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<!DOCTYPE html>
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<title>第 16 章 分析三向和高阶处理结构 | 混乱数据分析：设计的实验</title>
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<ul class="summary">
<li><a href="./">混乱数据分析：设计的实验</a></li>
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<li class="chapter" data-level="" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i>介绍</a></li>
<li class="part"><span><b>I 热身</b></span></li>
<li class="chapter" data-level="1" data-path="chap1.html"><a href="chap1.html"><i class="fa fa-check"></i><b>1</b> 最简单的情况：具有同质误差的完全随机设计结构中的单向处理结构</a>
<ul>
<li class="chapter" data-level="1.1" data-path="chap1.html"><a href="chap1.html#sec1-1"><i class="fa fa-check"></i><b>1.1</b> 模型定义和假设</a></li>
<li class="chapter" data-level="1.2" data-path="chap1.html"><a href="chap1.html#sec1-2"><i class="fa fa-check"></i><b>1.2</b> 参数估计</a></li>
<li class="chapter" data-level="1.3" data-path="chap1.html"><a href="chap1.html#sec1-3"><i class="fa fa-check"></i><b>1.3</b> 线性组合的推断：检验与置信区间</a></li>
<li class="chapter" data-level="1.4" data-path="chap1.html"><a href="chap1.html#sec1-4"><i class="fa fa-check"></i><b>1.4</b> 示例：任务和脉搏率</a></li>
<li class="chapter" data-level="1.5" data-path="chap1.html"><a href="chap1.html#sec1-5"><i class="fa fa-check"></i><b>1.5</b> 几个线性组合的同时检验</a></li>
<li class="chapter" data-level="1.6" data-path="chap1.html"><a href="chap1.html#sec1-6"><i class="fa fa-check"></i><b>1.6</b> 示例：任务和脉搏率（续）</a></li>
<li class="chapter" data-level="1.7" data-path="chap1.html"><a href="chap1.html#sec1-7"><i class="fa fa-check"></i><b>1.7</b> 检验所有均值相等</a></li>
<li class="chapter" data-level="1.8" data-path="chap1.html"><a href="chap1.html#sec1-8"><i class="fa fa-check"></i><b>1.8</b> 示例：任务和脉搏率（续）</a></li>
<li class="chapter" data-level="1.9" data-path="chap1.html"><a href="chap1.html#sec1-9"><i class="fa fa-check"></i><b>1.9</b> 比较两种模型的一般方法：条件误差原理</a></li>
<li class="chapter" data-level="1.10" data-path="chap1.html"><a href="chap1.html#sec1-10"><i class="fa fa-check"></i><b>1.10</b> 示例：任务和脉搏率（续）</a></li>
<li class="chapter" data-level="1.11" data-path="chap1.html"><a href="chap1.html#sec1-11"><i class="fa fa-check"></i><b>1.11</b> 计算机分析</a></li>
<li class="chapter" data-level="1.12" data-path="chap1.html"><a href="chap1.html#sec1-12"><i class="fa fa-check"></i><b>1.12</b> 结束语</a></li>
<li class="chapter" data-level="1.13" data-path="chap1.html"><a href="chap1.html#sec1-13"><i class="fa fa-check"></i><b>1.13</b> 练习</a></li>
<li class="chapter" data-level="1.14" data-path="chap1.html"><a href="chap1.html#sec1-14"><i class="fa fa-check"></i><b>1.14</b> R 代码</a></li>
</ul></li>
<li class="chapter" data-level="2" data-path="chap2.html"><a href="chap2.html"><i class="fa fa-check"></i><b>2</b> 具有异质误差的完全随机设计结构中的单向处理结构</a>
<ul>
<li class="chapter" data-level="2.1" data-path="chap2.html"><a href="chap2.html#sec2-1"><i class="fa fa-check"></i><b>2.1</b> 模型定义和假设</a></li>
<li class="chapter" data-level="2.2" data-path="chap2.html"><a href="chap2.html#sec2-2"><i class="fa fa-check"></i><b>2.2</b> 参数估计</a></li>
<li class="chapter" data-level="2.3" data-path="chap2.html"><a href="chap2.html#sec2-3"><i class="fa fa-check"></i><b>2.3</b> 方差齐性检验</a>
<ul>
<li class="chapter" data-level="2.3.1" data-path="chap2.html"><a href="chap2.html#sec2-3-1"><i class="fa fa-check"></i><b>2.3.1</b> Hartley’s <em>F</em>-Max Test</a></li>
<li class="chapter" data-level="2.3.2" data-path="chap2.html"><a href="chap2.html#sec2-3-2"><i class="fa fa-check"></i><b>2.3.2</b> Bartlett’s Test</a></li>
<li class="chapter" data-level="2.3.3" data-path="chap2.html"><a href="chap2.html#sec2-3-3"><i class="fa fa-check"></i><b>2.3.3</b> Levene’s Test</a></li>
<li class="chapter" data-level="2.3.4" data-path="chap2.html"><a href="chap2.html#sec2-4-4"><i class="fa fa-check"></i><b>2.3.4</b> Brown and Forsythe’s Test</a></li>
<li class="chapter" data-level="2.3.5" data-path="chap2.html"><a href="chap2.html#sec2-3-5"><i class="fa fa-check"></i><b>2.3.5</b> O’Brien’s Test</a></li>
<li class="chapter" data-level="2.3.6" data-path="chap2.html"><a href="chap2.html#sec2-3-6"><i class="fa fa-check"></i><b>2.3.6</b> 一些建议</a></li>
</ul></li>
<li class="chapter" data-level="2.4" data-path="chap2.html"><a href="chap2.html#sec2-4"><i class="fa fa-check"></i><b>2.4</b> 示例：药物和错误</a></li>
<li class="chapter" data-level="2.5" data-path="chap2.html"><a href="chap2.html#sec2-5"><i class="fa fa-check"></i><b>2.5</b> 关于线性组合的推断</a></li>
