtest[label="1 group\n(fix other\ngroup to\n one value)"];
+
+	twosampNN->signrank[label="paired"];
+	twosampNN->indepTwosampNN[label="independent"];
+
+	data->ordinal[label="ordinal"];
+
+	subgraph cluster_O {
+		label = "ordinal";
+		bgcolor=lightblue;
+		indepTwosampNN[label="Wilcoxon-Mann-Whitney\ntest"];
+	
+
+	
+		twosampOrd[label="paired or\nindependent?"];
+		ordinal->twosampOrd[label="2 groups"];
+		twosampOrd->indepTwosampNN[label="independent"];
+
+		signtest[label="sign test"];
+		ordinal[label="1, 2, or >2 groups?"];
+		ordinal->signtest[label="1 group\n(fix other\ngroup to\n one value)"];
+	}
+
+	
+	subgraph cluster_ND {
+		label = "nominal/discrete";
+		bgcolor=lightblue;
+		nd_test_type[label="1, 2, or >2 variables",color="green"];
+		onesampND[label="chi square for\ngoodness of fit"];
+		twosampND[label="chi square for\nindependence"];
+
+		nd_test_type->onesampND[label="1 variable"];
+		nd_test_type->onesampND[label="n variables",color="red"];
+		nd_test_type->twosampND[label="2 variables"];
+	}
+
+	
+	
+
+
+	data[label="type of data?"];
+	
+	data->IR[label="interval/ratio"];
+	data->nd_test_type[label="nominal/discrete"];
+
+
+
+	twosampNN->signtest[label="paired"];
+	twosampOrd->signtest[label="paired"];
+
+
+}
+	
+

statistics/figs/fig05.dot

@@ -0,0 +1,99 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled, nodesep=0.95,ranksep=0.95];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	subgraph cluster_IR {
+		label = "interval/ ratio";
+		bgcolor=lightblue;
+		
+		IR[label="data normal distributed\nor n large?"];
+		
+		normal[label="1, 2, or >2 groups?",color="green"];
+		notnormal[label="transform into\nnormal?"];
+		trulynotnormal[label="1, 2, or >2 groups?"];
+
+		IR->normal[label="normal"];
+		IR->notnormal[label="not normal"];
+		notnormal->normal[label="yes"];
+		notnormal->trulynotnormal[label="no"];
+
+		onesamp[label="one-sample\nt-test"];
+		normal->onesamp[label="1 group"];
+
+		ttest[label="t-test"];
+		twosamp->ttest[label="independent"];
+
+
+		twosamp[label="paired or\nindependent?"];
+		pairedttest[label="paired\nt-test"];
+		normal->twosamp[label="2 groups"];
+		twosamp->pairedttest[label="paired"];
+
+		twosampNN[label="paired or\nindependent?"];
+
+		trulynotnormal->twosampNN[label="2 groups"];
+
+		signrank[label="Wilcoxon signed\nrank test"];
+
+		trulynotnormal->signrank[label="1 group\n(fix other\ngroup to\n one value)"];
+		
+		
+	}
+
+	trulynotnormal->signtest[label="1 group\n(fix other\ngroup to\n one value)"];
+
+	twosampNN->signrank[label="paired"];
+	twosampNN->indepTwosampNN[label="independent"];
+
+	data->ordinal[label="ordinal"];
+
+	subgraph cluster_O {
+		label = "ordinal";
+		bgcolor=lightblue;
+		indepTwosampNN[label="Wilcoxon-Mann-Whitney\ntest"];
+	
+
+	
+		twosampOrd[label="paired or\nindependent?"];
+		ordinal->twosampOrd[label="2 groups"];
+		twosampOrd->indepTwosampNN[label="independent"];
+
+		signtest[label="sign test"];
+		ordinal[label="1, 2, or >2 groups?"];
+		ordinal->signtest[label="1 group\n(fix other\ngroup to\n one value)"];
+	}
+
+	
+	subgraph cluster_ND {
+		label = "nominal/discrete";
+		bgcolor=lightblue;
+		nd_test_type[label="1, 2, or >2 variables"];
+		onesampND[label="chi square for\ngoodness of fit"];
+		twosampND[label="chi square for\nindependence"];
+
+		nd_test_type->onesampND[label="1 variable"];
+		nd_test_type->onesampND[label="n variables"];
+		nd_test_type->twosampND[label="2 variables"];
+	}
+
+	
+	
+
+
+	data[label="type of data?"];
+	
+	data->IR[label="interval/ratio"];
+	data->nd_test_type[label="nominal/discrete"];
+
+
+
+	twosampNN->signtest[label="paired"];
+	twosampOrd->signtest[label="paired"];
+
+
+}
+	
+

statistics/figs/fig06.dot

@@ -0,0 +1,101 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled, nodesep=0.95,ranksep=0.95];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	subgraph cluster_IR {
+		label = "interval/ ratio";
+		bgcolor=lightblue;
+		
+		IR[label="data normal distributed\nor n large?"];
+		
+		normal[label="1, 2, or >2 groups?",color="green"];
+		notnormal[label="transform into\nnormal?"];
+		trulynotnormal[label="1, 2, or >2 groups?"];
+
+		IR->normal[label="normal"];
+		IR->notnormal[label="not normal"];
+		notnormal->normal[label="yes"];
+		notnormal->trulynotnormal[label="no"];
+
+		onesamp[label="one-sample\nt-test"];
+		normal->onesamp[label="1 group"];
+
+		ttest[label="t-test"];
+		twosamp->ttest[label="independent"];
+
+
+		twosamp[label="paired or\nindependent?"];
+		pairedttest[label="paired\nt-test"];
+		normal->twosamp[label="2 groups"];
+		twosamp->pairedttest[label="paired"];
+
+		twosampNN[label="paired or\nindependent?"];
+
+		trulynotnormal->twosampNN[label="2 groups"];
+
+		signrank[label="Wilcoxon signed\nrank test"];
+
+		trulynotnormal->signrank[label="1 group\n(fix other\ngroup to\n one value)"];
+		
+		ANOVA;
+		normal->ANOVA[color="red"];
+		
+	}
+
+	trulynotnormal->signtest[label="1 group\n(fix other\ngroup to\n one value)"];
+
+	twosampNN->signrank[label="paired"];
+	twosampNN->indepTwosampNN[label="independent"];
+
+	data->ordinal[label="ordinal"];
+
+	subgraph cluster_O {
+		label = "ordinal";
+		bgcolor=lightblue;
+		indepTwosampNN[label="Wilcoxon-Mann-Whitney\ntest"];
+	
+
+	
+		twosampOrd[label="paired or\nindependent?"];
+		ordinal->twosampOrd[label="2 groups"];
+		twosampOrd->indepTwosampNN[label="independent"];
+
+		signtest[label="sign test"];
+		ordinal[label="1, 2, or >2 groups?"];
+		ordinal->signtest[label="1 group\n(fix other\ngroup to\n one value)"];
+	}
+
+	
+	subgraph cluster_ND {
+		label = "nominal/discrete";
+		bgcolor=lightblue;
+		nd_test_type[label="1, 2, or >2 variables"];
+		onesampND[label="chi square for\ngoodness of fit"];
+		twosampND[label="chi square for\nindependence"];
+
+		nd_test_type->onesampND[label="1 variable"];
+		nd_test_type->onesampND[label="n variables"];
+		nd_test_type->twosampND[label="2 variables"];
+	}
+
+	
+	
+
+
+	data[label="type of data?"];
+	
+	data->IR[label="interval/ratio"];
+	data->nd_test_type[label="nominal/discrete"];
+
+
+
+	twosampNN->signtest[label="paired"];
+	twosampOrd->signtest[label="paired"];
+
+
+}
+	
+

