<div dir="ltr"><div class="gmail_default" style="font-family:times new roman,serif;font-size:small">Caro César, obrigado pela didática resposta.</div><div class="gmail_default" style="font-family:times new roman,serif;font-size:small"><br></div><div class="gmail_default" style="font-family:times new roman,serif;font-size:small">Como se diz por ai, eu concordo em numéro, gênero e grau com você, no entanto busco por alternativas seria viável usar alguma técnica de oversampling para aumentar a amostra?</div><div class="gmail_default" style="font-family:times new roman,serif;font-size:small"><br></div><div class="gmail_default" style="font-family:times new roman,serif;font-size:small"><br></div><div class="gmail_default" style="font-family:times new roman,serif;font-size:small"><br></div></div><br><div class="gmail_quote"><div dir="ltr">Em qua, 11 de jul de 2018 às 09:27, Cesar Rabak <<a href="mailto:cesar.rabak@gmail.com">cesar.rabak@gmail.com</a>> escreveu:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Elias,<div><br></div><div>Há vários possíveis comentários a fazer, embora, de antemão aviso-o, que pelo fato de você ter dezessete casos apenas, não há muito a melhorar.</div><div><br></div><div><ol><li>Calcular os coeficientes de associação quando a hipótese de independência não pode ser descartada tende a ser um exercício equivalente a tentar ler folhas de chá numa xícara após a merenda;</li><li>Ao você fazer múltiplas comparações <b>nos mesmos dados</b> você ainda teria que fazer uma correção para assegurar que seu Erro Tipo I não seria inflacionado;</li><li>A alternativa de fazer um <i>omnibus test</i>, por exemplo via uma regressão logística com G como desfecho e as outras como VI, esbarra no fato de que se precisaria muito mais casos¹.</li></ol><div>Então no seu caso a única coisa que a Estatística o autorizaria é dizer que as hipóteses de independências não podem ser descartadas e que devido ao tamanho da amostra mais nada pode ser dito (do ponto de vista de inferência).</div><div><br></div><div>Com o conhecimento do domínio do problema e a Descritiva você pode especular mais um pouco, mas irremediavelmente teria que propor um estudo com maior potências estatística se quiser alguma constatação do fenômeno que está estudando.</div><div><br></div><div><br></div><div>HTH</div><div>--</div><div>Cesar Rabak</div><div> </div></div><div><br></div><div>[1] A discussão sobre assunto é vasta com concordância apenas que é "um problema complexo", mas para colocar a bola em campo, Peduzzi et al. 1996, costuma ser citado como melhor referência. A fórmula seria N = 10∙k / p; N :: mínimo tamanho da amostra, k :: número de covariáveis; p :: mínimo da proporção casos ou não casos.</div><div><br></div><div><br></div><div>
<span style="color:rgb(0,0,0);font-family:Roboto,Arial,Helvetica,sans-serif;font-size:14px;text-align:justify;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">Peduzzi P, Concato J, Kemper E, Holford TR, Feinstein AR (1996) A simulation study of the number of events per variable in logistic regression analysis. Journal of Clinical Epidemiology 49:1373-1379.</span>
<br></div></div><div class="gmail_extra"><br><div class="gmail_quote">On Tue, Jul 10, 2018 at 8:38 PM, Elias Carvalho via R-br <span dir="ltr"><<a href="mailto:r-br@listas.c3sl.ufpr.br" target="_blank">r-br@listas.c3sl.ufpr.br</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_default" style="font-family:"times new roman",serif;font-size:small">Prezados</div><div class="gmail_default" style="font-family:"times new roman",serif;font-size:small"><br></div><div class="gmail_default" style="font-family:"times new roman",serif;font-size:small">Tenho uma amostra pequena com apenas 17 registros, e 7 variáveis dicotômicas, cujo resumo é:</div><div class="gmail_default"><br><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px"><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px"> A B C D E F G
0: 7 0:10 0: 6 0:11 0: 2 0: 1 0:15
