From f7c313307ceec5f78458848b0c0f313493088e82 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 6 Jun 2016 11:53:32 -0300 Subject: [PATCH 01/46] template vazio --- Aulas/BE-Nao_Param.tex | 154 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 154 insertions(+) create mode 100644 Aulas/BE-Nao_Param.tex diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex new file mode 100644 index 0000000..5b42d74 --- /dev/null +++ b/Aulas/BE-Nao_Param.tex @@ -0,0 +1,154 @@ +\everymath{\displaystyle} +\documentclass{beamer} +% \documentclass[handout]{beamer} + +%\usepackage[pdftex]{color,graphicx} +\usepackage{amsmath,amssymb,amsfonts} + +\mode +{ + % \usetheme{Darmstadt} + % \usetheme[hideothersubsections]{Hannover} + % \usetheme[hideothersubsections]{Goettingen} + \usetheme[hideothersubsections, right]{Berkeley} + + \usecolortheme{seahorse} + % \usecolortheme{dolphin} + \usecolortheme{rose} + % \usecolortheme{orchid} + + \useinnertheme[shadow]{rounded} + + \setbeamercovered{transparent} + % or whatever (possibly just delete it) +} + +\mode{ + \setbeamercolor{background canvas}{bg=black!5} + \usepackage{pgfpages} + \pgfpagesuselayout{4 on 1}[a4paper,border shrink=5mm, landscape] +} + +\usepackage[brazilian]{babel} +% or whatever + +% \usepackage[latin1]{inputenc} +\usepackage[utf8]{inputenc} +% or whatever + +\usepackage{times} +%\usepackage[T1]{fontenc} +% Or whatever. Note that the encoding and the font should match. If T1 +% does not look nice, try deleting the line with the fontenc. + + +\title%[] % (optional, use only with long paper titles) +{} + +\subtitle +{} % (optional) + +\author%[] % (optional, use only with lots of authors) +{Felipe Figueiredo}% \and S.~Another\inst{2}} +% - Use the \inst{?} command only if the authors have different +% affiliation. + +\institute[] % (optional, but mostly needed) +{ +} + % \inst{1}% + % Department of Computer Science\\ + % University of Somewhere + % \and + % \inst{2}% + % Department of Theoretical Philosophy\\ + % University of Elsewhere} +% - Use the \inst command only if there are several affiliations. +% - Keep it simple, no one is interested in your street address. + +\date%[] % (optional) +{} + +% \subject{Talks} +% This is only inserted into the PDF information catalog. Can be left +% out. + + + +% If you have a file called "university-logo-filename.xxx", where xxx +% is a graphic format that can be processed by latex or pdflatex, +% resp., then you can add a logo as follows: + +\pgfdeclareimage[height=1.6cm]{university-logo}{../logo} +\logo{\pgfuseimage{university-logo}} + + + +% Delete this, if you do not want the table of contents to pop up at +% the beginning of each subsection: +\AtBeginSubsection[] +%\AtBeginSection[] +{ + \begin{frame}{Sumário} + \tableofcontents[currentsection,currentsubsection] + \end{frame} +} + + +% If you wish to uncover everything in a step-wise fashion, uncomment +% the following command: + +\beamerdefaultoverlayspecification{<+->} + + +\begin{document} + +\begin{frame} + \titlepage +\end{frame} + +\begin{frame}{Sumário} + \tableofcontents + % You might wish to add the option [pausesections] +\end{frame} + + +%% Template +% \section{} + +% \subsection{} + +% \begin{frame}{} +% \begin{itemize} +% \item +% \end{itemize} +% \end{frame} + +% \begin{frame} +% \begin{columns} +% \begin{column}{5cm} +% \end{column} +% \begin{column}{5cm} +% \end{column} +% \end{columns} +% \end{frame} + +% \begin{frame}{} +% \includegraphics[height=0.4\textheight]{file1} +% \includegraphics[height=0.4\textheight]{file2} +% \includegraphics[height=0.4\textheight]{file3} +% \begin{figure} +% \caption{} +% \end{figure} +% \end{frame} + +% \begin{frame}{} +% \begin{definition} +% \end{definition} +% \begin{example} +% \end{example} +% \begin{block}{Exercício} +% \end{block} +% \end{frame} + +\end{document} From 8ff39fb1b7dd9691f0830bc8c8205a18fbdc70ce Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 6 Jun 2016 16:08:32 -0300 Subject: [PATCH 02/46] =?UTF-8?q?t=C3=ADtulo=20e=20capa?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Aulas/BE-Nao_Param.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 5b42d74..2075030 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -43,18 +43,18 @@ \title%[] % (optional, use only with long paper titles) -{} +{Testes não-paramétricos} \subtitle -{} % (optional) +{Ou: o que fazer caso seus dados não sejam normais?} % (optional) \author%[] % (optional, use only with lots of authors) {Felipe Figueiredo}% \and S.~Another\inst{2}} % - Use the \inst{?} command only if the authors have different % affiliation. -\institute[] % (optional, but mostly needed) -{ +\institute[INTO] % (optional, but mostly needed) +{Instituto Nacional de Traumatologia e Ortopedia } % \inst{1}% % Department of Computer Science\\ From 0d05f090b483b284cf9edf55fc59552803737b4a Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 6 Jun 2016 16:10:23 -0300 Subject: [PATCH 03/46] estrutura --- Aulas/BE-Nao_Param.tex | 18 ++++++++++++++++++ 1 file changed, 18 insertions(+) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 2075030..125e424 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -151,4 +151,22 @@ % \end{block} % \end{frame} +\section{Normalidade} + +\subsection{Revisão} + +\subsection[Normalidade]{Testes contra a normalidade} + +\section{Testes} + +\subsection{Revisão} + +\subsection[1 média]{Teste para 1 média} + +\subsection[2 médias]{Teste para 2 médias} + +\subsection[3+ médias]{Teste para 3 ou mais médias} + +\subsection[Correlação]{Teste de correlação} + \end{document} From 3594633cb8f89721fbabbc27d4ed991c8a303df0 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 6 Jun 2016 16:12:13 -0300 Subject: [PATCH 04/46] resumo (estrutura) --- Aulas/BE-Nao_Param.tex | 3 +++ 1 file changed, 3 insertions(+) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 125e424..e80fab3 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -169,4 +169,7 @@ \subsection{Revisão} \subsection[Correlação]{Teste de correlação} +\section{Resumo} + + \end{document} From c813a05ad42b3bb7a851ebe48f8083e94412fa44 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 6 Jun 2016 16:12:22 -0300 Subject: [PATCH 05/46] resumo rascunho --- Aulas/BE-Nao_Param.tex | 17 +++++++++++++++++ 1 file changed, 17 insertions(+) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index e80fab3..56506f4 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -171,5 +171,22 @@ \subsection{Revisão} \section{Resumo} +\begin{frame}{Resumo} + \begin{tabular}{|l|l|} + \hline + Paramétrico & Não-paramétrico\\ + \hline + t-teste pareado & Wilcoxon\\ + \hline + t-teste não-pareado & Mann-Whitney\\ + \hline + ANOVA 1 fator & Kruskal-Wallis\\ + \hline + Correlação de Pearson & Correlação de Spearman\\ + \hline +% \hline + \end{tabular} + +\end{frame} \end{document} From 45128722a31bd4d8cab1f60982d1358f18f9d088 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 6 Jun 2016 16:13:40 -0300 Subject: [PATCH 06/46] rascunho testes de normalidade --- Aulas/BE-Nao_Param.tex | 16 ++++++++++++++++ 1 file changed, 16 insertions(+) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 56506f4..193f94e 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -157,6 +157,22 @@ \subsection{Revisão} \subsection[Normalidade]{Testes contra a normalidade} +\begin{frame} + \begin{itemize} + \item Objetivo: é possível \alert{determinar} se uma amostra veio de uma população normalmente distribuída? + \item Resposta curta: \alert<3->{NÃO}. + \item<4> Resposta longa: podemos examinar se há evidências para ``aceitar'' esta hipótese\footnote{Lembre que {\bf nunca} aceitamos uma hipótese -- apenas deixamos de rejeitar sua recíproca.