<li class="chapter" data-level="2.6" data-path="chap2.html"><a href="chap2.html#sec2-6"><i class="fa fa-check"></i><b>2.6</b> 示例：药物和错误（续）</a></li>
<li class="chapter" data-level="2.7" data-path="chap2.html"><a href="chap2.html#sec2-7"><i class="fa fa-check"></i><b>2.7</b> 自由度的一般 Satterthwaite 近似</a></li>
<li class="chapter" data-level="2.8" data-path="chap2.html"><a href="chap2.html#sec2-8"><i class="fa fa-check"></i><b>2.8</b> 比较所有均值</a></li>
<li class="chapter" data-level="2.9" data-path="chap2.html"><a href="chap2.html#sec2-9"><i class="fa fa-check"></i><b>2.9</b> 结束语</a></li>
<li class="chapter" data-level="2.10" data-path="chap2.html"><a href="chap2.html#sec2-10"><i class="fa fa-check"></i><b>2.10</b> 练习</a></li>
<li class="chapter" data-level="2.11" data-path="chap2.html"><a href="chap2.html#sec2-11"><i class="fa fa-check"></i><b>2.11</b> R 代码</a></li>
</ul></li>
<li class="part"><span><b>II 磨刀</b></span></li>
<li class="chapter" data-level="3" data-path="chap3.html"><a href="chap3.html"><i class="fa fa-check"></i><b>3</b> 同时推断程序和多重比较</a>
<ul>
<li class="chapter" data-level="3.1" data-path="chap3.html"><a href="chap3.html#sec3-1"><i class="fa fa-check"></i><b>3.1</b> 错误率</a></li>
<li class="chapter" data-level="3.2" data-path="chap3.html"><a href="chap3.html#sec3-2"><i class="fa fa-check"></i><b>3.2</b> 建议</a></li>
<li class="chapter" data-level="3.3" data-path="chap3.html"><a href="chap3.html#sec3-3"><i class="fa fa-check"></i><b>3.3</b> 最小显著差异</a></li>
<li class="chapter" data-level="3.4" data-path="chap3.html"><a href="chap3.html#sec3-4"><i class="fa fa-check"></i><b>3.4</b> Fisher’s LSD Procedure</a></li>
<li class="chapter" data-level="3.5" data-path="chap3.html"><a href="chap3.html#sec3-5"><i class="fa fa-check"></i><b>3.5</b> Bonferroni’s Method</a></li>
<li class="chapter" data-level="3.6" data-path="chap3.html"><a href="chap3.html#sec3-6"><i class="fa fa-check"></i><b>3.6</b> Scheffé’s Procedure</a></li>
<li class="chapter" data-level="3.7" data-path="chap3.html"><a href="chap3.html#sec3-7"><i class="fa fa-check"></i><b>3.7</b> Tukey–Kramer Method</a></li>
<li class="chapter" data-level="3.8" data-path="chap3.html"><a href="chap3.html#sec3-8"><i class="fa fa-check"></i><b>3.8</b> 模拟方法</a></li>
<li class="chapter" data-level="3.9" data-path="chap3.html"><a href="chap3.html#sec3-9"><i class="fa fa-check"></i><b>3.9</b> Šidák Procedure</a></li>
<li class="chapter" data-level="3.10" data-path="chap3.html"><a href="chap3.html#sec3-10"><i class="fa fa-check"></i><b>3.10</b> 示例：成对比较</a></li>
<li class="chapter" data-level="3.11" data-path="chap3.html"><a href="chap3.html#sec3-11"><i class="fa fa-check"></i><b>3.11</b> Dunnett’s Procedure</a></li>
<li class="chapter" data-level="3.12" data-path="chap3.html"><a href="chap3.html#sec3-12"><i class="fa fa-check"></i><b>3.12</b> 示例：与对照比较</a></li>
<li class="chapter" data-level="3.13" data-path="chap3.html"><a href="chap3.html#sec3-13"><i class="fa fa-check"></i><b>3.13</b> 多元 <span class="math inline">\(t\)</span></a></li>
<li class="chapter" data-level="3.14" data-path="chap3.html"><a href="chap3.html#sec3-14"><i class="fa fa-check"></i><b>3.14</b> 示例：线性独立比较</a></li>
<li class="chapter" data-level="3.15" data-path="chap3.html"><a href="chap3.html#sec3-15"><i class="fa fa-check"></i><b>3.15</b> 序贯拒绝方法</a>
<ul>
<li class="chapter" data-level="3.15.1" data-path="chap3.html"><a href="chap3.html#sec3-15-1"><i class="fa fa-check"></i><b>3.15.1</b> Bonferroni–Holm Method</a></li>
<li class="chapter" data-level="3.15.2" data-path="chap3.html"><a href="chap3.html#sec3-15-2"><i class="fa fa-check"></i><b>3.15.2</b> Šidák–Holm Method</a></li>
<li class="chapter" data-level="3.15.3" data-path="chap3.html"><a href="chap3.html#sec3-15-3"><i class="fa fa-check"></i><b>3.15.3</b> 控制 FDR 的 Benjamini 和 Hochberg Method</a></li>
</ul></li>
<li class="chapter" data-level="3.16" data-path="chap3.html"><a href="chap3.html#sec3-16"><i class="fa fa-check"></i><b>3.16</b> 示例：线性相关比较</a></li>
<li class="chapter" data-level="3.17" data-path="chap3.html"><a href="chap3.html#sec3-17"><i class="fa fa-check"></i><b>3.17</b> 多重极差检验</a>
<ul>
<li class="chapter" data-level="3.17.1" data-path="chap3.html"><a href="chap3.html#sec3-17-1"><i class="fa fa-check"></i><b>3.17.1</b> Student–Newman–Keul’s Method</a></li>
<li class="chapter" data-level="3.17.2" data-path="chap3.html"><a href="chap3.html#sec3-17-2"><i class="fa fa-check"></i><b>3.17.2</b> Duncan’s New Multiple Range Method</a></li>
</ul></li>