statistics/figs/fig1.dot

@@ -0,0 +1,22 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	data[label="type of data?"];
+	IR[label="data normal distributed\nor n large?"];
+	ordinal[label="?"];
+	nominal[label="?"];
+			 
+	data->IR[label="interval/ratio"];
+	data->nominal[label="nominal/discrete"];
+	data->ordinal[label="ordinal"];
+
+	normal[label="?"];
+
+	IR->normal[label="normal"];
+
+
+}

statistics/figs/fig10.dot

@@ -0,0 +1,58 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled, nodesep=0.95,ranksep=0.95];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	data[label="type of data?"];
+	IR[label="data normal distributed\nor n large?"];
+	ordinal[label="1, 2, or >2 groups?"];
+	nominal[label="?"];
+			 
+	data->IR[label="interval/ratio"];
+	data->nominal[label="nominal/discrete"];
+	data->ordinal[label="ordinal"];
+
+	normal[label="1, 2, or >2 groups?"];
+	notnormal[label="transform into\nnormal?"];
+	trulynotnormal[label="1, 2, or >2 groups?"];
+
+	IR->normal[label="normal"];
+	IR->notnormal[label="not normal"];
+	notnormal->normal[label="yes"];
+	notnormal->trulynotnormal[label="no"];
+
+	onesamp[label="one-sample\nt-test"];
+	normal->onesamp[label="1 group"];
+
+
+	twosamp[label="paired or\nindependent?"];
+	pairedttest[label="paired\nt-test"];
+	normal->twosamp[label="2 groups"];
+	twosamp->pairedttest[label="paired"];
+
+	twosampNN[label="paired or\nindependent?"];
+	indepTwosampNN[label="Wilcoxon-Mann-Whitney\ntest"];
+
+	trulynotnormal->twosampNN[label="2 groups"];
+	twosampNN->indepTwosampNN[label="independent"];
+	
+	twosampOrd[label="paired or\nindependent?"];
+	ordinal->twosampOrd[label="2 groups"];
+	twosampOrd->indepTwosampNN[label="independent"];
+
+
+	ttest[label="t-test"];
+	twosamp->ttest[label="independent"];
+
+	signtest[label="sign test"];
+	signrank[label="Wilcoxon signed\nrank test",color="lightblue"];
+	twosampNN->signtest[label="paired"];
+	twosampOrd->signtest[label="paired"];
+
+	twosampNN->signrank[label="paired"];
+
+}
+	
+

statistics/figs/fig11.dot

@@ -0,0 +1,81 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled, nodesep=0.95,ranksep=0.95];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	subgraph cluster_IR {
+		label = "interval/ ratio";
+		bgcolor=lightblue;
+		
+		IR[label="data normal distributed\nor n large?"];
+		
+		normal[label="1, 2, or >2 groups?"];
+		notnormal[label="transform into\nnormal?"];
+		trulynotnormal[label="1, 2, or >2 groups?"];
+
+		IR->normal[label="normal"];
+		IR->notnormal[label="not normal"];
+		notnormal->normal[label="yes"];
+		notnormal->trulynotnormal[label="no"];
+
+		onesamp[label="one-sample\nt-test"];
+		normal->onesamp[label="1 group"];
+
+		ttest[label="t-test"];
+		twosamp->ttest[label="independent"];
+
+
+		twosamp[label="paired or\nindependent?"];
+		pairedttest[label="paired\nt-test"];
+		normal->twosamp[label="2 groups"];
+		twosamp->pairedttest[label="paired"];
+
+		twosampNN[label="paired or\nindependent?"];
+
+		trulynotnormal->twosampNN[label="2 groups"];
+
+		signrank[label="Wilcoxon signed\nrank test"];
+
+
+		
+	}
+
+
+	twosampNN->signrank[label="paired"];
+	twosampNN->indepTwosampNN[label="independent"];
+
+	data->ordinal[label="ordinal"];
+
+	subgraph cluster_O {
+		label = "ordinal";
+		bgcolor=lightblue;
+		indepTwosampNN[label="Wilcoxon-Mann-Whitney\ntest"];
+	
+
+	
+		twosampOrd[label="paired or\nindependent?"];
+		ordinal->twosampOrd[label="2 groups"];
+		twosampOrd->indepTwosampNN[label="independent"];
+
+		signtest[label="sign test"];
+
+	}
+	
+	data[label="type of data?"];
+	ordinal[label="1, 2, or >2 groups?"];
+	nominal[label="?"];
+			 
+	data->IR[label="interval/ratio"];
+	data->nominal[label="nominal/discrete"];
+
+
+
+	twosampNN->signtest[label="paired"];
+	twosampOrd->signtest[label="paired"];
+
+
+}
+	
+

statistics/figs/fig12.dot

@@ -0,0 +1,83 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled, nodesep=0.95,ranksep=0.95];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	subgraph cluster_IR {
+		label = "interval/ ratio";
+		bgcolor=lightblue;
+		
+		IR[label="data normal distributed\nor n large?"];
+		
+		normal[label="1, 2, or >2 groups?"];
+		notnormal[label="transform into\nnormal?"];
+		trulynotnormal[label="1, 2, or >2 groups?"];
+
+		IR->normal[label="normal"];
+		IR->notnormal[label="not normal"];
+		notnormal->normal[label="yes"];
+		notnormal->trulynotnormal[label="no"];
+
+		onesamp[label="one-sample\nt-test"];
+		normal->onesamp[label="1 group"];
+
+		ttest[label="t-test"];
+		twosamp->ttest[label="independent"];
+
+
+		twosamp[label="paired or\nindependent?"];
+		pairedttest[label="paired\nt-test"];
+		normal->twosamp[label="2 groups"];
+		twosamp->pairedttest[label="paired"];
+
+		twosampNN[label="paired or\nindependent?"];
+
+		trulynotnormal->twosampNN[label="2 groups"];
+
+		signrank[label="Wilcoxon signed\nrank test"];
+
+		trulynotnormal->signrank[label="1 group\n(fix other\ngroup to\n one value)",color="red"];
+
+		
+	}
+
+	trulynotnormal->signtest[label="1 group\n(fix other\ngroup to\n one value)",color="red"];
+
+	twosampNN->signrank[label="paired"];
+	twosampNN->indepTwosampNN[label="independent"];
+
+	data->ordinal[label="ordinal"];
+
+	subgraph cluster_O {
+		label = "ordinal";
+		bgcolor=lightblue;
+		indepTwosampNN[label="Wilcoxon-Mann-Whitney\ntest"];
+	
+
+	
+		twosampOrd[label="paired or\nindependent?"];
+		ordinal->twosampOrd[label="2 groups"];
+		twosampOrd->indepTwosampNN[label="independent"];
+
+		signtest[label="sign test"];
+		ordinal[label="1, 2, or >2 groups?"];
+		ordinal->signtest[label="1 group\n(fix other\ngroup to\n one value)",color="red"];
+	}
+	
+	data[label="type of data?"];
+	nominal[label="?"];
+			 
+	data->IR[label="interval/ratio"];
+	data->nominal[label="nominal/discrete"];
+
+
+
+	twosampNN->signtest[label="paired"];
+	twosampOrd->signtest[label="paired"];
+
+
+}
+	
+

statistics/figs/fig2.dot

@@ -0,0 +1,28 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	data[label="type of data?"];
+	IR[label="data normal distributed\nor n large?"];
+	ordinal[label="?"];
+	nominal[label="?"];
+			 
+	data->IR[label="interval/ratio"];
+	data->nominal[label="nominal/discrete"];
+	data->ordinal[label="ordinal"];
+
+	normal[label="?",color="lightblue"];
+	notnormal[label="transform into\nnormal?"];
+	trulynotnormal[label="?"];
+
+	IR->normal[label="normal"];
+	IR->notnormal[label="not normal"];
+	notnormal->normal[label="yes"];
+	notnormal->trulynotnormal[label="no"];
+
+
+}
+	