} + \end{itemize} +\end{frame} + +\begin{frame} + \begin{itemize} + \item Shapiro-Wilk + \item Anderson-Darling + \item Kolmongorv-Smirnov + \end{itemize} +\end{frame} + \section{Testes} \subsection{Revisão} From 4dcd376764c986fe59ced94e7ed9e701ff7837b9 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 6 Jun 2016 16:26:44 -0300 Subject: [PATCH 07/46] testes para 2 amostras MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit ocorrências de "média" foram substituídas por "amostras". --- Aulas/BE-Nao_Param.tex | 23 +++++++++++++++++++---- 1 file changed, 19 insertions(+), 4 deletions(-) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 193f94e..c0d691d 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -177,11 +177,26 @@ \section{Testes} \subsection{Revisão} -\subsection[1 média]{Teste para 1 média} - -\subsection[2 médias]{Teste para 2 médias} +\subsection[1 amostra]{Teste para 1 amostra} + +\subsection[2 médias]{Testes para 2 amostras} + +\begin{frame}{Testes para 2 amostras} + \begin{block}{Dados normais} + \begin{itemize} + \item amostras independentes $\Rightarrow$ t-teste não-pareado + \item amostras pareadas $\Rightarrow$ t-teste pareado + \end{itemize} + \end{block} + \begin{block}{Dados não-normais} + \begin{itemize} + \item amostras independentes $\Rightarrow$ Wilcoxon (signed rank test) + \item amostras pareadas $\Rightarrow$ Mann-Whitney \footnote{Também conhecido como Wilcoxon (rank sum test)} + \end{itemize} + \end{block} +\end{frame} -\subsection[3+ médias]{Teste para 3 ou mais médias} +\subsection[3+ amostras]{Teste para 3 ou mais amostras} \subsection[Correlação]{Teste de correlação} From e33d321e4a037b877733056b8765d9be942a496c Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 6 Jun 2016 16:42:13 -0300 Subject: [PATCH 08/46] typo Digitei as coisas na ordem errada --- Aulas/BE-Nao_Param.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index c0d691d..16d971a 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -190,8 +190,8 @@ \subsection{Revisão} \end{block} \begin{block}{Dados não-normais} \begin{itemize} - \item amostras independentes $\Rightarrow$ Wilcoxon (signed rank test) - \item amostras pareadas $\Rightarrow$ Mann-Whitney \footnote{Também conhecido como Wilcoxon (rank sum test)} + \item amostras independentes $\Rightarrow$ Mann-Whitney \footnote{Também conhecido como Wilcoxon (rank sum test)} + \item amostras pareadas $\Rightarrow$ Wilcoxon (signed rank test) \end{itemize} \end{block} \end{frame} From 6426561619cabe661bcb0718b895ded62c31bae4 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 6 Jun 2016 16:48:42 -0300 Subject: [PATCH 09/46] =?UTF-8?q?formata=C3=A7=C3=A3o?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Aulas/BE-Nao_Param.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 16d971a..eb29dbc 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -203,10 +203,11 @@ \subsection{Revisão} \section{Resumo} \begin{frame}{Resumo} - \begin{tabular}{|l|l|} + \begin{tabular}{||l||l||} \hline Paramétrico & Não-paramétrico\\ \hline + \hline t-teste pareado & Wilcoxon\\ \hline t-teste não-pareado & Mann-Whitney\\ @@ -215,7 +216,6 @@ \section{Resumo} \hline Correlação de Pearson & Correlação de Spearman\\ \hline -% \hline \end{tabular} \end{frame} From b3a8df2a1bbd9a24d0a2f69027a212ee288cf06d Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 15:34:16 -0300 Subject: [PATCH 10/46] histogramas --- Aulas/BE-Nao_Param.tex | 34 +++++++++++++++++++++++++++++++ Aulas/Nao_Param/lognormal1-h.png | Bin 0 -> 4706 bytes Aulas/Nao_Param/lognormal2-h.png | Bin 0 -> 11691 bytes Aulas/Nao_Param/normal1-h.png | Bin 0 -> 5190 bytes Aulas/Nao_Param/normal2-h.png | Bin 0 -> 12156 bytes 5 files changed, 34 insertions(+) create mode 100644 Aulas/Nao_Param/lognormal1-h.png create mode 100644 Aulas/Nao_Param/lognormal2-h.png create mode 100644 Aulas/Nao_Param/normal1-h.png create mode 100644 Aulas/Nao_Param/normal2-h.png diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index eb29dbc..ed00716 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -155,6 +155,40 @@ \section{Normalidade} \subsection{Revisão} +\begin{frame}{Visualização - Histograma} + \centering + \includegraphics[width=.7\textwidth]{Nao_Param/normal1-h} + + Dados normais +\end{frame} + +\begin{frame}{Visualização - Histograma} + \centering + \includegraphics[width=.7\textwidth]{Nao_Param/lognormal1-h} + + Dados não-normais +\end{frame} + +\begin{frame}{Visualização - Histograma} + \centering + \includegraphics[width=.7\textwidth]{Nao_Param/normal2-h} + + Dados normais +\end{frame} + +\begin{frame}{Visualização - Histograma} + \centering + \includegraphics[width=.7\textwidth]{Nao_Param/lognormal2-h} + + Dados não-normais +\end{frame} + +\begin{frame}{Visualização - Histograma} + \centering + \includegraphics[width=.5\textwidth]{Nao_Param/normal2-h} + \includegraphics[width=.5\textwidth]{Nao_Param/lognormal2-h} +\end{frame} + 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b/Aulas/BE-Nao_Param.tex @@ -189,6 +189,15 @@ \subsection{Revisão} \includegraphics[width=.5\textwidth]{Nao_Param/lognormal2-h} \end{frame} +\begin{frame}{Visualização - boxplot} + \centering + \includegraphics[width=.5\textwidth]{Nao_Param/normal1-h} + \includegraphics[width=.5\textwidth]{Nao_Param/lognormal1-h} + + \includegraphics[width=.5\textwidth]{Nao_Param/normal-bp} + \includegraphics[width=.5\textwidth]{Nao_Param/lognormal-bp} +\end{frame} + \subsection[Normalidade]{Testes contra a normalidade} \begin{frame} diff --git a/Aulas/Nao_Param/lognormal-bp.png b/Aulas/Nao_Param/lognormal-bp.png new file mode 100644 index 0000000000000000000000000000000000000000..d0f5b97419cc8631a12498b354173e8647fd68dd GIT binary patch literal 3816 zcmd^BXIPWjwx+3oC_ zjg5_+o&Egz^Bf!;7cN}5c<~}9C+DS0mjD0&7Z=y%%a^ZQxx&rO&BMdP%gf8h$H&jl zfA#8B0RaI)K|vuQAz@)*5fKqlQPE$1`9(}j?Ao%*@=}{N~M@w{G3Cu&}VSw6wCavbMIi zv9YnWwFQI0c6N65_Vx}A4vvnFPEJnF&dx3_E)WRB)z#I_%?%2Ly1TpIxpU|4-Mbzh 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c8c4cd1d448dbe8bc8e8badb27b903a86cd1da70 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 15:46:26 -0300 Subject: [PATCH 12/46] qq plots --- Aulas/BE-Nao_Param.tex | 9 +++++++++ Aulas/Nao_Param/lognormal-qq.png | Bin 0 -> 11073 bytes Aulas/Nao_Param/normal-qq.png | Bin 0 -> 10932 bytes 3 files changed, 9 insertions(+) create mode 100644 Aulas/Nao_Param/lognormal-qq.png create mode 100644 Aulas/Nao_Param/normal-qq.png diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 496c2f5..0c59981 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -198,6 +198,15 @@ \subsection{Revisão} \includegraphics[width=.5\textwidth]{Nao_Param/lognormal-bp} \end{frame} +\begin{frame}{Visualização - QQ plot} + \centering + \includegraphics[width=.5\textwidth]{Nao_Param/normal1-h} + \includegraphics[width=.5\textwidth]{Nao_Param/lognormal1-h} + + \includegraphics[width=.5\textwidth]{Nao_Param/normal-qq} + \includegraphics[width=.5\textwidth]{Nao_Param/lognormal-qq} +\end{frame} + \subsection[Normalidade]{Testes contra a normalidade} \begin{frame} diff --git a/Aulas/Nao_Param/lognormal-qq.png b/Aulas/Nao_Param/lognormal-qq.png new file mode 100644 index 0000000000000000000000000000000000000000..15d6849dbcbdfe7ce2e84553836ab1424842618e GIT binary patch literal 11073 zcmcJ#Wl)??