1:10 1: 7 1:11 1: 6 1:15 1:16 1: 2 </pre><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px"><br></pre><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px">A variável G seria meu desfecho e o resto possíveis preditores</pre><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px"><br></pre><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px">Para veficiar a associação entre o desfecho e as outras variáveisexecutei o teste exato de fisher por ser uma amostra pequena, mas o resutados mostraram que o desfecho não depende de nenhuma variável:</pre><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px"><br></pre><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px"><span class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBCPB m_7409923482931161904m_-6231691581519696251gmail-ace_keyword" style="color:rgb(147,15,128);white-space:pre-wrap">> </span><span class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBCOB m_7409923482931161904m_-6231691581519696251gmail-ace_keyword" style="color:rgb(147,15,128)">fisher.test(<a href="http://data.to.work" target="_blank">data.to.work</a>$G, <a href="http://data.to.work" target="_blank">data.to.work</a>$A)
</span>
Fisher's Exact Test for Count Data
data: <a href="http://data.to.work" target="_blank">data.to.work</a>$G and <a href="http://data.to.work" target="_blank">data.to.work</a>$A
p-value = 0.4853
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
0.1311443 Inf
sample estimates:
odds ratio
Inf
<span class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBCPB m_7409923482931161904m_-6231691581519696251gmail-ace_keyword" style="color:rgb(147,15,128);white-space:pre-wrap">> </span><span class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBCOB m_7409923482931161904m_-6231691581519696251gmail-ace_keyword" style="color:rgb(147,15,128)">fisher.test(<a href="http://data.to.work" target="_blank">data.to.work</a>$G, <a href="http://data.to.work" target="_blank">data.to.work</a>$B)
</span>
Fisher's Exact Test for Count Data
data: <a href="http://data.to.work" target="_blank">data.to.work</a>$G and <a href="http://data.to.work" target="_blank">data.to.work</a>$B
p-value = 0.4853
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
0.000000 7.625189
sample estimates:
odds ratio
0
<span class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBCPB m_7409923482931161904m_-6231691581519696251gmail-ace_keyword" style="color:rgb(147,15,128);white-space:pre-wrap">> </span><span class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBCOB m_7409923482931161904m_-6231691581519696251gmail-ace_keyword" style="color:rgb(147,15,128)">fisher.test(<a href="http://data.to.work" target="_blank">data.to.work</a>$G, <a href="http://data.to.work" target="_blank">data.to.work</a>$C)
</span>
Fisher's Exact Test for Count Data
data: <a href="http://data.to.work" target="_blank">data.to.work</a>$G and <a href="http://data.to.work" target="_blank">data.to.work</a>$C
p-value = 0.5147
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
0.1003871 Inf
sample estimates:
odds ratio
Inf
<span class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBCPB m_7409923482931161904m_-6231691581519696251gmail-ace_keyword" style="color:rgb(147,15,128);white-space:pre-wrap">> </span><span class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBCOB m_7409923482931161904m_-6231691581519696251gmail-ace_keyword" style="color:rgb(147,15,128)">fisher.test(<a href="http://data.to.work" target="_blank">data.to.work</a>$G, <a href="http://data.to.work" target="_blank">data.to.work</a>$D)
</span>
Fisher's Exact Test for Count Data
data: <a href="http://data.to.work" target="_blank">data.to.work</a>$G and <a href="http://data.to.work" target="_blank">data.to.work</a>$D
p-value = 0.5147
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
0.00000 9.96144
sample estimates:
odds ratio
0
<span class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBCPB m_7409923482931161904m_-6231691581519696251gmail-ace_keyword" style="color:rgb(147,15,128);white-space:pre-wrap">> </span><span class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBCOB m_7409923482931161904m_-6231691581519696251gmail-ace_keyword" style="color:rgb(147,15,128)">fisher.test(<a href="http://data.to.work" target="_blank">data.to.work</a>$G, <a href="http://data.to.work" target="_blank">data.to.work</a>$E)
</span>
Fisher's Exact Test for Count Data
data: <a href="http://data.to.work" target="_blank">data.to.work</a>$G and <a href="http://data.to.work" target="_blank">data.to.work</a>$E
p-value = 1
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
0.01971228 Inf
sample estimates:
odds ratio
Inf