statistics/figs/fig3.dot

@@ -0,0 +1,28 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled, nodesep=0.75,ranksep=0.75];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	data[label="type of data?"];
+	IR[label="data normal distributed\nor n large?"];
+	ordinal[label="?"];
+	nominal[label="?"];
+			 
+	data->IR[label="interval/ratio"];
+	data->nominal[label="nominal/discrete"];
+	data->ordinal[label="ordinal"];
+
+	normal[label="1, 2, or >2 groups?"];
+	notnormal[label="transform into\nnormal?"];
+	trulynotnormal[label="?"];
+
+	IR->normal[label="normal"];
+	IR->notnormal[label="not normal"];
+	notnormal->normal[label="yes"];
+	notnormal->trulynotnormal[label="no"];
+
+
+}
+	

statistics/figs/fig4.dot

@@ -0,0 +1,30 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled, nodesep=0.75,ranksep=0.75];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	data[label="type of data?"];
+	IR[label="data normal distributed\nor n large?"];
+	ordinal[label="?"];
+	nominal[label="?"];
+			 
+	data->IR[label="interval/ratio"];
+	data->nominal[label="nominal/discrete"];
+	data->ordinal[label="ordinal"];
+
+	normal[label="1, 2, or >2 groups?"];
+	notnormal[label="transform into\nnormal?"];
+	trulynotnormal[label="?"];
+
+	IR->normal[label="normal"];
+	IR->notnormal[label="not normal"];
+	notnormal->normal[label="yes"];
+	notnormal->trulynotnormal[label="no"];
+
+	onesamp[label="one-sample\nt-test"];
+	normal->onesamp[label="1 group"];
+
+}
+	

statistics/figs/fig5.dot

@@ -0,0 +1,38 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled, nodesep=0.75,ranksep=0.75];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	data[label="type of data?"];
+	IR[label="data normal distributed\nor n large?"];
+	ordinal[label="?"];
+	nominal[label="?"];
+			 
+	data->IR[label="interval/ratio"];
+	data->nominal[label="nominal/discrete"];
+	data->ordinal[label="ordinal"];
+
+	normal[label="1, 2, or >2 groups?"];
+	notnormal[label="transform into\nnormal?"];
+	trulynotnormal[label="?"];
+
+	IR->normal[label="normal"];
+	IR->notnormal[label="not normal"];
+	notnormal->normal[label="yes"];
+	notnormal->trulynotnormal[label="no"];
+
+	onesamp[label="one-sample\nt-test"];
+	normal->onesamp[label="1 group"];
+
+
+	twosamp[label="paired or\nnot paired?"];
+	pairedttest[label="paired\nt-test"];
+	normal->twosamp[label="2 groups"];
+	twosamp->pairedttest[label="paired"];
+	
+
+}
+	
+

statistics/figs/fig6.dot

@@ -0,0 +1,49 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled, nodesep=0.75,ranksep=0.75];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	data[label="type of data?"];
+	IR[label="data normal distributed\nor n large?"];
+	ordinal[label="1, 2, or >2 groups?",color="lightblue"];
+	nominal[label="?"];
+			 
+	data->IR[label="interval/ratio"];
+	data->nominal[label="nominal/discrete"];
+	data->ordinal[label="ordinal"];
+
+	normal[label="1, 2, or >2 groups?"];
+	notnormal[label="transform into\nnormal?"];
+	trulynotnormal[label="1, 2, or >2 groups?",color="lightblue"];
+
+	IR->normal[label="normal"];
+	IR->notnormal[label="not normal"];
+	notnormal->normal[label="yes"];
+	notnormal->trulynotnormal[label="no"];
+
+	onesamp[label="one-sample\nt-test"];
+	normal->onesamp[label="1 group"];
+
+
+	twosamp[label="paired or\nindependent?"];
+	pairedttest[label="paired\nt-test"];
+	normal->twosamp[label="2 groups"];
+	twosamp->pairedttest[label="paired"];
+
+	twosampNN[label="paired or\nindependent?",color="lightblue"];
+	indepTwosampNN[label="Wilcoxon-Mann-Whitney\ntest",color="lightblue"];
+
+	trulynotnormal->twosampNN[label="2 groups"];
+	twosampNN->indepTwosampNN[label="independent"];
+	
+	twosampOrd[label="paired or\nindependent?",color="lightblue"];
+	ordinal->twosampOrd[label="2 groups"];
+	twosampOrd->indepTwosampNN[label="independent"];
+
+	
+
+}
+	
+

statistics/figs/fig7.dot

@@ -0,0 +1,52 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled, nodesep=0.75,ranksep=0.75];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	data[label="type of data?"];
+	IR[label="data normal distributed\nor n large?"];
+	ordinal[label="1, 2, or >2 groups?"];
+	nominal[label="?"];
+			 
+	data->IR[label="interval/ratio"];
+	data->nominal[label="nominal/discrete"];
+	data->ordinal[label="ordinal"];
+
+	normal[label="1, 2, or >2 groups?"];
+	notnormal[label="transform into\nnormal?"];
+	trulynotnormal[label="1, 2, or >2 groups?"];
+
+	IR->normal[label="normal"];
+	IR->notnormal[label="not normal"];
+	notnormal->normal[label="yes"];
+	notnormal->trulynotnormal[label="no"];
+
+	onesamp[label="one-sample\nt-test"];
+	normal->onesamp[label="1 group"];
+
+
+	twosamp[label="paired or\nindependent?"];
+	pairedttest[label="paired\nt-test"];
+	normal->twosamp[label="2 groups"];
+	twosamp->pairedttest[label="paired"];
+
+	twosampNN[label="paired or\nindependent?"];
+	indepTwosampNN[label="Wilcoxon-Mann-Whitney\ntest"];
+
+	trulynotnormal->twosampNN[label="2 groups"];
+	twosampNN->indepTwosampNN[label="independent"];
+	
+	twosampOrd[label="paired or\nindependent?"];
+	ordinal->twosampOrd[label="2 groups"];
+	twosampOrd->indepTwosampNN[label="indepdendent"];
+
+
+	ttest[label="?",color="lightblue"];
+	twosamp->ttest[label="independent"];
+
+
+}
+	
+

statistics/figs/fig8.dot

@@ -0,0 +1,54 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled, nodesep=0.75,ranksep=0.75];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	data[label="type of data?"];
+	IR[label="data normal distributed\nor n large?"];
+	ordinal[label="1, 2, or >2 groups?"];
+	nominal[label="?"];
+			 
+	data->IR[label="interval/ratio"];
+	data->nominal[label="nominal/discrete"];
+	data->ordinal[label="ordinal"];
+
+	normal[label="1, 2, or >2 groups?"];
+	notnormal[label="transform into\nnormal?"];
+	trulynotnormal[label="1, 2, or >2 groups?"];
+
+	IR->normal[label="normal"];
+	IR->notnormal[label="not normal"];
+	notnormal->normal[label="yes"];
+	notnormal->trulynotnormal[label="no"];
+
+	onesamp[label="one-sample\nt-test"];
+	normal->onesamp[label="1 group"];
+
+
+	twosamp[label="paired or\nindependent?"];
+	pairedttest[label="paired\nt-test"];
+	normal->twosamp[label="2 groups"];
+	twosamp->pairedttest[label="paired"];
+
+	twosampNN[label="paired or\nindependent?"];
+	indepTwosampNN[label="Wilcoxon-Mann-Whitney\ntest"];
+
+	trulynotnormal->twosampNN[label="2 groups"];
+	twosampNN->indepTwosampNN[label="independent"];
+	
+	twosampOrd[label="paired or\nindependent?"];
+	ordinal->twosampOrd[label="2 groups"];
+	twosampOrd->indepTwosampNN[label="indepdendent"];
+
+
+	ttest[label="t-test",color="lightblue"];
+	twosamp->ttest[label="independent"];
+
+	pairedTwosampNN[label="?",color="lightblue"];
+	twosampNN->pairedTwosampNN[label="paired"];
+	twosampOrd->pairedTwosampNN[label="paired"];
+}
+	
+