@GgqGli-rzwzv~Kgy61=ySuvv4J08f4k5TZ1b1CD$l?|j2#YT6hy4Dh zZr!T;<$gHl!&JTVcF!~2BRyTuOq{x^JT4Xm76JkSuENLnng|Gp(3kQB1Nr4o31TcA z0s=CEy0W(1OBE3j5eW$i85tP`1qBrq6%7py9UUD50|OHi6AKFq8yg!32L~4y7Y`2) zA0MB9fPj#Ykcfzgn3(w0t5>gIza}9eAtfaxBO@axC#RsGproXvqN1Xvrlz5xp{1pL z^XARlw{Pj_=;-O`85kHC85x^KfPkQ&ppcM|u&}U*h={1DsF;}8yLa!z#l@|DJd%}tEi}`s;a7~si~{0YiMX_YHDg} zX=!U~>*(m{>gww0>FMk18yFZE8X5wDKqDg~V`F0z6BAQYQ!_I&b8~YG3kyq2ODiiY zYiny88yj0&TRS^DdwY8a2M0$-M<*vIXJ=;@7Z+DoS2s5|cXxLW4-ZdIPcJVoZ*OlO zA0J;|Uq3%Te}DggfPlcjz@VU@;NakpkdV;O(6F$u@bK`6h=|C@$f&5O=;-KApFYLJ z#KgwN#>K_O$HylmBqSy#e*XM9DJdyAIr+<%FJHfY{r2r!N=nN2@845XQ$Zk5T3T9q 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(titulo) --- Aulas/BE-Nao_Param.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 0c59981..1c7c6c2 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -153,7 +153,7 @@ \section{Normalidade} -\subsection{Revisão} +\subsection{Visualização} \begin{frame}{Visualização - Histograma} \centering From e63a1289987b8e2880c6ae47297672ad63a45f66 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 16:31:33 -0300 Subject: [PATCH 14/46] exemplo 2 amostras --- Aulas/BE-Nao_Param.tex | 46 ++++++++++++++++++++++++++++++++ Aulas/Nao_Param/2samples-bp.png | Bin 0 -> 4894 bytes Aulas/Nao_Param/2samples-h.png | Bin 0 -> 7316 bytes Aulas/Nao_Param/2samples-qq.png | Bin 0 -> 13066 bytes 4 files changed, 46 insertions(+) create mode 100644 Aulas/Nao_Param/2samples-bp.png create mode 100644 Aulas/Nao_Param/2samples-h.png create mode 100644 Aulas/Nao_Param/2samples-qq.png diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 1c7c6c2..5a80d07 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -248,6 +248,52 @@ \subsection{Revisão} \end{block} \end{frame} +\begin{frame}{Exemplo} +P: Estas amostras são significativamente diferentes? + + \centering + \includegraphics[height=\textheight]{Nao_Param/2samples-bp} +\end{frame} + +\begin{frame}{Exemplo} + \begin{itemize} + \item Assumindo\footnote{pelo desenho experimental} que elas são independentes, poderíamos fazer um teste t não-pareado. + \item Resultado: p-valor = \alert{0.259} + \item Então elas não são diferentes? + \end{itemize} +\end{frame} + +\begin{frame}{Histogramas} + \includegraphics[width=\textwidth]{Nao_Param/2samples-h} + +%p-valores Shapiro-Wilk: (x) = 5.515e-16, (y) = 5.274e-09 +\end{frame} + +\begin{frame}{QQ-plots} + \includegraphics[width=\textwidth]{Nao_Param/2samples-qq} + +%p-valores Shapiro-Wilk: (x) = 5.515e-16, (y) = 5.274e-09 +\end{frame} + +\begin{frame}{Shapiro-Wilk} + \begin{block}{Teste t} + p-valor = 0.259 (não são diferentes) + \end{block} + \begin{itemize} + \item<2-> Aplicando o teste de Shapiro-Wilk em x e y + \begin{itemize} + \item<2-> x: p-valor = 5.515e-16 + \item<2-> y: p-valor = 5.274e-09 + \end{itemize} + \item Devemos rejeitar a hipótese de normalidade. + \item Então o teste t \alert{não é} apropriado! + \item Substituto: teste de Mann-Whitney + \end{itemize} + \begin{block}{Teste de Mann-Whitney} + p-value = \alert{0.0001346} (são diferentes) + \end{block} +\end{frame} + \subsection[3+ amostras]{Teste para 3 ou mais amostras} \subsection[Correlação]{Teste de correlação} diff --git a/Aulas/Nao_Param/2samples-bp.png b/Aulas/Nao_Param/2samples-bp.png new file mode 100644 index 0000000000000000000000000000000000000000..c9eca9fb2dc36a9375baec0f7ed14abbe39c06cc GIT binary patch literal 4894 zcmdT{XHZjJw+0DFCsgSi1Q8*CfDoj5L?noyAYF>|ml~Rc4u+~!0Y$n6Q4pl}-UL*d 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ze}h#D#eHOha3N!ZYQ{H5}OT) z2gZHKU;Gy*-a_VgW@ZX_R^OzEGr-r1(@hvjV#E?GTgIXrpCR92TMhUXiadOee|QfL zHR@c2n{{Rj+Un&+(XvK(@;Osy+O$eGsxpSx_suh~R#zlm{|$9ujC+!n1*4qH><0Kx rC}c<%UqWB5F?$!{Xtw3T5>a~+4pi@2LKdgRHQ2;jlcgN0D}aX literal 0 HcmV?d00001 From 672e361300e56d384a15ae1d8dafa8e40b7b30f4 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 16:59:44 -0300 Subject: [PATCH 15/46] 1 amostra --- Aulas/BE-Nao_Param.tex | 11 +++++++++++ 1 file changed, 11 insertions(+) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 5a80d07..b517eef 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -231,6 +231,17 @@ \subsection{Revisão} \subsection[1 amostra]{Teste para 1 amostra} +\begin{frame}{Teste para 1 amostra} + \begin{itemize} + \item Desvios da normalidade severos impactam os testes paramétricos + \item Nesses casos, deve-se transformar os dados, se possível + \item Caso não seja, deve-se usar um teste não-paramétrico + \end{itemize} + \begin{block}{Teste para uma amostra} + Ao invés do teste t, usar o teste de Wilcoxon + \end{block} +\end{frame} + \subsection[2 médias]{Testes para 2 amostras} \begin{frame}{Testes para 2 amostras} From 3301cd25d5d39bb4481b5a42728fabdf3d5e4ab8 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 17:03:49 -0300 Subject: [PATCH 16/46] testes, estrutura revisada MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Alerta no teste SW, e "revisão" removida --- Aulas/BE-Nao_Param.tex | 10 ++++------ 1 file changed, 4 insertions(+), 6 deletions(-) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index b517eef..64dbb2c 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -217,18 +217,16 @@ \subsection{Visualização} \end{itemize} \end{frame} -\begin{frame} +\begin{frame}{Alguns testes de normalidade} \begin{itemize} - \item Shapiro-Wilk - \item Anderson-Darling - \item Kolmongorv-Smirnov + \item<1-> \alert<2>{Shapiro-Wilk} + \item<1-> Anderson-Darling + \item<1-> Kolmongorv-Smirnov \end{itemize} \end{frame} \section{Testes} -\subsection{Revisão} - \subsection[1 amostra]{Teste para 1 amostra} \begin{frame}{Teste para 1 amostra} From 7059b43a0d51655963a6a195dde47f182bc6a20e Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 17:15:13 -0300 Subject: [PATCH 17/46] =?UTF-8?q?transforma=C3=A7=C3=B5es=20histograma?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Aulas/BE-Nao_Param.tex | 22 ++++++++++++++++++++++ 1 file changed, 22 insertions(+) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 64dbb2c..b123602 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -225,6 +225,28 @@ \subsection{Visualização} \end{itemize} \end{frame} +\subsection{Transformações} + +\begin{frame}{Transformações} + \begin{itemize} + \item Algumas vezes, podemos aplicar uma transformação nos dados, para que eles se adequem às premissas requeridas + \item Transformações comuns incluem: + \begin{itemize} + \item logaritmo + \item exponencial + \item raiz quadrada + \item potências + \end{itemize} + \end{itemize} +\end{frame} + +\begin{frame}{Exemplo} + \centering + \includegraphics[width=\textwidth]{Nao_Param/transf-h} + +Dados normais x dados transformados (log) +\end{frame} + \section{Testes} \subsection[1 amostra]{Teste para 1 amostra} From 5bb58c5ac31effd07fd8973d2ffd91d75b26c919 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 17:20:03 -0300 Subject: [PATCH 18/46] =?UTF-8?q?transforma=C3=A7=C3=B5es=20qq=20plot?