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<b> Parte 2.2 - Introdução à análise exploratória de dados </b>
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<b> Medidas de associação e análise gráfica </b>
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<div id="analise-exploratoria" class="section level1">
<h1><span class="header-section-number">1</span> <strong>Análise exploratória</strong></h1>
<p>Dando continuidade ao material a respeito de análise exploratória de dados, nesta parte serão apresentadas as medidas de associação, gráficos e ainda uma breve apresentação do conceito de assimetria.</p>
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<h1><span class="header-section-number">2</span> <strong>Medidas de Associação</strong></h1>
<p>O objetivo das medidas de associação é mensurar quanto uma variável influencia outra. Duas medidas de associação destacam-se: o <span class="math inline">\(Q^2\)</span> e a correlação.</p>
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<div id="q2" class="section level2">
<h2><span class="header-section-number">2.1</span> <span class="math inline">\(Q^2\)</span></h2>
<p>O coeficiente <span class="math inline">\(Q^2\)</span> baseia-se na comparação de tabelas de frequência. O que é feito é confrontar os valores reais nas caselas da tabela de frequência de dupla entrada original com as frequências esperadas. O coeficiente é dado por:</p>
<p><span class="math display">\[Q^2 = \sum_{i,j} \frac{(o_{ij}-e_{ij})^2}{e_{ij}}\]</span></p>
<p><span class="math inline">\(o_{ij}\)</span> e <span class="math inline">\(e_{ij}\)</span> representam as frequências observadas e esperadas na linha <span class="math inline">\(i\)</span> e coluna <span class="math inline">\(j\)</span>. A diferença entre observado e esperado ao quadrado evita o cancelamento de termos positivos com negativos enquanto que a divisão pelo valor esperado padroniza a medida.</p>
<p>Se as frequências esperadas forem muito próximas das observadas, espera-se que o coeficiente fique próximo de zero. Valores diferentes de 0 indicam associação, isto é, dependência entre as variáveis.</p>
<p>O procedimento para cálculo do <span class="math inline">\(Q^2\)</span> é:</p>
<ol style="list-style-type: decimal">
<li>Obter a tabela de dupla entrada com as frequências observadas (<span class="math inline">\(o_{ij}\)</span>).</li>
<li>Obter a tabela de dupla entrada com as frequências relativas por coluna (a soma da coluna deve ser igual a 1), inclusive para a coluna de total.</li>
<li>Obter a tabela de dupla entrada com as frequências esperadas (<span class="math inline">\(e_{ij}\)</span>).
<ul>
<li>Para obter a frequência esperada basta multiplicar a frequência relativa da coluna de soma pelo total da coluna da tabela de frequências observadas.</li>
</ul></li>
<li>Aplicar os valores obtidos na fórmula do <span class="math inline">\(Q^2\)</span>
<ul>
<li>Se o valor for próximo de 0, então não há associação entre as variáveis.</li>
<li>Se o valor for diferente de 0, então há associação entre as variáveis.</li>
</ul></li>
</ol>
<p>Considere o exemplo a seguir com duas variáveis <span class="math inline">\(T\)</span> e <span class="math inline">\(A\)</span> quaisquer:</p>
<ol style="list-style-type: decimal">
<li>Tabela de frequências observadas</li>
</ol>
<table style="border-collapse:collapse;border-spacing:0;margin:0px auto" class="tg">
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
T/A
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
1
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
2
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
3
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
4
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
Soma
</td>
</tr>
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
5
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
4
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
2
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
3
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
1
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
15
</td>
</tr>
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
1
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
2
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
8
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
6
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
4
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
1
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
21
</td>
</tr>
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
2
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
4
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
8
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
8
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
5
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
2
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
27
</td>
</tr>
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
3
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
4
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
2
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
2
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
5
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
4
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
17
</td>
</tr>
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
Soma
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
15
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
22
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
18
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
17
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
8
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
80
</td>
</tr>
</table>
<p><span class="math inline">\(\\\)</span></p>
<ol start="2" style="list-style-type: decimal">
<li>Tabela de frequências relativas por linha</li>
</ol>
<table style="border-collapse:collapse;border-spacing:0;margin:0px auto" class="tg">
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
T/A
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
1
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
2
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
3
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
4
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
Total linha/ Total
</td>
</tr>
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0.33
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0.18
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0.11
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0.18
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
0.12
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
0.19
</td>
</tr>
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
1
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0.13
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0.36
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0.33
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0.24
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
0.12
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
0.26
</td>
</tr>
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
2
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0.27
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0.36
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0.44
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0.29
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
0.25
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
0.34
</td>
</tr>
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
3
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0.27
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0.09
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0.11
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:middle">
0.29
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
0.50
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
0.21
</td>
</tr>
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
Soma
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
1.00
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
1.00
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
1.00
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
1.00
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
1.00
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;text-align:center;vertical-align:top">
1.00
</td>
</tr>
</table>
<p><span class="math inline">\(\\\)</span></p>
<ol start="3" style="list-style-type: decimal">
<li>Tabela de frequências esperadas</li>
</ol>
<p><span class="math inline">\(\\\)</span></p>
<table style="border-collapse:collapse;border-spacing:0;margin:0px auto" class="tg">
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
T/A
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
0
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
1
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
2
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
3
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
4
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
Total linha/ Total
</td>
</tr>
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
0
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
0,19*15=2,85
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
0,19*22=4,18
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
0,19*18=3,42
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
0,19*17=3,23
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
0,19*8=1,52
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
0.19
</td>
</tr>
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
1
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
0,26*15 = 3,9
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
5,72
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
4,68
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
4,42
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
2,08
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
0.26
</td>
</tr>
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
2
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
0,34*15 = 5,1
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
7,48
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
6,12
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
5,78
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
2,72
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
0.34
</td>
</tr>
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
3
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
0,21*15 = 3,15
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
4,62
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
3,78
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:middle">
3,57
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
1,68
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
0.21
</td>
</tr>
<tr>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
Total coluna <br>freq.