statistics/figs/fig9.dot

@@ -0,0 +1,54 @@
+digraph G {
+	rankdir=TB;
+	ranksep=0.2;
+	node [fontsize=12, shape=rectangle, style=filled, nodesep=0.75,ranksep=0.95];
+        edge [penwidth=2, fontsize=10 ];
+
+
+	data[label="type of data?"];
+	IR[label="data normal distributed\nor n large?"];
+	ordinal[label="1, 2, or >2 groups?"];
+	nominal[label="?"];
+			 
+	data->IR[label="interval/ratio"];
+	data->nominal[label="nominal/discrete"];
+	data->ordinal[label="ordinal"];
+
+	normal[label="1, 2, or >2 groups?"];
+	notnormal[label="transform into\nnormal?"];
+	trulynotnormal[label="1, 2, or >2 groups?"];
+
+	IR->normal[label="normal"];
+	IR->notnormal[label="not normal"];
+	notnormal->normal[label="yes"];
+	notnormal->trulynotnormal[label="no"];
+
+	onesamp[label="one-sample\nt-test"];
+	normal->onesamp[label="1 group"];
+
+
+	twosamp[label="paired or\nindependent?"];
+	pairedttest[label="paired\nt-test"];
+	normal->twosamp[label="2 groups"];
+	twosamp->pairedttest[label="paired"];
+
+	twosampNN[label="paired or\nindependent?"];
+	indepTwosampNN[label="Wilcoxon-Mann-Whitney\ntest"];
+
+	trulynotnormal->twosampNN[label="2 groups"];
+	twosampNN->indepTwosampNN[label="independent"];
+	
+	twosampOrd[label="paired or\nindependent?"];
+	ordinal->twosampOrd[label="2 groups"];
+	twosampOrd->indepTwosampNN[label="independent"];
+
+
+	ttest[label="t-test"];
+	twosamp->ttest[label="independent"];
+
+	signtest[label="sign test"];
+	twosampNN->signtest[label="paired"];
+	twosampOrd->signtest[label="paired"];
+}
+	
+

statistics/figs/generate.py

@@ -0,0 +1,106 @@
+from __future__ import division
+import seaborn as sns
+import sys
+sys.path.append('/home/fabee/code/')
+from matplotlib.pyplot import *
+from fabee.Plotting import *
+from scipy import stats
+from numpy import *
+
+sns.set_context("talk", font_scale=1.5, rc={"lines.linewidth": 2.5})
+
+# ---------------------------------------------------------------------------
+fig, ax = subplots()
+fig.subplots_adjust(bottom=.3, left=.3)
+n = 50
+x = loadtxt('scripts/thymusglandweights.dat')[:n]
+ax.bar([0,1],[mean(x),mean(x)],yerr = [std(x,ddof=1), std(x,ddof=1)/sqrt(n)],
+       facecolor='dodgerblue', alpha=.8,width=.7, align='center',
+       error_kw={'color':'k','lw':2}, capsize=10, ecolor='k')
+ax.set_title('standard deviation or standard error?',fontsize=14, fontweight='bold')
+
+ax.set_xlim([-.5,1.5])
+box_off(ax)
+#disjoint_axes(ax)
+ax.set_xticks([0,1])
+ax.set_xticklabels([r'$\hat\sigma$', r'$\frac{\hat\sigma}{\sqrt{n}}$'], fontsize=30)
+
+ax.set_ylabel(r'$\frac{1}{n}\sum_{i=1}^n x_i$',fontsize=30, fontweight='bold')
+
+fig.savefig('figs/StandardErrorOrStandardDeviation.pdf')
+
+# ---------------------------------------------------------------------------
+fig, ax = subplots()
+
+t = linspace(-5,5,1000)
+t2 = linspace(stats.laplace.ppf(0.025),stats.laplace.ppf(1-0.025),1000)
+
+ax.fill_between(t,stats.laplace.pdf(t),color='dodgerblue')
+ax.set_xticks([])
+ax.text(5,-0.05, r'$\hat m$',fontsize=30)
+ax.text(0,0.7, r'$m$',fontsize=30)
+ax.set_yticks([])
+#disjoint_axes(ax)
+box_off(ax)
+
+ax.set_title('putative sampling distribution of the median',fontsize=14, fontweight='bold')
+ax.axis([-5,5,0,.8])
+ax.plot([0,0],[0,.7],'--k',lw=2)
+
+fig.savefig('figs/samplingDistributionMedian00.pdf')
+
+ax.fill_between(t2,stats.laplace.pdf(t2),color='crimson')
+
+fig.savefig('figs/samplingDistributionMedian01.pdf')
+
+# ---------------------------------------------------------------------------
+fig, ax = subplots()
+k = 7
+N = 21
+F = stats.f
+t = linspace(1e-6,8,1000)
+t2= linspace(F.ppf(0.95,k-1,N-k),8,1000)
+
+ax.fill_between(t,F.pdf(t,k-1,N-k),color='dodgerblue')
+ax.fill_between(t2,F.pdf(t2,k-1,N-k),color='crimson')
+ax.set_xlabel('group MS/ error MS')
+ax.set_ylabel(r'p(group MS/ error MS| $H_0$)')
+ax.set_title('F-distribution',fontsize=14, fontweight='bold')
+ax.set_ylim((0,0.8))
+box_off(ax)
+fig.savefig('figs/Fdistribution00.pdf')
+
+# ---------------------------------------------------------------------------
+fig, ax = subplots()
+n = 5
+p = stats.t.pdf
+t = linspace(-5,8,1000)
+t0 = 1.5
+t00 = 1.
+
+mu0 = 3
+t1 = linspace(-5,t00,1000)
+t2 = linspace(t0,8,1000)
+t3 = linspace(-5,-t0,1000)
+ax.fill_between(t,p(t,n-1),color='dodgerblue',alpha=1)
+ax.fill_between(t2,p(t2,n-1),color='indigo',alpha=1)
+ax.fill_between(t3,p(t3,n-1),color='indigo',alpha=1)
+ax.set_xlabel('t')
+ax.set_ylabel(r'sampling distribution')
+ax.set_ylim((0,0.8))
+box_off(ax)
+fig.savefig('figs/experimentalDesign00.pdf')
+
+
+ax.fill_between(t,p(t,n-1,loc=mu0),color='lime',alpha=.5)
+ax.fill_between(t1,p(t1,n-1,loc=mu0),color='magenta',alpha=1)
+ax.arrow(0,.4,mu0,0,head_width=0.05)
+ax.arrow(mu0,.4,-mu0,0,head_width=0.05)
+ax.text(mu0/2,.45,r'$\delta$',fontsize=20)
+ax.set_xlabel('t')
+ax.set_ylabel(r'sampling distribution')
+ax.set_ylim((0,0.8))
+box_off(ax)
+fig.savefig('figs/experimentalDesign01.pdf')
+
+