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Aulas/BE-Nao_Param.tex | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index b123602..2dd30f7 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -247,6 +247,13 @@ \subsection{Transformações} Dados normais x dados transformados (log) \end{frame} +\begin{frame}{Exemplo} + \centering + \includegraphics[width=\textwidth]{Nao_Param/transf-qq} + +Dados normais x dados transformados (log) +\end{frame} + \section{Testes} \subsection[1 amostra]{Teste para 1 amostra} From 7bf842e5e1fa149e07da6527dea5eab98d4b2eee Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 17:20:10 -0300 Subject: [PATCH 19/46] clareza MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Complementação da explicação sobre transformações --- Aulas/BE-Nao_Param.tex | 2 ++ 1 file changed, 2 insertions(+) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 2dd30f7..908124e 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -237,6 +237,8 @@ \subsection{Transformações} \item raiz quadrada \item potências \end{itemize} + \item Geralmente envolve tentativa e erro + \item Hipóteses sobre o problema ou desenho experimental ajudam \end{itemize} \end{frame} From cf2c14b1c515c1d9e9a90bdccb74ccb793fb91dc Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 17:25:53 -0300 Subject: [PATCH 20/46] clareza --- Aulas/BE-Nao_Param.tex | 12 +++++++++--- 1 file changed, 9 insertions(+), 3 deletions(-) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 908124e..9a7e8df 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -297,9 +297,15 @@ \section{Testes} \begin{frame}{Exemplo} \begin{itemize} - \item Assumindo\footnote{pelo desenho experimental} que elas são independentes, poderíamos fazer um teste t não-pareado. - \item Resultado: p-valor = \alert{0.259} - \item Então elas não são diferentes? + \item<1-> Assumindo\footnote{pelo desenho experimental} que elas são + \begin{itemize} + \item<1-> normalmente distribuídas, e + \item<1-> independentes, + \end{itemize} +poderíamos fazer um teste t não-pareado. + + \item<2-> Resultado: p-valor = \alert{0.259} + \item<3-> Então elas não são diferentes? \end{itemize} \end{frame} From 4bbafbd265c5b00ef38ec7ce021fb668694c6e2f Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 17:25:57 -0300 Subject: [PATCH 21/46] =?UTF-8?q?motiva=C3=A7=C3=A3o?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit título renomeado para motivar --- Aulas/BE-Nao_Param.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 9a7e8df..49106c1 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -288,7 +288,7 @@ \section{Testes} \end{block} \end{frame} -\begin{frame}{Exemplo} +\begin{frame}{Em termos práticos...} P: Estas amostras são significativamente diferentes? \centering From d204d6c7d16a85b5b58725e6f9682bc9785e020d Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 17:26:23 -0300 Subject: [PATCH 22/46] =?UTF-8?q?transforma=C3=A7=C3=B5es?= MIME-Version: 1.0 Content-Type: text/plain; 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z4v&r29n6EId+&_VNEghbiwb~xRDox0KKYlC@hO1j!^vBNzB3hvpt;;N#oeA_Rn>w` zW8?1@$1bgv)b3SL0`abxuUjwpu5XSw;gf#X9o2YI+UK@K=Nm@e=Kl_eyz$|98XLJC zV4=O#NH~_lEw<9K5=n5a5?49A_MP;Sl#-aw@AyqcEj`4zU0A;7Is`w-R68-sVZv{Y z;Awu)dwyh)y^SRM;_s9xRYjYn!yifA0cL>kg|WFhS2IC7j@=qJM)m}k`Kn`zvW0eM z&0x=R-}?(DwQ*&p6y@^HZ#%%SWUK zpX+4u#H41+P-Wmlhfla}+41%>X)8{d3z&^0rEMUI+?^}sXWNSt*$02G#^A7-R z4!D79-$w9OUuD!$yklm1xz`RuO$nBDw>l*@6s#lC+vCa56X_V#EbA;O_Ennnx{h!s zy%s!XgwOjz&$p>zUICRtOUVxa!O|n;a6@gV=jTCm*`tKkXDk5^=(D@#l;726VmpL^ z*fc2)$t#{4CLctGR|_p&nT1F)19eO2A%Fif-QvF-ZU%?!kY0M83tN7}wQU1l%aRp( z55F(~KUQVu+l}nSA^I0PZ2Tc>n+a literal 0 HcmV?d00001 From 31e97610af84751dc9aac12de9ebb891e3680ea7 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 17:28:32 -0300 Subject: [PATCH 23/46] alerta --- Aulas/BE-Nao_Param.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 49106c1..3616077 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -282,7 +282,7 @@ \section{Testes} \end{block} \begin{block}{Dados não-normais} \begin{itemize} - \item amostras independentes $\Rightarrow$ Mann-Whitney \footnote{Também conhecido como Wilcoxon (rank sum test)} + \item amostras independentes $\Rightarrow$ \alert{Mann-Whitney} \footnote{Também conhecido como Wilcoxon (rank sum test)} \item amostras pareadas $\Rightarrow$ Wilcoxon (signed rank test) \end{itemize} \end{block} From 7cb6db622416e4f4f52027f396527739289cae26 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 17:35:14 -0300 Subject: [PATCH 24/46] =?UTF-8?q?clareza=20e=20cad=C3=AAncia?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit A formatação foi melhorada, e o boxplot foi re-exibido, para criar um suspense... --- Aulas/BE-Nao_Param.tex | 11 +++++++++-- 1 file changed, 9 insertions(+), 2 deletions(-) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 3616077..9e87ad5 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -299,16 +299,23 @@ \section{Testes} \begin{itemize} \item<1-> Assumindo\footnote{pelo desenho experimental} que elas são \begin{itemize} - \item<1-> normalmente distribuídas, e + \item<1-> \alert<3>{normalmente distribuídas}, e \item<1-> independentes, \end{itemize} poderíamos fazer um teste t não-pareado. \item<2-> Resultado: p-valor = \alert{0.259} - \item<3-> Então elas não são diferentes? + \begin{block}{Pergunta} + Isto significa que as amostras não são significativamente diferentes? + \end{block} \end{itemize} \end{frame} +\begin{frame}{Novamente...} + \centering + \includegraphics[height=\textheight]{Nao_Param/2samples-bp} +\end{frame} + \begin{frame}{Histogramas} \includegraphics[width=\textwidth]{Nao_Param/2samples-h} From 121f1a611f3d0c767b342cad9fc0c3eb8913fe52 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 17:36:25 -0300 Subject: [PATCH 25/46] =?UTF-8?q?precis=C3=A3o=20do=20vocabul=C3=A1rio?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit É melhor manter o uso do termo "significativo", ao invés de linguagem informal --- Aulas/BE-Nao_Param.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 9e87ad5..c897163 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -330,7 +330,7 @@ \section{Testes} \begin{frame}{Shapiro-Wilk} \begin{block}{Teste t} - p-valor = 0.259 (não são diferentes) + p-valor = 0.259 (não significativo) \end{block} \begin{itemize} \item<2-> Aplicando o teste de Shapiro-Wilk em x e y @@ -343,7 +343,7 @@ \section{Testes} \item Substituto: teste de Mann-Whitney \end{itemize} \begin{block}{Teste de Mann-Whitney} - p-value = \alert{0.0001346} (são diferentes) + p-value = \alert{0.0001346} (significativo) \end{block} \end{frame} From 645811f2da5076cecc77c595e2125e86ee861555 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 17:55:03 -0300 Subject: [PATCH 26/46] abertura --- Aulas/BE-Nao_Param.tex | 10 ++++++++++ 1 file changed, 10 insertions(+) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index c897163..d301d38 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -153,6 +153,16 @@ \section{Normalidade} +\begin{frame}{A hipótese da normalidade} + \begin{itemize} + \item Todos os métodos que vimos até aqui presumem que os dados são normalmente distribuídos + \item Desvios da normalidade precisam ser contornados\footnote{há controvérsias: \url{http://www.r-bloggers.com/normality-tests-don\%E2\%80\%99t-do-what-you-think-they-do/}} + \item Veremos duas maneiras: transformações e alternativas + \item Mas antes, como identificar essa necessidade? + \end{itemize} + +\end{frame} + \subsection{Visualização} \begin{frame}{Visualização - Histograma} From 4f70e602b77f4939c2c10df8deaa1c671faf88f6 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 17:59:57 -0300 Subject: [PATCH 27/46] qq plot - intro --- Aulas/BE-Nao_Param.tex | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index d301d38..4075712 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -208,6 +208,15 @@ \subsection{Visualização} \includegraphics[width=.5\textwidth]{Nao_Param/lognormal-bp} \end{frame} +\begin{frame}{O Q-Q plot} + \begin{itemize} + \item Gráfico que compara os quantis da amostra com os quantis teóricos + \item Adicionalmente uma reta ``ideal'' é sobreposta, como referência + \item Dados normalmente distribuídos, ficam próximos da reta + \item Quanto maior o desvio da normalidade, maior a distância à reta + \end{itemize} +\end{frame} + \begin{frame}{Visualização - QQ plot} \centering \includegraphics[width=.5\textwidth]{Nao_Param/normal1-h} From c52dcd03f83f0f6d2a301785de392c1bd6443ab7 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Mon, 13 Jun 2016 18:01:55 -0300 Subject: [PATCH 28/46] typo --- Aulas/BE-Nao_Param.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 4075712..7fef326 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -240,7 +240,7 @@ \subsection{Visualização} \begin{itemize} \item<1-> \alert<2>{Shapiro-Wilk} \item<1-> Anderson-Darling - \item<1-> Kolmongorv-Smirnov + \item<1-> Kolmogorov-Smirnov \end{itemize} \end{frame} From abeb7f682ee57eba61df3e97152a5d923e05c91c Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Tue, 14 Jun 2016 16:23:51 -0300 Subject: [PATCH 29/46] script e dados dos exemplos --- Aulas/Nao_Param/2samples.dat | 101 +++++++++++++++++++++++++++ Aulas/Nao_Param/exemplos.R | 53 ++++++++++++++ Aulas/Nao_Param/normal-lognormal.dat | 101 +++++++++++++++++++++++++++ 3 files changed, 255 insertions(+) create mode 100644 Aulas/Nao_Param/2samples.dat create mode 100644 Aulas/Nao_Param/exemplos.R create mode 100644 Aulas/Nao_Param/normal-lognormal.dat diff --git a/Aulas/Nao_Param/2samples.dat b/Aulas/Nao_Param/2samples.dat new file mode 100644 index 0000000..3642256 --- /dev/null +++ b/Aulas/Nao_Param/2samples.dat @@ -0,0 +1,101 @@ +"x" "y" +"1" 0.414866884375096 1.89420610842434 +"2" 1.01611469092812 0.754270720866576 +"3" 1.44297027579302 1.83516136172635 +"4" 2.04093533037603 3.69696738919632 +"5" 4.17796459465859 2.71726123588387 +"6" 0.182923097447724 4.48116460702706 +"7" 1.46906819333901 0.832282167993215 +"8" 2.7198149642396 1.38682089804199 +"9" 0.986145861804612 2.47450261758507 +"10" 1.30082159712837 1.21263190507734 +"11" 0.164805048293293 1.89234843249925 +"12" 0.865984132816494 2.6857669249323 +"13" 12.4772881276213 1.11956927378963 +"14" 0.404781765693609 3.23869147731471 +"15" 0.28375753677922 2.45964881486327 +"16" 2.46507288983983 4.41030458958362 +"17" 1.59877023340669 0.835145612069019 +"18" 0.454521743093519 1.61772384221428 +"19" 1.03011231829559 1.49168789193563 +"20" 2.10250222914702 0.791715820273371 +"21" 2.41144997208797 1.88956162059084 +"22" 1.0421746406694 3.17428279797567 +"23" 0.592717798955148 1.48577023945371 +"24" 1.86420274512285 0.860497231433947 +"25" 0.273754747791621 5.42532082383444 +"26" 2.65778553138925 1.20005738582596 +"27" 0.601140670645266 4.60736683844748 +"28" 1.13599333584913 1.48569074553496 +"29" 0.493949001909606 8.09642015845426 +"30" 0.397055263543262 1.82504231167739 +"31" 0.927434642100752 1.10047221262075 +"32" 2.47623133113492 0.892403955316809 +"33" 1.38550463143087 1.28265982455966 +"34" 1.40267108954403 0.914878350038933 +"35" 2.13723082145224 1.44733044157185 +"36" 0.655104959283668 0.987077008229831 +"37" 3.35389600196833 1.30017608049899 +"38" 0.805058333439688 1.37161050497779 +"39" 0.172129507089209 0.735474379270603 +"40" 1.09205209493401 1.57392434325595 +"41" 3.6068185843425 1.08455936224044 +"42" 0.577945405592813 1.03913215856953 +"43" 0.543825934573162 1.58496871264478 +"44" 0.683480395800239 5.70255815670579 +"45" 0.570455061543169 3.42952155293841 +"46" 3.63893519467953 2.59894457359684 +"47" 20.241563716081 1.17623305919986 +"48" 0.38734578143956 0.689102102914652 +"49" 5.96970352795529 1.88679534126298 +"50" 3.25690639978696 1.6177487058797 +"51" 0.52047239927517 5.99467841384203 +"52" 0.527310449893038 3.35002505421159 +"53" 4.48413937666519 0.704978117736546 +"54" 2.12897672948101 1.13608200996832 +"55" 3.83441744472717 0.620361739602417 +"56" 2.87306455580042 0.923454109282174 +"57" 0.372462581680341 6.21656078373656 +"58" 1.24073846587114 4.88905516332982 +"59" 0.794623200181997 1.4643216394124 +"60" 2.61233064434514 5.39359561980745 +"61" 0.921966706710064 3.45427617866244 +"62" 0.642791919435502 2.13788804160224 +"63" 6.1037017313607 2.47505955035816 +"64" 0.578074793926844 2.39099556032838 +"65" 0.26717209539394 1.10985919653891 +"66" 2.51760230044099 0.718003057110566 +"67" 3.63891116645856 0.813272064569329 +"68" 0.756771174328342 1.57524046195684 +"69" 0.60270990499317 2.06648273157859 +"70" 0.395216814782632 7.1295101015546 +"71" 1.29816932641383 3.11836820006082 +"72" 1.75473856306636 3.89225560689059 +"73" 1.67287656172119 1.31817832710168 +"74" 2.23658890938697 0.752036582709042 +"75" 1.15861521097605 2.15980413870449 +"76" 1.55054352405069 2.43545626432936 +"77" 0.337628029932128 4.86363484823899 +"78" 0.931587320916169 0.80820478668879 +"79" 1.0286614241161 2.5972438413553 +"80" 1.31434633889625 2.74212920735058 +"81" 1.41526493078472 0.971022060284481 +"82" 0.917442664942019 0.93051729996639 +"83" 0.759003867953231 2.19325438883556 +"84" 8.46248474800835 0.745008964216615 +"85" 0.277233222377171 3.11714204158836 +"86" 3.5677695391498 2.02169828468359 +"87" 0.873416397535684 4.07960623379037 +"88" 0.147652852265147 0.988018445886991 +"89" 3.29398119326343 0.64986558556295 +"90" 1.13097411016084 2.23250486811435 +"91" 5.9998211438477 2.49136393136012 +"92" 0.351192171624199 0.740833803726196 +"93" 2.29521308399538 4.37260772751142 +"94" 1.26535639366583 2.67877274996622 +"95" 1.2838631307908 1.32302014808785 +"96" 0.287794513169364 1.53649622587148 +"97" 0.666672243031857 2.00802794806759 +"98" 0.656077640299591 1.04484347404931 +"99" 0.528361041960162 2.43114720149355 +"100" 1.24725403451655 1.85225328953814 diff --git a/Aulas/Nao_Param/exemplos.R b/Aulas/Nao_Param/exemplos.R new file mode 100644 index 0000000..8446533 --- /dev/null +++ b/Aulas/Nao_Param/exemplos.R @@ -0,0 +1,53 @@ +## normal x lognormal #### +nl <- read.table("Aulas/Nao_Param/normal-lognormal.dat") +attach(nl) + +par(mfrow = c(1,2)) +hist(x1, main = "") +hist(x2, main = "") +par(mfrow = c(1,1)) +boxplot(x1) +boxplot(x2) +par(mfrow = c(1,2)) +qqnorm(x1); qqline(x1); qqnorm(x2); qqline(x2) +shapiro.test(x1) +shapiro.test(x2) + + +## Transformação #### +par(mfrow = c(1,2)) + +hist(x2); hist(log(x2)) +hist(log(x2)); qqnorm(log(x2)); qqline(log(x2)) +hist(x2); hist(log(x2)) +qqnorm(x2, main = "Dados originais"); qqline(x2); qqnorm(log(x2), main = "Dados (log)"); qqline(log(x2)) +shapiro.test(log(x2)) + +detach(nl) +rm(nl) + +## 2 amostras #### +twosamples <- read.table("Aulas/Nao_Param/2samples.dat") +attach(twosamples) + +par(mfrow = c(1,1)) +boxplot(x,y) +qqnorm(x); qqline(x); qqnorm(y); qqline(y) +par(mfrow = c(1,2)) +qqnorm(x); qqline(x); qqnorm(y); qqline(y) +qqnorm(x, main = "Amostra 1"); qqline(x); qqnorm(y); qqline(y) +qqnorm(x, main = "Amostra 1"); qqline(x); qqnorm(y, main = "Amostra 2"); qqline(y) +hist(x, main = "Amostra 1") +hist(y, main = "Amostra 2") + +detach(twosamples) +rm(twosamples) + +## 3 amostras #### +m.p <- aov(Ozone ~ Month, data = airquality) +m.np <- kruskal.test(Ozone ~ Month, data = airquality) +m.ols <- lm(Ozone ~ Month, data = airquality) + +summary(m.p) # não significativo +m.np # significativo +summary(m.ols) diff --git a/Aulas/Nao_Param/normal-lognormal.dat b/Aulas/Nao_Param/normal-lognormal.dat new file mode 100644 index 0000000..2080bc2 --- /dev/null +++ b/Aulas/Nao_Param/normal-lognormal.dat @@ -0,0 +1,101 @@ +"x1" "x2" +"1" 169.755476522883 27.490203435636 +"2" 173.022111247771 36.2049013449093 +"3" 166.905182933215 7.68402686357979 +"4" 180.209622641602 4.28372879097162 +"5" 161.373468573945 6.2979901609884 +"6" 164.463524729859 5.5449184252189 +"7" 171.656962768664 16.3861993654349 +"8" 163.648443339469 21.7900269701168 +"9" 168.093165484974 22.3501625480265 +"10" 161.316531158161 61.3976731501277 +"11" 164.602212209002 2.29447737769415 +"12" 173.28609914827 42.344224093174 +"13" 168.644492932317 1.66835168066355 +"14" 149.698297395244 5.47941042961393 +"15" 173.248133867218 13.0797785536955 +"16" 168.128785924485 4.27309862479843 +"17" 169.929584001154 6.99191821861193 +"18" 164.634846560472 26.3176054487897 +"19" 170.027628594492 10.9524936517388 +"20" 143.338344564398 38.6455352563344 +"21" 177.380191647883 25.1936178391789 +"22" 177.621062776306 12.0292239255561 +"23" 177.875792649399 40.6007575754022 +"24" 177.50857687332 25.2246135237443 +"25" 153.278788137519 11.1660851361605 +"26" 159.589589596735 4.66751629288557 +"27" 183.995345753636 4.26587840564204 +"28" 165.155798795996 7.18640746028805 +"29" 180.088172047501 11.6761302590689 +"30" 154.875055707017 6.20067163050287 +"31" 166.050489400567 0.738718578572874 +"32" 149.570613700438 7.10317641011334 +"33" 177.985188492244 16.7597940063713 +"34" 160.755705722325 17.0600187905148 +"35" 175.302279100109 3.5904658863486 +"36" 164.293478902595 48.0781748017698 +"37" 169.515753644785 9.66363096384818 +"38" 159.704823616481 1.59087937227103 +"39" 189.237449655342 5.77452518936472 +"40" 166.436733771226 32.2522152450237 +"41" 158.326455964613 8.3908689975446 +"42" 171.1983565865 58.940964015191 +"43" 175.82149155692 6.3128190033691 +"44" 172.654206617536 20.6372262580933 +"45" 186.433889975785 9.03381384313897 +"46" 170.659704644713 7.43786451552792 +"47" 158.898520843496 1.93624498549937 +"48" 170.459833370029 31.0788009847089 +"49" 163.352637284319 4.80513521955927 +"50" 166.693409375943 1.31297474623954 +"51" 168.125609619244 7.44882308521904 +"52" 151.174911725686 7.18201929058828 +"53" 162.786283331806 19.4355700233568 +"54" 168.397690036996 8.34491728065827 +"55" 178.506147570942 18.3881847826378 +"56" 161.514451490588 55.6887271519618 +"57" 174.717426611842 14.5521454741755 +"58" 163.505487023063 6.00268813725921 +"59" 180.222861298204 11.3749712146495 +"60" 152.676559180352 3.68201247765954 +"61" 151.810562053453 45.6464514941798 +"62" 161.046368363843 1.46214113804418 +"63" 165.887014139784 7.16587417381714 +"64" 165.48166135002 5.69247935803672 +"65" 168.080198950816 46.2474711165369 +"66" 166.012470821276 0.770105510908293 +"67" 162.57980846052 10.9586036862823 +"68" 167.722553933864 15.5413947126782 +"69" 178.641046650511 4.25952228924351 +"70" 168.055047678008 8.5019561901876 +"71" 172.318342641826 10.1638638690349 +"72" 191.638617032837 16.4367952151966 +"73" 169.076243252429 52.0066735160805 +"74" 155.329880151174 24.125038228089 +"75" 172.632104826934 5.12133351587006 +"76" 164.624067640723 13.724924875812 +"77" 156.2131469304 11.3880143917468 +"78" 172.679469802853 8.53103903014929 +"79" 146.085894158874 22.4548358171442 +"80" 174.584893801198 4.08839482775758 +"81" 174.63508301925 13.2841427359659 +"82" 159.227379192067 0.606283000631059 +"83" 158.960337914484 5.32541814553164 +"84" 164.38384564676 31.8791912514737 +"85" 184.775553243041 7.81052527559181 +"86" 168.433324204531 10.5383819620834 +"87" 165.110220229639 14.5192699724768 +"88" 172.272031936237 8.55252558268741 +"89" 169.586041345716 23.8383643988892 +"90" 167.784870686101 11.6345363269546 +"91" 176.069183631742 3.61254023381558 +"92" 183.967542148951 4.43497478642761 +"93" 164.924603697481 11.4727881079049 +"94" 173.035699304751 10.6614510908347 +"95" 166.987154734338 37.3107711641538 +"96" 181.202970859198 3.01587552850251 +"97" 168.952510739711 29.2530256132274 +"98" 166.455357537461 35.3198198089548 +"99" 176.164807782963 6.80760096362674 +"100" 171.088021081087 12.4626264452389 From a69c6b9553bbd38ca0518ac882b8d3b0178efe84 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Tue, 14 Jun 2016 16:37:36 -0300 Subject: [PATCH 30/46] Exemplos de shapiro-wilk --- Aulas/BE-Nao_Param.tex | 15 +++++++++++++++ 1 file changed, 15 insertions(+) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 7fef326..f9a321a 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -244,6 +244,21 @@ \subsection{Visualização} \end{itemize} \end{frame} +\begin{frame}{Shapiro-Wilk} + \centering + \includegraphics[width=.8\textwidth]{Nao_Param/normal1-h} + + p-value = 0.7766 +\end{frame} + + +\begin{frame}{Shapiro-Wilk} + \centering + \includegraphics[width=.8\textwidth]{Nao_Param/lognormal1-h} + + p-value = 1.657e-09 +\end{frame} + \subsection{Transformações} \begin{frame}{Transformações} From 8cbc3a5f792507e284c507607dffb62ab8da5edd Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Tue, 14 Jun 2016 16:43:39 -0300 Subject: [PATCH 31/46] =?UTF-8?q?estrutura=20melhorada,=20t=C3=ADtulo=20mo?= =?UTF-8?q?dificado?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Aulas/BE-Nao_Param.tex | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index f9a321a..3a3b9e4 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -43,7 +43,7 @@ \title%[] % (optional, use only with long paper titles) -{Testes não-paramétricos} +{Métodos não-paramétricos} \subtitle {Ou: o que fazer caso seus dados não sejam normais?} % (optional) @@ -259,6 +259,8 @@ \subsection{Visualização} p-value = 1.657e-09 \end{frame} +\section{Transformações} + \subsection{Transformações} \begin{frame}{Transformações} @@ -276,6 +278,8 @@ \subsection{Transformações} \end{itemize} \end{frame} +\subsection{Exemplo} + \begin{frame}{Exemplo} \centering \includegraphics[width=\textwidth]{Nao_Param/transf-h} @@ -290,7 +294,7 @@ \subsection{Transformações} Dados normais x dados transformados (log) \end{frame} -\section{Testes} +\section{Métodos não-paramétricos} \subsection[1 amostra]{Teste para 1 amostra} From 6fea72521214197e3f3cbd0991dd2bce3a4aead7 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Tue, 14 Jun 2016 16:59:27 -0300 Subject: [PATCH 32/46] =?UTF-8?q?reorganiza=C3=A7=C3=A3o?