<li class="chapter" data-level="3.18" data-path="chap3.html"><a href="chap3.html#sec3-18"><i class="fa fa-check"></i><b>3.18</b> Waller–Duncan Procedure</a></li>
<li class="chapter" data-level="3.19" data-path="chap3.html"><a href="chap3.html#sec3-19"><i class="fa fa-check"></i><b>3.19</b> 示例：成对比较的多重极差</a></li>
<li class="chapter" data-level="3.20" data-path="chap3.html"><a href="chap3.html#sec3-20"><i class="fa fa-check"></i><b>3.20</b> 警示</a></li>
<li class="chapter" data-level="3.21" data-path="chap3.html"><a href="chap3.html#sec3-21"><i class="fa fa-check"></i><b>3.21</b> 结束语</a></li>
<li class="chapter" data-level="3.22" data-path="chap3.html"><a href="chap3.html#sec3-22"><i class="fa fa-check"></i><b>3.22</b> 练习</a></li>
<li class="chapter" data-level="3.23" data-path="chap3.html"><a href="chap3.html#sec3-23"><i class="fa fa-check"></i><b>3.23</b> R 代码</a></li>
</ul></li>
<li class="chapter" data-level="4" data-path="chap4.html"><a href="chap4.html"><i class="fa fa-check"></i><b>4</b> 实验设计基础</a>
<ul>
<li class="chapter" data-level="4.1" data-path="chap4.html"><a href="chap4.html#sec4-1"><i class="fa fa-check"></i><b>4.1</b> 介绍基本概念</a></li>
<li class="chapter" data-level="4.2" data-path="chap4.html"><a href="chap4.html#sec4-2"><i class="fa fa-check"></i><b>4.2</b> 设计实验的结构</a>
<ul>
<li class="chapter" data-level="4.2.1" data-path="chap4.html"><a href="chap4.html#sec4-2-1"><i class="fa fa-check"></i><b>4.2.1</b> 设计结构类型</a></li>
<li class="chapter" data-level="4.2.2" data-path="chap4.html"><a href="chap4.html#sec4-2-2"><i class="fa fa-check"></i><b>4.2.2</b> 处理结构类型</a></li>
</ul></li>
<li class="chapter" data-level="4.3" data-path="chap4.html"><a href="chap4.html#sec4-3"><i class="fa fa-check"></i><b>4.3</b> 不同设计实验的示例</a>
<ul>
<li class="chapter" data-level="4.3.1" data-path="chap4.html"><a href="chap4.html#sec4-3-1"><i class="fa fa-check"></i><b>4.3.1</b> 示例 4.1: 饮食</a></li>
<li class="chapter" data-level="4.3.2" data-path="chap4.html"><a href="chap4.html#sec4-3-2"><i class="fa fa-check"></i><b>4.3.2</b> 示例 4.2: 房屋油漆</a></li>
<li class="chapter" data-level="4.3.3" data-path="chap4.html"><a href="chap4.html#sec4-3-3"><i class="fa fa-check"></i><b>4.3.3</b> 示例 4.3: 钢板</a></li>
<li class="chapter" data-level="4.3.4" data-path="chap4.html"><a href="chap4.html#sec4-3-4"><i class="fa fa-check"></i><b>4.3.4</b> 示例 4.4: 氮和钾的水平</a></li>
<li class="chapter" data-level="4.3.5" data-path="chap4.html"><a href="chap4.html#sec4-3-5"><i class="fa fa-check"></i><b>4.3.5</b> 示例 4.5: 区组和重复</a></li>
<li class="chapter" data-level="4.3.6" data-path="chap4.html"><a href="chap4.html#sec4-3-6"><i class="fa fa-check"></i><b>4.3.6</b> 示例 4.6：行区组和列区组</a></li>
</ul></li>
<li class="chapter" data-level="4.4" data-path="chap4.html"><a href="chap4.html#sec4-4"><i class="fa fa-check"></i><b>4.4</b> 结束语</a></li>
<li class="chapter" data-level="4.5" data-path="chap4.html"><a href="chap4.html#sec4-5"><i class="fa fa-check"></i><b>4.5</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="5" data-path="chap5.html"><a href="chap5.html"><i class="fa fa-check"></i><b>5</b> 多水平设计：裂区、条区、重复测量及其组合</a>
<ul>
<li class="chapter" data-level="5.1" data-path="chap5.html"><a href="chap5.html#sec5-1"><i class="fa fa-check"></i><b>5.1</b> 识别实验单元的尺寸——四种基本设计结构</a></li>
<li class="chapter" data-level="5.2" data-path="chap5.html"><a href="chap5.html#sec5-2"><i class="fa fa-check"></i><b>5.2</b> 分层设计：一种多水平的设计结构</a></li>
<li class="chapter" data-level="5.3" data-path="chap5.html"><a href="chap5.html#sec5-3"><i class="fa fa-check"></i><b>5.3</b> 裂区设计结构：两水平设计结构</a>
<ul>
<li class="chapter" data-level="5.3.1" data-path="chap5.html"><a href="chap5.html#sec5-3-1"><i class="fa fa-check"></i><b>5.3.1</b> 示例 5.1：烹饪大豆——最简单的裂区或两水平设计结构</a></li>
<li class="chapter" data-level="5.3.2" data-path="chap5.html"><a href="chap5.html#sec5-3-2"><i class="fa fa-check"></i><b>5.3.2</b> 示例 5.2：磨小麦——通常的裂区或两水平设计结构</a></li>
<li class="chapter" data-level="5.3.3" data-path="chap5.html"><a href="chap5.html#sec5-3-3"><i class="fa fa-check"></i><b>5.3.3</b> 示例 5.3：烘焙面包——具有不完全块设计结构的裂区</a></li>
<li class="chapter" data-level="5.3.4" data-path="chap5.html"><a href="chap5.html#sec5-3-4"><i class="fa fa-check"></i><b>5.3.4</b> 示例 5.4：展示柜中的肉——复杂裂区或四水平设计</a></li>
</ul></li>
<li class="chapter" data-level="5.4" data-path="chap5.html"><a href="chap5.html#sec5-4"><i class="fa fa-check"></i><b>5.4</b> 条区设计结构：一种无层次的多水平设计</a>
<ul>
<li class="chapter" data-level="5.4.1" data-path="chap5.html"><a href="chap5.html#sec5-4-1"><i class="fa fa-check"></i><b>5.4.1</b> 示例 5.5：制作奶酪</a></li>
</ul></li>