statistics/figs/generate03.py

@@ -0,0 +1,265 @@
+import sys
+import seaborn as sns
+sys.path.append('/home/fabee/code/')
+from matplotlib.pyplot import *
+from fabee.Plotting import *
+from scipy import stats
+from numpy import *
+
+sns.set_context("talk", font_scale=1.5, rc={"lines.linewidth": 2.5})
+
+def hinton(matrix, max_weight=None, ax=None):
+    """Draw Hinton diagram for visualizing a weight matrix."""
+    ax = ax if ax is not None else gca()
+
+    if not max_weight:
+        max_weight = 2**np.ceil(np.log(np.abs(matrix).max())/np.log(2))
+
+    ax.patch.set_facecolor('gray')
+    ax.set_aspect('equal', 'box')
+    ax.xaxis.set_major_locator(NullLocator())
+    ax.yaxis.set_major_locator(NullLocator())
+
+    for (x,y),w in np.ndenumerate(matrix):
+        color = 'white' if w > 0 else 'black'
+        size = np.sqrt(np.abs(w))
+        rect = Rectangle([x - size / 2, y - size / 2], size, size,
+                             facecolor=color, edgecolor=color)
+        ax.add_patch(rect)
+
+    ax.autoscale_view()
+    ax.invert_yaxis()
+
+# ---------------------------------------------------------------------------
+fig, ax = subplots()
+fig.subplots_adjust(bottom=.2)
+
+ax.bar([0,1],[.2,.8],facecolor='dodgerblue', alpha=.8,width=.7, align='center')
+ax.set_title('Bernoulli distribution',fontsize=16, fontweight='bold')
+
+ax.set_xlim([-.5,1.5])
+box_off(ax)
+#disjoint_axes(ax)
+ax.set_xlabel('outcomes',fontsize=14, fontweight='bold')
+ax.set_ylabel('P(outcome)',fontsize=14, fontweight='bold')
+ax.set_xticks([0,1])
+ax.set_xticklabels([0,1])
+ax.set_ylim((0,1))
+
+fig.savefig('figs/Bernoulli.pdf')
+
+# ---------------------------------------------------------------------------
+fig, ax = subplots()
+fig.subplots_adjust(bottom=.2)
+n = 5
+k = arange(0,n)
+ax.bar(k,0*k+1./n,facecolor='dodgerblue', alpha=.8,width=.7, align='center')
+ax.set_title('uniform distribution',fontsize=16, fontweight='bold')
+
+box_off(ax)
+#disjoint_axes(ax)
+ax.set_xlabel('k',fontsize=14, fontweight='bold')
+ax.set_ylabel('P(X=k)',fontsize=14, fontweight='bold')
+ax.set_xticks(k)
+ax.set_xticklabels(k+1)
+ax.set_ylim((0,1))
+fig.savefig('figs/Uniform.pdf')
+
+# ---------------------------------------------------------------------------
+
+for i,(n,p) in enumerate(zip([10,20],[.5,.8])):
+    fig, ax = subplots()
+
+    fig.subplots_adjust(bottom=.2)
+    k = arange(n+1)
+    
+    ax.bar(k,stats.binom.pmf(k,n,p),facecolor='dodgerblue', alpha=.8,width=.7, align='center')
+    ax.set_title(r'binomial distribution $B\left(%.2f, %i\right)$' % (p,n),fontsize=16, fontweight='bold')
+    
+    box_off(ax)
+    #disjoint_axes(ax)
+    ax.set_xlabel('k',fontsize=14, fontweight='bold')
+    ax.set_ylabel('P(k)',fontsize=14, fontweight='bold')
+    ax.set_xticks(k)
+    ax.set_xticklabels(k)
+    ax.set_xlim((-1,n+1))
+    ax.set_ylim((0,1))
+    fig.savefig('figs/Binomial%02i.pdf' % (i,))
+
+
+# ---------------------------------------------------------------------------
+n = 20
+for i, lam in enumerate([5, 0.05]):
+    fig, ax = subplots()
+
+    fig.subplots_adjust(bottom=.2)
+    k = arange(n+1)
+    
+    ax.bar(k,stats.poisson.pmf(k,lam),facecolor='dodgerblue', alpha=.8,width=.7, align='center')
+    ax.set_title(r'Poisson distribution $\lambda=%.2f$' % (lam,),fontsize=16, fontweight='bold')
+    
+    box_off(ax)
+    #disjoint_axes(ax)
+    ax.set_xlabel('k',fontsize=14, fontweight='bold')
+    ax.set_ylabel('P(k)',fontsize=14, fontweight='bold')
+    ax.set_xticks(k)
+    ax.set_xticklabels(k)
+    ax.set_xlim((-1,n+1))
+    ax.set_ylim((0,1))
+    fig.savefig('figs/Poisson%02i.pdf' % (i,))
+
+# ---------------------------------------------------------------------------
+fig, ax = subplots()
+
+fig.subplots_adjust(bottom=.2)
+t = linspace(-3,3,200)
+ax.fill_between(t,stats.norm.pdf(t),facecolor='dodgerblue', alpha=.8)
+ax.set_title(r'Gaussian/Normal distribution $N(\mu,\sigma)$',fontsize=16, fontweight='bold')
+    
+box_off(ax)
+#disjoint_axes(ax)
+ax.set_xlabel('x',fontsize=14, fontweight='bold')
+ax.set_ylabel('p(x)',fontsize=14, fontweight='bold')
+fig.savefig('figs/Gaussian00.pdf')
+
+# ---------------------------------------------------------------------------