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
15
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
22
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
18
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
17
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
8
</td>
<td style="font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:inherit;text-align:center;vertical-align:top">
</td>
</tr>
</table>
<p><span class="math inline">\(\\\)</span></p>
<ol start="4" style="list-style-type: decimal">
<li>Coeficiente</li>
</ol>
<p><span class="math display">\[Q^2 = \frac{(5-2.81)^2}{2.81}+...+\frac{(4-1.7)^2}{1.7} = 12.63\]</span></p>
<p>Como o valor não está próximo de 0, conclui-se que há associação entre as variáveis.</p>
<hr />
</div>
<div id="correlacao" class="section level2">
<h2><span class="header-section-number">2.2</span> Correlação</h2>
<p>Considere um conjunto de dados com <span class="math inline">\(n\)</span> pares de valores para as variáveis <span class="math inline">\(X\)</span> e <span class="math inline">\(Y\)</span>, representados por (<span class="math inline">\(x_i, y_i\)</span>), <span class="math inline">\(i=1,2,...,n\)</span>. O coeficiente de correlação mede a dependência linear entre as variáveis e é calculado da seguinte forma:</p>
<p><span class="math display">\[\rho_{X,Y} = \frac{\sum_{i=1}^{n} (x_i-\bar{x})(y_i-\bar{y})}{\sqrt{[\sum_{j=1}^{n} (x_j-\bar{x})^2][\sum_{j=1}^{n} (y_j-\bar{y})^2]}}\]</span></p>
<p>ou ainda:</p>
<p><span class="math display">\[\rho_{X,Y} = \frac{\sum_{i=1}^{n}x_{i}y_{i}-n\bar{x}\bar{y}}{\sqrt{[\sum_{j=1}^{n}x_{j}^{2}-n\bar{x}^{2}] [\sum_{j=1}^{n}y_{j}^{2}-n\bar{y}^{2}]}}\]</span></p>
<p>A correlação varia de -1 até 1 em que valores acima de 0 indicam correlação positiva (a medida que uma variável aumenta a outra também aumenta), valores abaixo de 0 indicam correlação negativa (a medida que uma variável aumenta a outra diminui) e valores próximos de 0 indicam ausência de correlação.</p>
<p><img src="npest2_2_files/figure-html/unnamed-chunk-1-1.png" width="864" style="display: block; margin: auto;" /></p>
<hr />
</div>
</div>
<div id="graficos" class="section level1 tabset tabset-fade">
<h1><span class="header-section-number">3</span> <strong>Gráficos</strong></h1>
<p>A organização dos dados em tabelas de frequência proporciona um meio eficaz de estudo do comportamento das características de interesse, contudo a informação pode ser melhor representada por meio de gráficos.</p>
<p>Visualização de dados é um assunto interessante pois não requer elevada proficiência em tópicos avançados de Estatística para aplicação e interpretação dos resultados, fazendo com que se caracterize como uma técnica simples, com grande apelo visual e extremamente informativa quanto ao conjunto de dados.</p>
<p>Cuidados devem ser tomados no que diz respeito à escolha do tipo de gráfico para representar a variável com o intuito de evitar que o gráfico fique desproporcional ou privilegiando determinados valores a fim de induzir conclusões àqueles que utilizam o gráfico como forma de visualização.</p>
<p><strong>O uso e divulgação ética e criteriosa de dados devem ser pré-requisitos indispensáveis e inegociáveis</strong></p>
<p>A escolha do gráfico está diretamente ligada ao tipo das variáveis. Além disso, existem gráficos que permitem análises de mais de uma variável simultâneamente a fim de verificar como uma influencia a outra(s). Algumas possibilidades de gráficos para cada tipo de variável são:</p>
<ul>
<li><p><strong>Qualitativa nominal ou ordinal</strong>: setores, barras.</p></li>
<li><p><strong>Quantitativa discreta</strong>: barras, histograma, boxplot.</p></li>
<li><p><strong>Quantitativas contínuas</strong>: histograma ou boxplot.</p></li>
<li><strong>Análises bivariadas</strong>:
<ul>
<li><em>Quantivativa vs Quantitativa</em>: Diagrama de dispersão.</li>