<li class="chapter" data-level="5.5" data-path="chap5.html"><a href="chap5.html#sec5-5"><i class="fa fa-check"></i><b>5.5</b> 重复测量设计</a>
<ul>
<li class="chapter" data-level="5.5.1" data-path="chap5.html"><a href="chap5.html#sec5-5-1"><i class="fa fa-check"></i><b>5.5.1</b> 示例 5.6：马足——基本重复测量设计</a></li>
<li class="chapter" data-level="5.5.2" data-path="chap5.html"><a href="chap5.html#sec5-5-2"><i class="fa fa-check"></i><b>5.5.2</b> 示例 5.7：舒适度研究——重复测量设计</a></li>
<li class="chapter" data-level="5.5.3" data-path="chap5.html"><a href="chap5.html#示例-5.8交叉或转换设计"><i class="fa fa-check"></i><b>5.5.3</b> 示例 5.8：交叉或转换设计</a></li>
</ul></li>
<li class="chapter" data-level="5.6" data-path="chap5.html"><a href="chap5.html#sec5-6"><i class="fa fa-check"></i><b>5.6</b> 涉及嵌套因素的设计</a>
<ul>
<li class="chapter" data-level="5.6.1" data-path="chap5.html"><a href="chap5.html#sec5-6-1"><i class="fa fa-check"></i><b>5.6.1</b> 示例 5.9：动物遗传学</a></li>
<li class="chapter" data-level="5.6.2" data-path="chap5.html"><a href="chap5.html#sec5-6-2"><i class="fa fa-check"></i><b>5.6.2</b> 示例 5.10：大豆的生育期组</a></li>
<li class="chapter" data-level="5.6.3" data-path="chap5.html"><a href="chap5.html#sec5-6-3"><i class="fa fa-check"></i><b>5.6.3</b> 示例 5.11：飞机引擎</a></li>
<li class="chapter" data-level="5.6.4" data-path="chap5.html"><a href="chap5.html#sec5-6-4"><i class="fa fa-check"></i><b>5.6.4</b> 示例 5.12：简单的舒适度实验</a></li>
<li class="chapter" data-level="5.6.5" data-path="chap5.html"><a href="chap5.html#sec5-6-5"><i class="fa fa-check"></i><b>5.6.5</b> 示例 5.13：重复测量的多地点研究</a></li>
</ul></li>
<li class="chapter" data-level="5.7" data-path="chap5.html"><a href="chap5.html#sec5-7"><i class="fa fa-check"></i><b>5.7</b> 结束语</a></li>
<li class="chapter" data-level="5.8" data-path="chap5.html"><a href="chap5.html#sec5-8"><i class="fa fa-check"></i><b>5.8</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="6" data-path="chap6.html"><a href="chap6.html"><i class="fa fa-check"></i><b>6</b> 模型的矩阵形式</a>
<ul>
<li class="chapter" data-level="6.1" data-path="chap6.html"><a href="chap6.html#sec6-1"><i class="fa fa-check"></i><b>6.1</b> 基本符号</a>
<ul>
<li class="chapter" data-level="6.1.1" data-path="chap6.html"><a href="chap6.html#sec6-1-1"><i class="fa fa-check"></i><b>6.1.1</b> 简单线性回归模型</a></li>
<li class="chapter" data-level="6.1.2" data-path="chap6.html"><a href="chap6.html#sec6-1-2"><i class="fa fa-check"></i><b>6.1.2</b> 单向处理结构模型</a></li>
<li class="chapter" data-level="6.1.3" data-path="chap6.html"><a href="chap6.html#sec6-1-3"><i class="fa fa-check"></i><b>6.1.3</b> 双向处理结构模型</a></li>
<li class="chapter" data-level="6.1.4" data-path="chap6.html"><a href="chap6.html#sec6-1-4"><i class="fa fa-check"></i><b>6.1.4</b> 示例 6.1：双向处理结构的均值模型</a></li>
</ul></li>
<li class="chapter" data-level="6.2" data-path="chap6.html"><a href="chap6.html#sec6-2"><i class="fa fa-check"></i><b>6.2</b> 最小二乘估计</a>
<ul>
<li class="chapter" data-level="6.2.1" data-path="chap6.html"><a href="chap6.html#sec6-2-1"><i class="fa fa-check"></i><b>6.2.1</b> 最小二乘方程组</a></li>
<li class="chapter" data-level="6.2.2" data-path="chap6.html"><a href="chap6.html#sec6-2-2"><i class="fa fa-check"></i><b>6.2.2</b> 零和限制</a></li>
<li class="chapter" data-level="6.2.3" data-path="chap6.html"><a href="chap6.html#sec6-2-3"><i class="fa fa-check"></i><b>6.2.3</b> 置零限制</a></li>
<li class="chapter" data-level="6.2.4" data-path="chap6.html"><a href="chap6.html#sec6-2-4"><i class="fa fa-check"></i><b>6.2.4</b> 示例 6.2：单向处理结构</a></li>
</ul></li>
<li class="chapter" data-level="6.3" data-path="chap6.html"><a href="chap6.html#sec6-3"><i class="fa fa-check"></i><b>6.3</b> 可估性和连通的设计</a>
<ul>
<li class="chapter" data-level="6.3.1" data-path="chap6.html"><a href="chap6.html#sec6-3-1"><i class="fa fa-check"></i><b>6.3.1</b> 可估函数</a></li>
<li class="chapter" data-level="6.3.2" data-path="chap6.html"><a href="chap6.html#sec6-3-2"><i class="fa fa-check"></i><b>6.3.2</b> 连通性</a></li>
</ul></li>
<li class="chapter" data-level="6.4" data-path="chap6.html"><a href="chap6.html#sec6-4"><i class="fa fa-check"></i><b>6.4</b> 关于线性模型参数的检验假设</a></li>
<li class="chapter" data-level="6.5" data-path="chap6.html"><a href="chap6.html#sec6-5"><i class="fa fa-check"></i><b>6.5</b> 总体边际均值</a></li>
<li class="chapter" data-level="6.6" data-path="chap6.html"><a href="chap6.html#sec6-6"><i class="fa fa-check"></i><b>6.6</b> 结束语</a></li>
<li class="chapter" data-level="6.7" data-path="chap6.html"><a href="chap6.html#sec6-7"><i class="fa fa-check"></i><b>6.7</b> 练习</a></li>