+
+fig, ax = subplots()
+n = 10
+kk = 5
+p = .5
+fig.subplots_adjust(bottom=.2)
+k = arange(n+1)
+    
+ax.bar(k,stats.binom.pmf(k,n,p),facecolor='dodgerblue', alpha=.8,width=.7, align='center')
+ax.bar(k[:kk+1],stats.binom.pmf(k[:kk+1],n,p),facecolor='crimson', alpha=.5,width=.7, align='center')
+ax.set_title(r'binomial distribution $B\left(\frac{1}{2}, %i\right)$' % (n,), fontsize=16, fontweight='bold')
+
+box_off(ax)
+#disjoint_axes(ax)
+ax.set_xlabel('k',fontsize=14, fontweight='bold')
+ax.set_ylabel('P(k)',fontsize=14, fontweight='bold')
+ax.set_xticks(k)
+ax.set_xticklabels(k)
+ax.set_xlim((-1,n+1))
+ax.set_ylim((0,1))
+fig.savefig('figs/BinomialCdf00.pdf' )
+
+
+fig, ax = subplots()
+n = 10
+kk = 5
+p = .5
+fig.subplots_adjust(bottom=.2)
+k = arange(n+1)
+    
+ax.bar(k,stats.binom.pmf(k,n,p),facecolor='dodgerblue', alpha=.8,width=.7, align='center',label='p.m.f.')
+ax.bar(k[:kk+1],stats.binom.pmf(k[:kk+1],n,p),facecolor='crimson', alpha=.5,width=.7, align='center')
+ax.plot(k,stats.binom.cdf(k,n,p),'ok',mfc='crimson', alpha=1.,label='c.d.f.', ms=15)
+
+ax.set_title(r'binomial distribution $B\left(\frac{1}{2}, %i\right)$' % (n,), fontsize=16, fontweight='bold')
+ax.legend(frameon=False, loc='best')
+box_off(ax)
+#disjoint_axes(ax)
+ax.set_xlabel('k',fontsize=14, fontweight='bold')
+ax.set_ylabel('P(k)',fontsize=14, fontweight='bold')
+ax.set_xticks(k)
+ax.set_xticklabels(k)
+ax.set_xlim((-1,n+1))
+ax.set_ylim((0,1.1))
+fig.savefig('figs/BinomialCdf01.pdf' )
+
+fig, ax = subplots()
+n = 10
+kk = 2
+p = .5
+fig.subplots_adjust(bottom=.2)
+k = arange(n+1)
+    
+ax.bar(k,stats.binom.pmf(k,n,p),facecolor='dodgerblue', alpha=.8,width=.7, align='center',label='p.m.f.')
+ax.bar(k[:kk+1],stats.binom.pmf(k[:kk+1],n,p),facecolor='crimson', alpha=.5,width=.7, align='center')
+ax.bar(k[-kk-1:],stats.binom.pmf(k[-kk-1:],n,p),facecolor='crimson', alpha=.5,width=.7, align='center')
+
+ax.set_title(r'binomial distribution $B\left(\frac{1}{2}, %i\right)$' % (n,), fontsize=16, fontweight='bold')
+ax.legend(frameon=False, loc='best')
+box_off(ax)
+#disjoint_axes(ax)
+ax.set_xlabel('k',fontsize=14, fontweight='bold')
+ax.set_ylabel('P(k)',fontsize=14, fontweight='bold')
+ax.set_xticks(k)
+ax.set_xticklabels(k)
+ax.set_xlim((-1,n+1))
+ax.set_ylim((0,1.1))
+fig.savefig('figs/BinomialExample00.pdf' )
+
+
+#------------------------------------------------------
+fig = figure(figsize=(10,3.5))
+ax = fig.add_axes([.1,.13,.6,.3])
+
+n = 10
+p = [.5,.8]
+q = [.7, .3]
+fig.subplots_adjust(bottom=0.2)
+k = arange(n+1)
+P = vstack((stats.binom.pmf(k,n,p[0])*q[0], stats.binom.pmf(k,n,p[1])*q[1])).T
+
+hinton(P, ax = None)
+
+#disjoint_axes(ax)
+ax.set_xticks(k)
+ax.set_xticklabels(k)
+ax.set_yticks([0,1])
+ax.set_ylim((-.5,1.5))
+ax.set_xlim((-.5,n+.5))
+ax.set_yticklabels(['subject #1', 'subject #2'])
+fig.savefig('figs/Joint00.pdf' )
+
+ax = fig.add_axes([.75,.13,.2,.3])
+ax.barh([0,1],q, facecolor='dodgerblue',alpha=.8, align='center')
+box_off(ax)
+#disjoint_axes(ax)
+ax.set_xticks([0,.5,1.])
+ax.set_yticks([])
+ax.set_ylim((-.5,1.5))
+fig.savefig('figs/Joint01.pdf' )
+
+ax = fig.add_axes([.1,.6,.6,.2])
+ax.bar(k,sum(P,axis=1), facecolor='dodgerblue',alpha=.8, align='center')
+a = .7
+ax.axis([-a,n-a+1.5,0,1])
+box_off(ax)
+#disjoint_axes(ax)
+ax.set_xticks([])
+ax.set_yticks([0,.3])
+ax.set_ylim((0,.3))
+fig.savefig('figs/Joint02.pdf' )
+
+
+#------------------------------------------------------
+n = 10
+k = arange(n+1)
+p = [.5,.8]
+q = [.7, .3]
+P = vstack((stats.binom.pmf(k,n,p[0])*q[0], stats.binom.pmf(k,n,p[1])*q[1]))
+Pk = sum(P,axis=0)
+
+fig = figure()
+for i,kk in enumerate(k):
+    ax = fig.add_subplot(3,4,i+1)
+    fig.subplots_adjust(bottom=0.2)
+
+    ax.bar([0,1],P[:,i]/Pk[i], facecolor='dodgerblue',alpha=.8, align='center')
+
+    
+    #disjoint_axes(ax)
+    ax.set_xticks([0,1])
+    ax.set_xticklabels(['#1','#2'], fontsize=8)
+    ax.set_yticks([0,.5,1])
+    ax.set_yticklabels([0,.5,1],fontsize=8)
+    ax.set_xlim((-.5,1.5))
+    ax.set_ylim((0,1))
+    ax.set_title('P({#1,#2}| %i successes)'  % (i,), fontsize=8)
+
+fig.subplots_adjust(wspace=.8, hspace=.8)
+fig.savefig('figs/Posterior00.pdf')