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Código obsoleto removido. --- Aulas/Nao_Param/exemplos.R | 7 +------ 1 file changed, 1 insertion(+), 6 deletions(-) diff --git a/Aulas/Nao_Param/exemplos.R b/Aulas/Nao_Param/exemplos.R index 8446533..bf794de 100644 --- a/Aulas/Nao_Param/exemplos.R +++ b/Aulas/Nao_Param/exemplos.R @@ -13,13 +13,11 @@ qqnorm(x1); qqline(x1); qqnorm(x2); qqline(x2) shapiro.test(x1) shapiro.test(x2) - ## Transformação #### par(mfrow = c(1,2)) - hist(x2); hist(log(x2)) +hist(x2); qqnorm(log(x2)); qqline(log(x2)) hist(log(x2)); qqnorm(log(x2)); qqline(log(x2)) -hist(x2); hist(log(x2)) qqnorm(x2, main = "Dados originais"); qqline(x2); qqnorm(log(x2), main = "Dados (log)"); qqline(log(x2)) shapiro.test(log(x2)) @@ -32,10 +30,7 @@ attach(twosamples) par(mfrow = c(1,1)) boxplot(x,y) -qqnorm(x); qqline(x); qqnorm(y); qqline(y) par(mfrow = c(1,2)) -qqnorm(x); qqline(x); qqnorm(y); qqline(y) -qqnorm(x, main = "Amostra 1"); qqline(x); qqnorm(y); qqline(y) qqnorm(x, main = "Amostra 1"); qqline(x); qqnorm(y, main = "Amostra 2"); qqline(y) hist(x, main = "Amostra 1") hist(y, main = "Amostra 2") From cb0010d6923e56b8bf32a62ce0efe19fbcfe2dee Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Tue, 14 Jun 2016 17:00:14 -0300 Subject: [PATCH 33/46] =?UTF-8?q?gr=C3=A1ficos=20gerados=20na=20ordem=20da?= =?UTF-8?q?=20aula?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Aulas/Nao_Param/exemplos.R | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Aulas/Nao_Param/exemplos.R b/Aulas/Nao_Param/exemplos.R index bf794de..a8f0b66 100644 --- a/Aulas/Nao_Param/exemplos.R +++ b/Aulas/Nao_Param/exemplos.R @@ -31,9 +31,9 @@ attach(twosamples) par(mfrow = c(1,1)) boxplot(x,y) par(mfrow = c(1,2)) -qqnorm(x, main = "Amostra 1"); qqline(x); qqnorm(y, main = "Amostra 2"); qqline(y) hist(x, main = "Amostra 1") hist(y, main = "Amostra 2") +qqnorm(x, main = "Amostra 1"); qqline(x); qqnorm(y, main = "Amostra 2"); qqline(y) detach(twosamples) rm(twosamples) From 07fcbf04879ebf7f3c2c7cf7d5c2def9fd51e6da Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Tue, 14 Jun 2016 17:01:22 -0300 Subject: [PATCH 34/46] encurtar discurso MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Tirar ênfase das funções usadas em transformações, exibindo todas de uma vez. --- Aulas/BE-Nao_Param.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 3a3b9e4..113ace2 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -268,10 +268,10 @@ \subsection{Transformações} \item Algumas vezes, podemos aplicar uma transformação nos dados, para que eles se adequem às premissas requeridas \item Transformações comuns incluem: \begin{itemize} - \item logaritmo - \item exponencial - \item raiz quadrada - \item potências + \item<2-> logaritmo + \item<2-> exponencial + \item<2-> raiz quadrada + \item<2-> potências \end{itemize} \item Geralmente envolve tentativa e erro \item Hipóteses sobre o problema ou desenho experimental ajudam From 4e99cd84bfe59a6012773bae2c226b76ca0ef9f4 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Tue, 14 Jun 2016 17:06:36 -0300 Subject: [PATCH 35/46] intro ao exemplo MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Introduzir o exemplo da transformação log, marcando o contexto. --- Aulas/BE-Nao_Param.tex | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 113ace2..d33e2ee 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -280,6 +280,13 @@ \subsection{Transformações} \subsection{Exemplo} +\begin{frame}{Exemplo} + \centering + \includegraphics[width=.8\textwidth]{Nao_Param/lognormal1-h} + +Transformação sugerida: logaritmo. +\end{frame} + \begin{frame}{Exemplo} \centering \includegraphics[width=\textwidth]{Nao_Param/transf-h} From 799ec9cbc6915e1c30d887bb9f7754d340b65745 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Tue, 14 Jun 2016 17:14:24 -0300 Subject: [PATCH 36/46] intro anova --- Aulas/BE-Nao_Param.tex | 13 +++++++++++++ 1 file changed, 13 insertions(+) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index d33e2ee..3ff14a8 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -394,6 +394,19 @@ \section{Métodos não-paramétricos} \subsection[3+ amostras]{Teste para 3 ou mais amostras} +\begin{frame}{Relembrando} + \begin{itemize} + \item Para testar se há diferença significativa em 3 ou mais amostras + \begin{itemize} + \item Análise de Variâncias (ANOVA) + \item Leva em conta as variâncias entre os grupos (\alert{inter}) + \item Leva em conta a variância em cada grupo (\alert{intra}) + \item $H_0:$ Todos os grupos são $=$ + \item $H_1:$ pelo menos um grupo é significativamente $\ne$ + \end{itemize} + \end{itemize} +\end{frame} + \subsection[Correlação]{Teste de correlação} \section{Resumo} From 90137d3a161171a5563c67001a89b24f36b50f03 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Tue, 14 Jun 2016 17:20:12 -0300 Subject: [PATCH 37/46] boxplot para K-W --- Aulas/Nao_Param/exemplos.R | 2 ++ 1 file changed, 2 insertions(+) diff --git a/Aulas/Nao_Param/exemplos.R b/Aulas/Nao_Param/exemplos.R index a8f0b66..54ed335 100644 --- a/Aulas/Nao_Param/exemplos.R +++ b/Aulas/Nao_Param/exemplos.R @@ -39,6 +39,8 @@ detach(twosamples) rm(twosamples) ## 3 amostras #### +par(mfrow = c(1,1)) +boxplot(Ozone ~ Month, data = airquality, xlab="Mês", ylab="Ozônio", main="Medições de qualidade do ar em NY") m.p <- aov(Ozone ~ Month, data = airquality) m.np <- kruskal.test(Ozone ~ Month, data = airquality) m.ols <- lm(Ozone ~ Month, data = airquality) From 0658ccd1f3445200ee6bb80594d3da976b80ad34 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Tue, 14 Jun 2016 17:22:52 -0300 Subject: [PATCH 38/46] boxplot intro ao exemplo KW --- Aulas/BE-Nao_Param.tex | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 3ff14a8..23bc1d8 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -407,6 +407,13 @@ \section{Métodos não-paramétricos} \end{itemize} \end{frame} +\begin{frame}{Em termos práticos...} +P: Estas amostras são significativamente diferentes? + + \centering + \includegraphics[height=.9\textheight]{Nao_Param/3samples-bp} +\end{frame} + \subsection[Correlação]{Teste de correlação} \section{Resumo} From 8b07fdbec4b6cb58c27fcbde6ee5f23f2912a960 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Tue, 14 Jun 2016 17:28:15 -0300 Subject: [PATCH 39/46] kruskal-Wallis --- Aulas/BE-Nao_Param.tex | 22 ++++++++++++++++++++++ 1 file changed, 22 insertions(+) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 23bc1d8..dbf8677 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -414,6 +414,22 @@ \section{Métodos não-paramétricos} \includegraphics[height=.9\textheight]{Nao_Param/3samples-bp} \end{frame} +\begin{frame}{Kruskal-Wallis} + \begin{block}{ANOVA} + p-valor = 0.0776 (não significativo) + \end{block} + \begin{itemize} + \item Shapiro-Wilk (Ozônio): p-value = 2.79e-08 + \item Devemos rejeitar a hipótese de normalidade. + \item Então o ANOVA \alert{não é} apropriado! + \item Substituto: teste de Kruskal-Wallis + \end{itemize} + \begin{block}{Teste de Kruskal-Wallis} + p-value = \alert{6.901e-06} (significativo) + \end{block} +\end{frame} + + \subsection[Correlação]{Teste de correlação} \section{Resumo} @@ -437,3 +453,9 @@ \section{Resumo} \end{frame} \end{document} +% \begin{frame}{Relembrando} +% \begin{itemize} +% \item +% \end{itemize} +% \end{frame} + From 2a3361d8c75b4a30af1ab7ed636691511cea7630 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Tue, 14 Jun 2016 17:45:20 -0300 Subject: [PATCH 40/46] =?UTF-8?q?correla=C3=A7=C3=A3o=20de=20spearman?