<li class="chapter" data-level="6.8" data-path="chap6.html"><a href="chap6.html#sec6-8"><i class="fa fa-check"></i><b>6.8</b> R 代码</a></li>
</ul></li>
<li class="part"><span><b>III 砍柴</b></span></li>
<li class="chapter" data-level="7" data-path="chap7.html"><a href="chap7.html"><i class="fa fa-check"></i><b>7</b> 均衡双向处理结构</a>
<ul>
<li class="chapter" data-level="7.1" data-path="chap7.html"><a href="chap7.html#sec7-1"><i class="fa fa-check"></i><b>7.1</b> 模型定义和假设</a>
<ul>
<li class="chapter" data-level="7.1.1" data-path="chap7.html"><a href="chap7.html#sec7-1-1"><i class="fa fa-check"></i><b>7.1.1</b> 均值模型</a></li>
<li class="chapter" data-level="7.1.2" data-path="chap7.html"><a href="chap7.html#sec7-1-2"><i class="fa fa-check"></i><b>7.1.2</b> 效应模型</a></li>
</ul></li>
<li class="chapter" data-level="7.2" data-path="chap7.html"><a href="chap7.html#sec7-2"><i class="fa fa-check"></i><b>7.2</b> 参数估计</a></li>
<li class="chapter" data-level="7.3" data-path="chap7.html"><a href="chap7.html#sec7-3"><i class="fa fa-check"></i><b>7.3</b> 交互作用及它们的重要性</a></li>
<li class="chapter" data-level="7.4" data-path="chap7.html"><a href="chap7.html#sec7-4"><i class="fa fa-check"></i><b>7.4</b> 主效应</a></li>
<li class="chapter" data-level="7.5" data-path="chap7.html"><a href="chap7.html#sec7-5"><i class="fa fa-check"></i><b>7.5</b> 计算机分析</a></li>
<li class="chapter" data-level="7.6" data-path="chap7.html"><a href="chap7.html#sec7-6"><i class="fa fa-check"></i><b>7.6</b> 结束语</a></li>
<li class="chapter" data-level="7.7" data-path="chap7.html"><a href="chap7.html#sec7-7"><i class="fa fa-check"></i><b>7.7</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="8" data-path="chap8.html"><a href="chap8.html"><i class="fa fa-check"></i><b>8</b> 案例研究：均衡双向实验的完整分析</a>
<ul>
<li class="chapter" data-level="8.1" data-path="chap8.html"><a href="chap8.html#sec8-1"><i class="fa fa-check"></i><b>8.1</b> 主效应均值对比</a></li>
<li class="chapter" data-level="8.2" data-path="chap8.html"><a href="chap8.html#sec8-2"><i class="fa fa-check"></i><b>8.2</b> 交互对比</a></li>
<li class="chapter" data-level="8.3" data-path="chap8.html"><a href="chap8.html#sec8-3"><i class="fa fa-check"></i><b>8.3</b> 油漆铺路示例</a></li>
<li class="chapter" data-level="8.4" data-path="chap8.html"><a href="chap8.html#sec8-4"><i class="fa fa-check"></i><b>8.4</b> 分析定量处理因素</a></li>
<li class="chapter" data-level="8.5" data-path="chap8.html"><a href="chap8.html#sec8-5"><i class="fa fa-check"></i><b>8.5</b> 多重检验</a></li>
<li class="chapter" data-level="8.6" data-path="chap8.html"><a href="chap8.html#sec8-6"><i class="fa fa-check"></i><b>8.6</b> 结束语</a></li>
<li class="chapter" data-level="8.7" data-path="chap8.html"><a href="chap8.html#sec8-7"><i class="fa fa-check"></i><b>8.7</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="9" data-path="chap9.html"><a href="chap9.html"><i class="fa fa-check"></i><b>9</b> 使用均值模型分析子类数不等的均衡双向处理结构</a>
<ul>
<li class="chapter" data-level="9.1" data-path="chap9.html"><a href="chap9.html#sec9-1"><i class="fa fa-check"></i><b>9.1</b> 模型定义和假设</a></li>
<li class="chapter" data-level="9.2" data-path="chap9.html"><a href="chap9.html#sec9-2"><i class="fa fa-check"></i><b>9.2</b> 参数估计</a></li>
<li class="chapter" data-level="9.3" data-path="chap9.html"><a href="chap9.html#sec9-3"><i class="fa fa-check"></i><b>9.3</b> 检验所有均值是否相等</a></li>
<li class="chapter" data-level="9.4" data-path="chap9.html"><a href="chap9.html#sec9-4"><i class="fa fa-check"></i><b>9.4</b> 交互作用和主效应假设</a></li>
<li class="chapter" data-level="9.5" data-path="chap9.html"><a href="chap9.html#sec9-5"><i class="fa fa-check"></i><b>9.5</b> 总体边际均值</a></li>
<li class="chapter" data-level="9.6" data-path="chap9.html"><a href="chap9.html#sec9-6"><i class="fa fa-check"></i><b>9.6</b> 同时推断与多重比较</a></li>
<li class="chapter" data-level="9.7" data-path="chap9.html"><a href="chap9.html#sec9-7"><i class="fa fa-check"></i><b>9.7</b> 结束语</a></li>
<li class="chapter" data-level="9.8" data-path="chap9.html"><a href="chap9.html#sec9-8"><i class="fa fa-check"></i><b>9.8</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="10" data-path="chap10.html"><a href="chap10.html"><i class="fa fa-check"></i><b>10</b> 使用效应模型分析子类数不等的均衡双向处理结构</a>
<ul>
<li class="chapter" data-level="10.1" data-path="chap10.html"><a href="chap10.html#sec10-1"><i class="fa fa-check"></i><b>10.1</b> 模型定义</a></li>
<li class="chapter" data-level="10.2" data-path="chap10.html"><a href="chap10.html#sec10-2"><i class="fa fa-check"></i><b>10.2</b> 参数估计和 I 型分析</a></li>
<li class="chapter" data-level="10.3" data-path="chap10.html"><a href="chap10.html#sec10-3"><i class="fa fa-check"></i><b>10.3</b> 在 SAS 中使用可估函数</a></li>