statistics/figs/generatePlots.py

@@ -0,0 +1,216 @@
+import sys
+sys.path.append('/home/fabee/code/')
+import seaborn as sns
+from matplotlib.pyplot import *
+from scipy import stats
+from numpy import *
+
+from matplotlib.ticker import NullFormatter
+
+sns.set_context("talk", font_scale=1.5, rc={"lines.linewidth": 2.5})
+
+# --------------- PLOT 1 -------------------------
+# the random data
+distr = stats.uniform
+col = '+*0<>v'
+
+for k,distr in enumerate([stats.laplace, stats.norm, stats.expon,stats.uniform]):
+    col = [col[i] for i in random.permutation(6)]
+    x = random.randn(5000)
+
+    nullfmt   = NullFormatter()         # no labels
+
+    # definitions for the axes
+    left, width = 0.1, 0.65
+    bottom, height = 0.1, 0.65
+    bottom_h = left_h = left+width+0.02
+    
+    rect_scatter = [left + 0.22, bottom + 0.22 , width, height]
+    rect_histx = [left + 0.22, bottom, width, 0.2]
+    rect_histy = [left, bottom + 0.22 , 0.2, height]
+    
+    # start with a rectangular Figure
+    fig = figure(figsize=(8,8))
+    
+    axQQ = axes(rect_scatter)
+    axHistx = axes(rect_histx)
+    axHisty = axes(rect_histy)
+    
+    # no labels
+    axHistx.yaxis.set_major_formatter(nullfmt)
+    axHisty.xaxis.set_major_formatter(nullfmt)
+    axQQ.xaxis.set_major_formatter(nullfmt)
+    axQQ.yaxis.set_major_formatter(nullfmt)
+    
+    
+    
+    # the scatter plot:
+    z = distr.ppf(stats.norm.cdf(x))
+    y = linspace(amin(z),amax(z),1000)
+    
+    
+    z = distr.ppf(stats.norm.cdf(x))
+    if distr != stats.norm:
+        if distr == stats.uniform:
+            axQQ.plot(x, z,'ok',marker=col[0],ms=5,label='c.d.f.')
+        else:
+            axQQ.plot(x, z,'ok',marker=col[0],ms=5,label='correct')
+
+        if distr != stats.expon:
+            axQQ.plot((z-amin(z))/(amax(z)-amin(z))*(amax(x)-amin(x)) + amin(x),\
+                      (x-amin(x))/(amax(x)-amin(x))*(amax(z)-amin(z)) + amin(z),'ok',marker=col[1],ms=5)
+            axQQ.plot(x, (x-amin(x))/(amax(x)-amin(x))*(amax(z)-amin(z)) + amin(z),'ok',marker=col[2],ms=5)
+        
+    
+    # now determine nice limits by hand:
+    axHistx.hist(x, bins=100,normed=True)
+    if distr != stats.expon:
+        axHisty.plot(distr.pdf(y),y)
+        z2 = distr.pdf(y)
+        y = hstack((y[0],y,y[-1]))
+        z2 = hstack((0,z2,0))
+        axHisty.fill(z2,y,color=(.0,.0,1.))
+    
+    axQQ.set_xlim(axHistx.get_xlim())
+    axQQ.set_ylim(axHisty.get_ylim())
+
+    if distr == stats.uniform:
+        axQQ.set_ylim((-.1,1.1))
+        axHisty.set_ylim((-.1,1.1))
+        axHisty.set_xlim((.0,1.1))
+    
+    axHistx.set_xlabel('x',fontsize=16)
+    axHistx.set_ylabel('p(x)',fontsize=16)
+    axHisty.set_ylabel('y',fontsize=16)
+    axHisty.set_xlabel('p(y)',fontsize=16)
+
+    fig.savefig('figs/HE%i.png' % (k,))
+    if distr == stats.norm:
+        axQQ.plot(x, z,'ok',marker=col[0],ms=5)
+    elif distr == stats.expon:
+        axHisty.plot(distr.pdf(y),y)
+        z2 = distr.pdf(y)
+        y = hstack((y[0],y,y[-1]))
+        z2 = hstack((0,z2,0))
+        axHisty.fill(z2,y,color=(.0,.0,1.))
+       
+    else:
+        axQQ.legend(loc=2)
+    fig.savefig('figs/HE%iSolution.png' % (k,))
+
+# ####################################################3
+fig = figure()
+
+
+ax = fig.add_subplot(111)
+xx = linspace(-3.,stats.norm.ppf(1-0.2),1000)
+
+x = linspace(-3.,3.,1000)
+y = stats.norm.pdf(x,scale=1)
+yy = stats.norm.pdf(xx,scale=1)
+yy[0] = 0
+yy[-1] = 0
+
+ax.plot(x,y,'k-',lw=2)
+ax.plot(x,stats.norm.pdf(x),'k-',lw=1)
+ax.set_xlabel('x',fontsize=16)
+ax.set_ylabel('pdf',fontsize=16)
+ax.fill(xx,yy,'b')
+
+ax.set_xlim(-3.,3.)
+
+ax.text(xx[-1],-.1,'b');
+
+ax.text(xx[-1],.4,'p(x)',color='k');
+ax.text(xx[0],.3,'F(b) = P(x <= b)',color='b');
+
+#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
+
+fig.savefig('figs/cdf.png')
+
+#-----------------------------
+fig = figure()
+
+
+ax = fig.add_subplot(111)
+xx = linspace(-3.,stats.norm.ppf(1-0.2),1000)
+
+x = linspace(-3.,3.,1000)
+y = stats.norm.pdf(x,scale=1)
+yy = stats.norm.pdf(xx,scale=1)
+yy[0] = 0
+yy[-1] = 0
+
+ax.plot(x,y,'k-',lw=2)
+ax.plot(x,stats.norm.cdf(x),'b-',lw=1)
+ax.set_xlabel('x/b',fontsize=16)
+ax.set_ylabel('pdf/cdf',fontsize=16)
+
+ax.set_xlim(-3.,3.)
+
+ax.text(xx[-1],.4,'p(x)',color='k');
+ax.text(xx[0],.3,'F(b) = P(x <= b)',color='b');
+
+#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
+
+fig.savefig('figs/cdf2.png')
+
+# ####################################################3
+fig = figure()
+
+
+ax = fig.add_subplot(111)
+
+x = hstack((linspace(-3.,stats.norm.ppf(0.13),1000),\
+            linspace(stats.norm.ppf(1-0.13),3.,1000)))
+
+xx = hstack((linspace(-3.,stats.norm.ppf(0.2),1000),\
+            linspace(stats.norm.ppf(1-0.2),3.,1000)))
+
+y = stats.norm.pdf(x,scale=1)
+yy = stats.norm.pdf(xx,scale=1)
+
+y[[0,999,1000,-1]] = 0
+yy[[0,999,1000,-1]] = 0
+
+t = linspace(-3.,3.,1000)
+ax.plot(t,stats.norm.pdf(t),'k-',lw=2)
+
+ax.fill(xx[:1000],yy[:1000],'b')
+ax.fill(xx[1000:],yy[1000:],'b')
+ax.text(xx[1000],-.1,'b')
+ax.text(xx[999],-.1,'-b')
+ax.text(.2,.7,'P(|x|>b) =$\\alpha$',color='b');
+
+#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
+
+fig.savefig('figs/pval0.png')
+
+#---------------------------------------------------
+fig = figure()
+
+ax = fig.add_subplot(111)
+
+t = linspace(-3.,3.,1000)
+ax.plot(t,stats.norm.pdf(t),'k-',lw=2)
+
+
+ax.fill(x[:1000],y[:1000],'r')
+ax.fill(x[1000:],y[1000:],'r')
+
+
+ax.text(x[1000],-.1,'t')
+ax.text(x[999],-.1,'-t')
+
+ax.text(.2,.5,'P(|x| > t) = p-value',color='r');
+
+#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
+
+fig.savefig('figs/ pval1.png')
+
+
+
+# show()
+                      
+
+#-----------------------------