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Apenas informativo, sem exemplos --- Aulas/BE-Nao_Param.tex | 22 +++++++++++++--------- 1 file changed, 13 insertions(+), 9 deletions(-) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index dbf8677..4c05756 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -429,13 +429,23 @@ \section{Métodos não-paramétricos} \end{block} \end{frame} +\subsection{Correlação} -\subsection[Correlação]{Teste de correlação} +\begin{frame}{Relembrando} + \begin{itemize} + \item A correlação de Pearson associa dados numéricos + \item Mede a direção e força desta associação + \end{itemize} + \begin{block}{Correlação} + Ao invés da correlação linear de Pearson, usar a correlação de ranks de Spearman + \end{block} +\end{frame} \section{Resumo} \begin{frame}{Resumo} - \begin{tabular}{||l||l||} + \begin{block}{} + \begin{tabular}{||l||l||} \hline Paramétrico & Não-paramétrico\\ \hline @@ -449,13 +459,7 @@ \section{Resumo} Correlação de Pearson & Correlação de Spearman\\ \hline \end{tabular} - + \end{block} \end{frame} \end{document} -% \begin{frame}{Relembrando} -% \begin{itemize} -% \item -% \end{itemize} -% \end{frame} - From 3275705cfd21020d2a9e988d9c0499b0f0933847 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Tue, 14 Jun 2016 17:45:36 -0300 Subject: [PATCH 41/46] =?UTF-8?q?t=C3=ADtulo=20trocado,=20para=20consist?= =?UTF-8?q?=C3=AAncia=20com=20KW?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Aulas/BE-Nao_Param.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Aulas/BE-Nao_Param.tex b/Aulas/BE-Nao_Param.tex index 4c05756..06d37a7 100644 --- a/Aulas/BE-Nao_Param.tex +++ b/Aulas/BE-Nao_Param.tex @@ -373,7 +373,7 @@ \section{Métodos não-paramétricos} %p-valores Shapiro-Wilk: (x) = 5.515e-16, (y) = 5.274e-09 \end{frame} -\begin{frame}{Shapiro-Wilk} +\begin{frame}{Mann-Whitney} \begin{block}{Teste t} p-valor = 0.259 (não significativo) \end{block} From 769289b04bae8504907ca9b74b8e732111681007 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Tue, 14 Jun 2016 17:46:07 -0300 Subject: [PATCH 42/46] boxplot KW --- Aulas/Nao_Param/3samples-bp.png | Bin 0 -> 7519 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 Aulas/Nao_Param/3samples-bp.png diff --git a/Aulas/Nao_Param/3samples-bp.png b/Aulas/Nao_Param/3samples-bp.png new file mode 100644 index 0000000000000000000000000000000000000000..513c60946113e52d00a73c4bfe3aec1f5f1df4c4 GIT 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    f5I>@j~8%Z9vVt!U9^zg zJLzRVdMHy_+J3|@3!J}ZcU!Np?@)yY^zEfk9w($SD|UMfw)`$Ug_t;hBz*uK`+$%) zOu6vti|_LaAHpH$JKgI+XMHg}3?GBcZ#teMb~|JcmsKbGkE&nJj>i3RUHdjZ|Lq`n ztF(^qs&Ca?wn1A*$B#VE7M7lUylX*Mvc!R!^4Zpt!X&l>?WU@Q{gg;dLs2-RtxcTd z3E1gc+jW*3fDKcTeQG*|;h`*beY5K=?z>~} z`I*jQ*l?FSgd!CDm(&TPRvL^gNUuk!uEL>r;$|p^w$xw3tNX1#qZS7IqO~kPG*mLX z&+?*cAWP{?WuP{+Aq~l9Zt{@L8!Flt)tjZ_XaRRVpYW~*LVb*&$dS!l=9O1=fHuCx z_<9h_0M~l6nj)iOSJQlJ>O;bJNEzEP>9Z%778;bv?_2N2S3SgkoK1@JQ~DvI{0=ks zq%Je2G9heJ3wzrlVU^-h44s3CEt$DRJl(HIU-_Xq+1@P2TBNJ%wjg}ZFT(tIal zj%DWOpXc&LmO&vtHX%9vRu&H|6bfT$OP4_#$s(!yq1DMAK&RkyfkKWoi-`59z1HZm zwxjkWWm|ce9+RB4a1LNbFwiv}=!cBpN#>>DDe}`69KvA6E>#9uZZOlZks!tzNHo)BfSU9lsxrBWgGSEs061fP4O`XShZVjM}Eh0__6s z$27pmCzQAJsrn|auE*aCsB1J0+}VSnQJ;LbOLMN(-)9Lj1`?B3lNt3Ga~bbm4;s3Y zoDb_|n<&RHoeuQlodCnTZA({*Fg=~29(H`M!0W(D939)>Jk8eEaT7MKQt5^;7j>?1 zI_sh$d1>cRug=B~(2t?7tB*07HVaw_m&y$`Qn(C4t^gSd$$Hkv2FLQ)t!HHb1>CG> zQlAt+|E);@rh7;L;F!3)Az<5e(j4s1#2u;AM($t9N^e^k3w1-WENUz5-*^~T!tL${ zCZr9DzqckBQBKSK!Hs?70^6FcTE0%0`L!QrLbq`yE0TVCzN%+lzS@+RnO72?KkoB= z9^PiR(n8HY^C$F^xmS=!464ioF;w$_sisHsg~vyHdE;CoEo8qv5v=!`*x6+8Hse5 zoz}xxC#@3d*$74smRnH_xb`K|i&M!lR+=xU+Xa_fU2)>tcT2A;vNz;^5G4P`%Ct`O z$h1ytNMduMTwnXerB9#BrwUK}W2EliGM7p!+v&M=>~$(|tX}Z>e~Wn(|HE^(HX}HL z5xQPZgga1MX($SbwgV%~i9v+lAQ)i2wCpH~ebAsTf~EOga1Pc6Hi zvBp|o>$gFVJHqgucspN@oSV0Sa><8@Z!%!s9cY|E7{UDTu||RG(~`Z@dBe-3?P_X{*tpe zd$%{gMAQiJiny7Hs!13h^a!N0kG#5lsh!!o^ZFsi9wqOV$rp}?kWC@szB;kCXVX9O z!p7^*5Bkts;<&hbOXi*pb4cqdgCT}pazmZIid_zS5WYyXB53b~qVsVV`rwfwLqfe4 z`&x?O-AA?E;9N4nH&bD&f2N<1DCzq+=}H|hXq`Q08Pno++=R=?k+}|5Q!$~>1`BuC z?56EzgM?e1)e~EQPoFgLFEn3HKUY!qI6pN{Z&rd>DxAu_lNPsZ={>^*Duj|0Oz8FI zuR0hqyt1qI7xK64)!P&&l)TR|i_!Zk@w|#@IX?uVFlApq?DPZ$xKZYmmwHQYl4xr{ zK3?sjJp_bAL~nDPFm`m-ZC_T7)!AWIa0R|m6{js>OqVhF4Tw}c9F^cHb;?S`>qUw4 zls<0ej%%}Z9WhvfMHX`=nknin!AdCUQD&EvRKr%|?tV8s`Ek~M*`ZZ}I{EPdf}Zjq zVTuvWQQ2xi>V3V_4Nw-HnX#@)UUcMPhDf`ccsdqsp(_#}o!;RfX@Wi0@sS%!FhxF`1bs8FV9=>4zlNX}2K(X5Oe& zgh~HtvZ-FdQi36IG`+H#f3QGWsa=7iaqEZhX{P76i7bTQO7_;(P&HVXBaCbYi(`4& zH(n6wU(bBmhaZJ!Xj-CC23jpg+g)l{V1-44%OfPpqb`+4DwQWq`JIB+3w(YT?Vzbe zrFJ^+9;Q1${@#K=ji!x*rdjNK&b3m2K@=9|Zoz4w_zwNS7y7$}fJ+omHigcH!la~8 zJJmaKs;j+PHGX>w|5r3XktUoKcOkJG35jBZL?R*4!Umnf2LDVfz*A|U7@nV7=IE_c`M8ykK^6Nt=Yft zQnbqGIm6MR=uai;PX-E%^9~y_uZ-)qVgFGa_Ma8G%;0w#`1X&HqjmI|@_NDg$zJaL z{JjzX-$;j%4v@>jC+eCF6;uTG;~-i%&ORJ(sx*Ma@<7v-Z9&?@_z${qY1)1=rhC@L z=7KT9635PuPB&uo*Ok<^ku}tC6{eV4h{fOYdTX9fgi2(~QFr z#0<>#q?tQ1`O2wxBO8%BCItGEj1pmu#F-Wvf}~W3Xpt Date: Tue, 14 Jun 2016 17:50:28 -0300 Subject: [PATCH 45/46] =?UTF-8?q?link=20aula=20de=20m=C3=A9todos=20n=C3=A3?= =?UTF-8?q?o=20param=C3=A9tricos?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- README.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index ba60711..10dada3 100644 --- a/README.md +++ b/README.md @@ -22,7 +22,7 @@ A digulgação do material para os alunos é feita pelo endereço: https://sites - [Correlação e Regressão][] - [Tutorial - Descritiva][] - [Tutorial - Correlação e Regressão][] -- Testes não-paramétricos +- [Métodos não-paramétricos][] [Cronograma]: https://docs.google.com/document/d/1xb7Yqxae8sbbbkPYjg5ZGhxJ8NFfxOURBISeWVHkjUE [Introdução]: Aulas/BE-Intro_4em1.pdf @@ -38,6 +38,8 @@ A digulgação do material para os alunos é feita pelo endereço: https://sites [Correlação e Regressão]: Aulas/BE-Associacao_II_4em1.pdf [Tutorial - Descritiva]: Aulas/BE-Pratica_Descritiva_4em1.pdf [Tutorial - Correlação e Regressão]: Aulas/BE-Pratica_Associacao_4em1.pdf +[Métodos não-paramétricos]: Aulas/BE-Nao_Param_4em1.pdf + ##Bibliografia From 33d898f38d0ee31e3c487305ee2487b722284082 Mon Sep 17 00:00:00 2001 From: Felipe Figueiredo Date: Tue, 14 Jun 2016 17:50:52 -0300 Subject: [PATCH 46/46] estrutura MD corrigida --- README.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/README.md b/README.md index 10dada3..6a7eec2 100644 --- a/README.md +++ b/README.md @@ -4,7 +4,7 @@ Este é o repositório da disciplina de Bioestatística do professor Felipe Figu A digulgação do material para os alunos é feita pelo endereço: https://sites.google.com/site/proffelipefigueiredo/into/bioestatistica -##Planejamento de aulas de conteúdo +## Planejamento de aulas de conteúdo [Cronograma][] @@ -41,7 +41,7 @@ A digulgação do material para os alunos é feita pelo endereço: https://sites [Métodos não-paramétricos]: Aulas/BE-Nao_Param_4em1.pdf -##Bibliografia +## Bibliografia Livro texto: @@ -79,7 +79,7 @@ Online: [goodman1999]: http://annals.org/article.aspx?articleid=712762 [goodman1999-pdf]: http://www.perfendo.org/docs/bayesprobability/5.3_goodmanannintmed99all.pdf -##Avaliação +## Avaliação A avaliação final da disciplina consistirá na apresentação de um seminário, sobre um estudo publicado em um journal. Os alunos deverão preparar e apresentar o seminário em dupla. O objetivo da avaliação é que os alunos façam uma síntese crítica da análise estatística utilizada neste estudo à luz dos conteúdos vistos ao longo da disciplina.