<li class="chapter" data-level="10.4" data-path="chap10.html"><a href="chap10.html#sec10-4"><i class="fa fa-check"></i><b>10.4</b> I–IV 型假设</a></li>
<li class="chapter" data-level="10.5" data-path="chap10.html"><a href="chap10.html#sec10-5"><i class="fa fa-check"></i><b>10.5</b> 在 SAS-GLM 中使用 I–IV 型可估函数</a></li>
<li class="chapter" data-level="10.6" data-path="chap10.html"><a href="chap10.html#sec10-6"><i class="fa fa-check"></i><b>10.6</b> 总体边际均值与最小二乘均值</a></li>
<li class="chapter" data-level="10.7" data-path="chap10.html"><a href="chap10.html#sec10-7"><i class="fa fa-check"></i><b>10.7</b> 计算机分析</a></li>
<li class="chapter" data-level="10.8" data-path="chap10.html"><a href="chap10.html#sec10-8"><i class="fa fa-check"></i><b>10.8</b> 结束语</a></li>
</ul></li>
<li class="chapter" data-level="11" data-path="chap11.html"><a href="chap11.html"><i class="fa fa-check"></i><b>11</b> 分析子类数不等的大型均衡双向实验</a>
<ul>
<li class="chapter" data-level="11.1" data-path="chap11.html"><a href="chap11.html#sec11-1"><i class="fa fa-check"></i><b>11.1</b> 可行性问题</a></li>
<li class="chapter" data-level="11.2" data-path="chap11.html"><a href="chap11.html#sec11-2"><i class="fa fa-check"></i><b>11.2</b> 未加权均值法</a></li>
<li class="chapter" data-level="11.3" data-path="chap11.html"><a href="chap11.html#sec11-3"><i class="fa fa-check"></i><b>11.3</b> 同时推断与多重比较</a></li>
<li class="chapter" data-level="11.4" data-path="chap11.html"><a href="chap11.html#sec11-4"><i class="fa fa-check"></i><b>11.4</b> 未加权均值的示例</a></li>
<li class="chapter" data-level="11.5" data-path="chap11.html"><a href="chap11.html#sec11-5"><i class="fa fa-check"></i><b>11.5</b> 计算机分析</a></li>
<li class="chapter" data-level="11.6" data-path="chap11.html"><a href="chap11.html#sec11-6"><i class="fa fa-check"></i><b>11.6</b> 结束语</a></li>
</ul></li>
<li class="chapter" data-level="12" data-path="chap12.html"><a href="chap12.html"><i class="fa fa-check"></i><b>12</b> 案例研究：子类数不等的均衡双向处理结构</a>
<ul>
<li class="chapter" data-level="12.1" data-path="chap12.html"><a href="chap12.html#sec12-1"><i class="fa fa-check"></i><b>12.1</b> 脂肪-表面活性剂示例</a></li>
<li class="chapter" data-level="12.2" data-path="chap12.html"><a href="chap12.html#sec12-2"><i class="fa fa-check"></i><b>12.2</b> 结束语</a></li>
</ul></li>
<li class="chapter" data-level="13" data-path="chap13.html"><a href="chap13.html"><i class="fa fa-check"></i><b>13</b> 使用均值模型分析缺失处理组合的双向处理结构</a>
<ul>
<li class="chapter" data-level="13.1" data-path="chap13.html"><a href="chap13.html#sec13-1"><i class="fa fa-check"></i><b>13.1</b> 参数估计</a></li>
<li class="chapter" data-level="13.2" data-path="chap13.html"><a href="chap13.html#sec13-2"><i class="fa fa-check"></i><b>13.2</b> 假设检验和置信区间</a>
<ul>
<li class="chapter" data-level="13.2.1" data-path="chap13.html"><a href="chap13.html#sec13-2-1"><i class="fa fa-check"></i><b>13.2.1</b> 示例 13.1</a></li>
</ul></li>
<li class="chapter" data-level="13.3" data-path="chap13.html"><a href="chap13.html#sec13-3"><i class="fa fa-check"></i><b>13.3</b> 计算机分析</a></li>
<li class="chapter" data-level="13.4" data-path="chap13.html"><a href="chap13.html#sec13-4"><i class="fa fa-check"></i><b>13.4</b> 结束语</a></li>
<li class="chapter" data-level="13.5" data-path="chap13.html"><a href="chap13.html#sec13-5"><i class="fa fa-check"></i><b>13.5</b> 练习</a></li>
<li class="chapter" data-level="13.6" data-path="chap13.html"><a href="chap13.html#sec13-6"><i class="fa fa-check"></i><b>13.6</b> R 代码</a></li>
</ul></li>
<li class="chapter" data-level="14" data-path="chap14.html"><a href="chap14.html"><i class="fa fa-check"></i><b>14</b> 使用效应模型分析缺失处理组合的双向处理结构</a>
<ul>
<li class="chapter" data-level="14.1" data-path="chap14.html"><a href="chap14.html#i-型和-ii-型假设"><i class="fa fa-check"></i><b>14.1</b> I 型和 II 型假设</a></li>
<li class="chapter" data-level="14.2" data-path="chap14.html"><a href="chap14.html#iii-型假设"><i class="fa fa-check"></i><b>14.2</b> III 型假设</a></li>
<li class="chapter" data-level="14.3" data-path="chap14.html"><a href="chap14.html#sec14-3"><i class="fa fa-check"></i><b>14.3</b> IV 型假设</a></li>
<li class="chapter" data-level="14.4" data-path="chap14.html"><a href="chap14.html#sec14-4"><i class="fa fa-check"></i><b>14.4</b> 总体边际均值和最小二乘均值</a></li>
<li class="chapter" data-level="14.5" data-path="chap14.html"><a href="chap14.html#sec14-5"><i class="fa fa-check"></i><b>14.5</b> 计算机分析</a></li>
<li class="chapter" data-level="14.6" data-path="chap14.html"><a href="chap14.html#sec14-6"><i class="fa fa-check"></i><b>14.6</b> 结束语</a></li>