statistics/figs/generateTPlots.py

@@ -0,0 +1,184 @@
+import sys
+import seaborn as sns
+sys.path.append('/home/fabee/code')
+from matplotlib.pyplot import *
+from scipy import stats
+from numpy import *
+
+sns.set_context("talk", font_scale=1.5, rc={"lines.linewidth": 2.5})
+
+# define the curves
+x = np.linspace(2, 20, 200)
+n = 16.
+
+
+X =random.randn(n)*4.+12.5
+fig = figure()
+ax = fig.add_subplot(111)
+ax.set_xlim(5, 18)
+#ax.set_ylim(0, .5)
+ax.plot([10,10],[-.2,.2],'k-',lw=2)
+ax.text(10,.3,r'stimulus position',rotation=-30);
+ax.plot([12.5,12.5],[-.2,.2],'b-',lw=2)
+ax.text(12.5,.3,r'$\hat\mu$',rotation=-45);
+
+ax.set_xlabel('x eye position')
+#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
+ax.plot(X,0*X,'ob',label='fixations',mfc='orange',ms=10)
+fig.savefig('figs/repetition0.png')
+
+# ####################################################3
+fig = figure()
+
+
+ax = fig.add_subplot(111)
+
+ax.plot(x,-stats.norm.pdf(x,loc=10,scale=4),'orange',label=r'Null distribution of x')
+
+
+ax.set_xlim(5, 18)
+# ax.set_ylim(0, .5)
+
+ax.plot([10,10],[-.2,.2],'k-',lw=2)
+ax.text(10,.3,r'stimulus position',rotation=-30);
+ax.plot([12.5,12.5],[-.2,.2],'b-',lw=2)
+ax.text(12.5,.3,r'$\hat\mu$',rotation=-45);
+ax.legend()
+
+ax.set_xlabel('x eye position')
+#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
+ax.plot(X,0*X,'ob',label='fixations',mfc='orange',ms=10)
+
+fig.savefig('figs/repetition1.png')
+
+
+# ####################################################3
+fig = figure()
+
+
+ax = fig.add_subplot(111)
+
+ax.plot(x,-stats.norm.pdf(x,loc=10,scale=4),'orange',label=r'Null distribution of x')
+ax.plot(x,-stats.t.pdf(x,n-1,loc=10,scale=1),'b',label=r'Null distribution of $t$')
+
+ax.set_xlim(5, 18)
+# ax.set_ylim(0, .5)
+
+ax.plot([10,10],[-.2,.2],'k-',lw=2)
+ax.text(10,.3,r'stimulus position',rotation=-30);
+ax.plot([12.5,12.5],[-.2,.2],'b-',lw=2)
+ax.text(12.5,.3,r'$\hat\mu$',rotation=-45);
+ax.legend()
+
+ax.set_xlabel('x eye position')
+#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
+ax.plot(X,0*X,'ob',label='fixations',mfc='orange',ms=10)
+
+fig.savefig('figs/repetition2.png')
+
+# ####################################################3
+fig = figure()
+
+
+ax = fig.add_subplot(111)
+xx = linspace(stats.norm.ppf(0.05),stats.norm.ppf(1-0.05),100)
+xx += 10.
+
+yy = -stats.norm.pdf(xx,loc=10.,scale=1)
+xx = hstack((xx[0],xx,xx[-1]))
+yy = hstack((0,yy,0))
+
+ax.plot(x,-stats.norm.pdf(x,loc=10,scale=4),'orange',label=r'Null distribution of x')
+ax.plot(x,-stats.t.pdf(x,n-1,loc=10,scale=1),'b',label=r'Null distribution of $t$')
+
+ax.fill(xx,yy,'c')
+
+ax.set_xlim(5, 18)
+# ax.set_ylim(0, .5)
+
+ax.plot([10,10],[-.2,.2],'k-',lw=2)
+ax.text(10,.3,r'stimulus position',rotation=-30);
+ax.plot([12.5,12.5],[-.2,.2],'b-',lw=2)
+ax.text(12.5,.3,r'$\hat\mu$',rotation=-45);
+ax.legend()
+
+ax.set_xlabel('x eye position')
+#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
+ax.plot(X,0*X,'ob',label='fixations',mfc='orange',ms=10)
+
+fig.savefig('figs/repetition3.png')
+
+
+# ####################################################3
+fig = figure()
+
+
+ax = fig.add_subplot(111)
+xx = linspace(stats.norm.ppf(0.05),stats.norm.ppf(1-0.05),100)
+xx += 10.
+
+yy = -stats.norm.pdf(xx,loc=10.,scale=1)
+xx = hstack((xx[0],xx,xx[-1]))
+yy = hstack((0,yy,0))
+
+ax.plot(x,-stats.norm.pdf(x,loc=10,scale=4),'orange',label=r'Null distribution of x')
+ax.plot(x,-stats.t.pdf(x,n-1,loc=10,scale=1),'b',label=r'Null distribution of $t$')
+
+ax.fill(xx,yy,'c')
+
+ax.set_xlim(5, 18)
+# ax.set_ylim(0, .5)
+
+ax.plot([10,10],[-.2,.2],'k-',lw=2)
+ax.text(10,.3,r'stimulus position',rotation=-30);
+ax.plot([12.5,12.5],[-.2,.2],'b-',lw=2)
+ax.text(12.5,.3,r'$\hat\mu$',rotation=-45)
+
+ax.plot([xx[0],xx[-1]],[0,0],'-g',label=r'$H_0$',lw=4)
+ax.plot([0,xx[0]],[0,0],'-r',label=r'$H_1$',lw=4)
+ax.plot([xx[-1],20],[0,0],'-r',lw=4)
+
+ax.legend()
+
+ax.set_xlabel('x eye position')
+#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
+ax.plot(X,0*X,'ob',label='fixations',mfc='orange',ms=10)
+
+fig.savefig('figs/repetition4.png')
+
+
+# ####################################################3
+fig = figure()
+
+
+ax = fig.add_subplot(111)
+
+ax.plot(x,-stats.norm.pdf(x,loc=10,scale=4),'orange',label=r'Null distribution of x')
+ax.plot(x,-stats.t.pdf(x,n-1,loc=10,scale=1),'b',label=r'Null distribution of $t$')
+
+xx = linspace(0,stats.norm.ppf(0.05)+10.,100)
+yy = -stats.norm.pdf(xx,loc=10.,scale=1)
+xx = hstack((xx[0],xx,xx[-1]))
+yy = hstack((0,yy,0))
+ax.fill(xx,yy,'magenta')
+
+xx = linspace(stats.norm.ppf(1-0.05)+10.,20,100)
+yy = -stats.norm.pdf(xx,loc=10.,scale=1)
+xx = hstack((xx[0],xx,xx[-1]))
+yy = hstack((0,yy,0))
+ax.fill(xx,yy,'magenta')
+
+ax.set_xlim(5, 18)
+# ax.set_ylim(0, .5)
+
+ax.plot([10,10],[-.2,.2],'k-',lw=2)
+ax.text(10,.3,r'stimulus position',rotation=-30);
+ax.plot([12.5,12.5],[-.2,.2],'b-',lw=2)
+ax.text(12.5,.3,r'$\hat\mu$',rotation=-45);
+ax.legend()
+
+ax.set_xlabel('x eye position')
+#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
+ax.plot(X,0*X,'ob',label='fixations',mfc='orange',ms=10)
+
+fig.savefig('figs/repetition5.png')

statistics/figs/multipletesting.py

@@ -0,0 +1,72 @@
+from __future__ import division
+from numpy import *
+from scipy import stats
+from matplotlib.pyplot import *
+
+N = random.randn
+
+m = 2000
+n = 20
+
+T = zeros((m,))
+R = zeros((m,))
+pT = zeros((m,))
+pR = zeros((m,))
+
+for k in xrange(m):
+    x = N(n)
+    y = N(n)
+
+    T[k], pT[k] = stats.ttest_ind(x,y)
+    R[k], pR[k] = stats.ranksums(x,y)
+
+a = stats.t.ppf([0.025,1.-0.025], n-1)
+b = stats.norm.ppf([0.025,1.-0.025])
+
+
+fig = figure(figsize=(8,8),dpi=100)
+ax = fig.add_axes([.3,.3,.6,.6])
+axb = fig.add_axes([.3,.1,.6,.2])
+axl = fig.add_axes([.1,.3,.2,.6])
+
+ax.plot(T,R,'ok',mfc=(.7,.7,.7))
+axb.hist(T,bins=50,facecolor=(1.,.7,.7),normed=True)
+axl.hist(R,bins=50,facecolor=(.7,.7,1.),normed=True,orientation='horizontal')
+axl.axis([0,1,-5,5])
+axb.plot([a[0],a[0]],[0,1],'k--',lw=2)
+axb.plot([a[1],a[1]],[0,1],'k--',lw=2)
+
+axl.plot([0,1],[b[0],b[0]],'k--',lw=2)
+axl.plot([0,1],[b[1],b[1]],'k--',lw=2)
+axl.set_ylabel('standardized U statistic', fontsize=16)
+axb.set_xlabel('t statistic', fontsize=16)
+
+# print sum(1.*(T < a[0] ))/m + sum(1.*(T > a[1]))/m
+# print sum(1.*(R < b[0] ))/m + sum(1.*(R > b[1]))/m
+
+ax.fill([-5,a[0],a[0],-5],[-5,-5,5,5],color=(1.,.7,.7),alpha=.5)
+ax.fill([a[1],5,5,a[1]],[-5,-5,5,5],color=(1.,.7,.7),alpha=.5)
+axb.fill([-5,a[0],a[0],-5],[0,0,1,1],color=(1.,.7,.7),alpha=.5)
+axb.fill([a[1],5,5,a[1]],[0,0,1,1],color=(1.,.7,.7),alpha=.5)
+
+
+ax.fill([-5,-5,5,5],[-5,b[0],b[0],-5],color=(.7,.7,1.),alpha=.5)
+ax.fill([-5,-5,5,5],[b[1],5,5,b[1]],color=(.7,.7,1.),alpha=.5)
+axl.fill([0,0,1,1],[-5,b[0],b[0],-5],color=(.7,.7,1.),alpha=.5)
+axl.fill([0,0,1,1],[b[1],5,5,b[1]],color=(.7,.7,1.),alpha=.5)
+
+
+
+axb.axis([-5,5,0,1])
+ax.axis([-5,5,-5,5])
+
+axl.set_xticks([])
+axb.set_yticks([])
+axl = axl.twiny()
+axb = axb.twinx()
+axl.set_xticks([0,.5,1.])
+axb.set_yticks([0,.5,1.])
+
+
+
+fig.savefig('multipletesting.pdf')