<span class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBCPB m_7409923482931161904m_-6231691581519696251gmail-ace_keyword" style="color:rgb(147,15,128);white-space:pre-wrap">> </span><span class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBCOB m_7409923482931161904m_-6231691581519696251gmail-ace_keyword" style="color:rgb(147,15,128)">fisher.test(<a href="http://data.to.work" target="_blank">data.to.work</a>$G, <a href="http://data.to.work" target="_blank">data.to.work</a>$F)
</span>
Fisher's Exact Test for Count Data
data: <a href="http://data.to.work" target="_blank">data.to.work</a>$G and <a href="http://data.to.work" target="_blank">data.to.work</a>$F
p-value = 1
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
0.003434375 Inf
sample estimates:
odds ratio
</pre><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px"><span style="font-size:10.4pt"> Inf </span> </pre><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px"><br></pre><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px">Em seguida calculei o V de Cramer, Coeficiente de Contingência e phi e todos mostram independência e associação fraca.</pre><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px"><br></pre><font color="#000000" face="Ubuntu Mono"><span style="font-size:13.8667px;white-space:pre-wrap">summary(assocstats(tab_cont_G_A))
# Resultado:
# X^2 df P(> X^2)
# Likelihood Ratio 2.3071 1 0.12878 # P-Valor > 0.05 - independentes
# Pearson 1.5867 1 0.20780 # P-Valor > 0.05 - independentes
#
# Phi-Coefficient : 0.306 # Coef de Phi - Associação fraca
# Contingency Coeff.: 0.292 # Coef de Cont - Associação fraca
# Cramer's V : 0.306 # V de Crammer - Associação fraca
</span></font><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px"> </pre><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px">Pelo que pesquisei este seriam os métodos mais adequados para este tipo de análise</pre><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px"><br></pre><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px">Há um método melhor para avaliar esse tipo de dado?</pre><span class="m_7409923482931161904HOEnZb"><font color="#888888"><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px"><br></pre><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px"><br></pre><pre class="m_7409923482931161904m_-6231691581519696251gmail-GGHFMYIBMOB" id="m_7409923482931161904m_-6231691581519696251gmail-rstudio_console_output" style="color:rgb(0,0,0);font-family:"Ubuntu Mono";font-size:10.4pt;white-space:pre-wrap;outline:none;border:none;word-break:break-all;margin-top:0px;margin-bottom:0px;line-height:16px"><br></pre></font></span></pre></div><span class="m_7409923482931161904HOEnZb"><font color="#888888">-- <br><div dir="ltr" class="m_7409923482931161904m_-6231691581519696251gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><div><font face="times new roman, serif"><i><span style="font-size:12.8px">In Jesu et Maria</span><br><br style="font-size:small"></i></font><div><div dir="ltr"><div dir="ltr"><div dir="ltr"><div style="font-size:small"><font face="times new roman, serif"><i>Obrigado</i></font></div><div style="font-size:small"><font face="times new roman, serif"><i>Prof. Elias Carvalho</i></font></div><div style="font-size:small"><font face="times new roman, serif"><i><br></i></font></div><div><font face="times new roman, serif" size="2"><i><div>"Felix, qui potuit rerum cognoscere causas" (Virgil 29 BC)</div><div>"Blessed is he who has been able to understand the cause of things"</div></i></font></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></font></span></div>
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</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><div><font face="times new roman, serif"><i><span style="font-size:12.8px">In Jesu et Maria</span><br><br style="font-size:small"></i></font><div><div dir="ltr"><div dir="ltr"><div dir="ltr"><div style="font-size:small"><font face="times new roman, serif"><i>Obrigado</i></font></div><div style="font-size:small"><font face="times new roman, serif"><i>Prof. Elias Carvalho</i></font></div><div style="font-size:small"><font face="times new roman, serif"><i><br></i></font></div><div><font face="times new roman, serif" size="2"><i><div>"Felix, qui potuit rerum cognoscere causas" (Virgil 29 BC)</div><div>"Blessed is he who has been able to understand the cause of things"</div></i></font></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div>