<li class="chapter" data-level="14.7" data-path="chap14.html"><a href="chap14.html#sec14-7"><i class="fa fa-check"></i><b>14.7</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="15" data-path="chap15.html"><a href="chap15.html"><i class="fa fa-check"></i><b>15</b> 案例研究：缺失处理组合的双向处理结构</a>
<ul>
<li class="chapter" data-level="15.1" data-path="chap15.html"><a href="chap15.html#sec15-1"><i class="fa fa-check"></i><b>15.1</b> 案例研究</a></li>
<li class="chapter" data-level="15.2" data-path="chap15.html"><a href="chap15.html#sec15-2"><i class="fa fa-check"></i><b>15.2</b> 结束语</a></li>
</ul></li>
<li class="chapter" data-level="16" data-path="chap16.html"><a href="chap16.html"><i class="fa fa-check"></i><b>16</b> 分析三向和高阶处理结构</a>
<ul>
<li class="chapter" data-level="16.1" data-path="chap16.html"><a href="chap16.html#sec16-1"><i class="fa fa-check"></i><b>16.1</b> 一般策略</a></li>
<li class="chapter" data-level="16.2" data-path="chap16.html"><a href="chap16.html#sec16-2"><i class="fa fa-check"></i><b>16.2</b> 均衡和不均衡实验</a></li>
<li class="chapter" data-level="16.3" data-path="chap16.html"><a href="chap16.html#sec16-3"><i class="fa fa-check"></i><b>16.3</b> I 型和 II 型分析</a></li>
<li class="chapter" data-level="16.4" data-path="chap16.html"><a href="chap16.html#sec16-4"><i class="fa fa-check"></i><b>16.4</b> 结束语</a></li>
<li class="chapter" data-level="16.5" data-path="chap16.html"><a href="chap16.html#sec16-5"><i class="fa fa-check"></i><b>16.5</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="17" data-path="chap17.html"><a href="chap17.html"><i class="fa fa-check"></i><b>17</b> 案例研究：具有许多缺失处理组合的三向处理结构</a>
<ul>
<li class="chapter" data-level="17.1" data-path="chap17.html"><a href="chap17.html#sec17-1"><i class="fa fa-check"></i><b>17.1</b> 营养评分示例</a></li>
<li class="chapter" data-level="17.2" data-path="chap17.html"><a href="chap17.html#sec17-2"><i class="fa fa-check"></i><b>17.2</b> SAS-GLM 分析</a></li>
<li class="chapter" data-level="17.3" data-path="chap17.html"><a href="chap17.html#sec17-3"><i class="fa fa-check"></i><b>17.3</b> 一个完整的分析</a></li>
<li class="chapter" data-level="17.4" data-path="chap17.html"><a href="chap17.html#sec17-4"><i class="fa fa-check"></i><b>17.4</b> 结束语</a></li>
<li class="chapter" data-level="17.5" data-path="chap17.html"><a href="chap17.html#sec17-5"><i class="fa fa-check"></i><b>17.5</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="18" data-path="chap18.html"><a href="chap18.html"><i class="fa fa-check"></i><b>18</b> 随机效应模型和方差分量</a>
<ul>
<li class="chapter" data-level="18.1" data-path="chap18.html"><a href="chap18.html#sec18-1"><i class="fa fa-check"></i><b>18.1</b> 介绍</a>
<ul>
<li class="chapter" data-level="18.1.1" data-path="chap18.html"><a href="chap18.html#sec18-1-1"><i class="fa fa-check"></i><b>18.1.1</b> 示例 18.1：随机效应嵌套处理结构</a></li>
</ul></li>
<li class="chapter" data-level="18.2" data-path="chap18.html"><a href="chap18.html#sec18-2"><i class="fa fa-check"></i><b>18.2</b> 矩阵表示法中的一般随机效应模型</a>
<ul>
<li class="chapter" data-level="18.2.1" data-path="chap18.html"><a href="chap18.html#sec18-2-1"><i class="fa fa-check"></i><b>18.2.1</b> 示例 18.2：单向随机效应模型</a></li>
</ul></li>
<li class="chapter" data-level="18.3" data-path="chap18.html"><a href="chap18.html#sec18-3"><i class="fa fa-check"></i><b>18.3</b> 计算期望均方</a>
<ul>
<li class="chapter" data-level="18.3.1" data-path="chap18.html"><a href="chap18.html#sec18-3-1"><i class="fa fa-check"></i><b>18.3.1</b> 代数方法</a></li>
<li class="chapter" data-level="18.3.2" data-path="chap18.html"><a href="chap18.html#sec18-3-2"><i class="fa fa-check"></i><b>18.3.2</b> Hartley 综合法的计算</a></li>
</ul></li>
<li class="chapter" data-level="18.4" data-path="chap18.html"><a href="chap18.html#sec18-4"><i class="fa fa-check"></i><b>18.4</b> 结束语</a></li>
<li class="chapter" data-level="18.5" data-path="chap18.html"><a href="chap18.html#sec18-5"><i class="fa fa-check"></i><b>18.5</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="19" data-path="chap19.html"><a href="chap19.html"><i class="fa fa-check"></i><b>19</b> 方差分量的估计方法</a>
<ul>
<li class="chapter" data-level="19.1" data-path="chap19.html"><a href="chap19.html#sec19-1"><i class="fa fa-check"></i><b>19.1</b> 矩法</a>
<ul>
<li class="chapter" data-level="19.1.1" data-path="chap19.html"><a href="chap19.html#sec19-1-1"><i class="fa fa-check"></i><b>19.1.1</b> 应用。示例 19.1：不均衡单向模型</a></li>
<li class="chapter" data-level="19.1.2" data-path="chap19.html"><a href="chap19.html#sec19-1-2"><i class="fa fa-check"></i><b>19.1.2</b> 示例 19.2：单向随机效应模型中的小麦品种</a></li>
<li class="chapter" data-level="19.1.3" data-path="chap19.html"><a href="chap19.html#sec19-1-3"><i class="fa fa-check"></i><b>19.1.3</b> 示例 19.3：表 18.2 中的双向设计数据</a></li>
</ul></li>
<li class="chapter" data-level="19.2" data-path="chap19.html"><a href="chap19.html#sec19-2"><i class="fa fa-check"></i><b>19.2</b> 最大似然</a>
<ul>
<li class="chapter" data-level="19.2.1" data-path="chap19.html"><a href="chap19.html#sec19-2-1"><i class="fa fa-check"></i><b>19.2.1</b> 示例 19.4：均衡单向模型的最大似然解</a></li>
</ul></li>
<li class="chapter" data-level="19.3" data-path="chap19.html"><a href="chap19.html#sec19-3"><i class="fa fa-check"></i><b>19.3</b> 受限或残差最大似然估计</a>
<ul>
<li class="chapter" data-level="19.3.1" data-path="chap19.html"><a href="chap19.html#sec19-3-1"><i class="fa fa-check"></i><b>19.3.1</b> 示例 19.5：均衡单向模型的 REML 解</a></li>
</ul></li>
<li class="chapter" data-level="19.4" data-path="chap19.html"><a href="chap19.html#sec19-4"><i class="fa fa-check"></i><b>19.4</b> MIVQUE 法</a>
<ul>
<li class="chapter" data-level="19.4.1" data-path="chap19.html"><a href="chap19.html#sec19-4-1"><i class="fa fa-check"></i><b>19.4.1</b> 方法说明</a></li>
<li class="chapter" data-level="19.4.2" data-path="chap19.html"><a href="chap19.html#sec19-4-2"><i class="fa fa-check"></i><b>19.4.2</b> 应用。示例 19.6：MIVQUE 用于不均衡单向设计</a></li>
</ul></li>
<li class="chapter" data-level="19.5" data-path="chap19.html"><a href="chap19.html#sec19-5"><i class="fa fa-check"></i><b>19.5</b> 使用 JMP 估计方差分量</a></li>
<li class="chapter" data-level="19.6" data-path="chap19.html"><a href="chap19.html#sec19-6"><i class="fa fa-check"></i><b>19.6</b> 结束语</a></li>
<li class="chapter" data-level="19.7" data-path="chap19.html"><a href="chap19.html#sec19-7"><i class="fa fa-check"></i><b>19.7</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="20" data-path="chap20.html"><a href="chap20.html"><i class="fa fa-check"></i><b>20</b> 方差分量的推断方法</a>
<ul>
<li class="chapter" data-level="20.1" data-path="chap20.html"><a href="chap20.html#sec20-1"><i class="fa fa-check"></i><b>20.1</b> 假设检验</a>
<ul>
<li class="chapter" data-level="20.1.1" data-path="chap20.html"><a href="chap20.html#sec20-1-1"><i class="fa fa-check"></i><b>20.1.1</b> 使用方差分析表</a></li>
<li class="chapter" data-level="20.1.2" data-path="chap20.html"><a href="chap20.html#sec20-1-2"><i class="fa fa-check"></i><b>20.1.2</b> 示例 20.1：完全随机设计结构中的双向随机效应检验统计量</a></li>
<li class="chapter" data-level="20.1.3" data-path="chap20.html"><a href="chap20.html#sec20-1-3"><i class="fa fa-check"></i><b>20.1.3</b> 示例 20.2：复杂三向随机效应检验统计量</a></li>
<li class="chapter" data-level="20.1.4" data-path="chap20.html"><a href="chap20.html#sec20-1-4"><i class="fa fa-check"></i><b>20.1.4</b> 似然比检验</a></li>
<li class="chapter" data-level="20.1.5" data-path="chap20.html"><a href="chap20.html#sec20-1-5"><i class="fa fa-check"></i><b>20.1.5</b> 示例 20.3：小麦品种——单向随机效应模型</a></li>
<li class="chapter" data-level="20.1.6" data-path="chap20.html"><a href="chap20.html#sec20-1-6"><i class="fa fa-check"></i><b>20.1.6</b> 示例 20.4：不均衡双向</a></li>
</ul></li>
<li class="chapter" data-level="20.2" data-path="chap20.html"><a href="chap20.html#sec20-2"><i class="fa fa-check"></i><b>20.2</b> 构造置信区间</a>
<ul>
<li class="chapter" data-level="20.2.1" data-path="chap20.html"><a href="chap20.html#sec20-2-1"><i class="fa fa-check"></i><b>20.2.1</b> 残差方差 <span class="math inline">\(\sigma^2_\varepsilon\)</span></a></li>
<li class="chapter" data-level="20.2.2" data-path="chap20.html"><a href="chap20.html#sec20-2-2"><i class="fa fa-check"></i><b>20.2.2</b> 一般 Satterthwaite 近似</a></li>
<li class="chapter" data-level="20.2.3" data-path="chap20.html"><a href="chap20.html#sec20-2-3"><i class="fa fa-check"></i><b>20.2.3</b> 方差分量函数的近似置信区间</a></li>
<li class="chapter" data-level="20.2.4" data-path="chap20.html"><a href="chap20.html#sec20-2-4"><i class="fa fa-check"></i><b>20.2.4</b> 方差分量的 Wald 型置信区间</a></li>
<li class="chapter" data-level="20.2.5" data-path="chap20.html"><a href="chap20.html#sec20-2-5"><i class="fa fa-check"></i><b>20.2.5</b> 一些精确的置信区间</a></li>
<li class="chapter" data-level="20.2.6" data-path="chap20.html"><a href="chap20.html#sec20-2-6"><i class="fa fa-check"></i><b>20.2.6</b> 示例 20.5：均衡单向随机效应处理结构</a></li>
<li class="chapter" data-level="20.2.7" data-path="chap20.html"><a href="chap20.html#sec20-2-7"><i class="fa fa-check"></i><b>20.2.7</b> 示例 20.6</a></li>
<li class="chapter" data-level="20.2.8" data-path="chap20.html"><a href="chap20.html#sec20-2-8"><i class="fa fa-check"></i><b>20.2.8</b> 示例 20.6 （续）</a></li>
</ul></li>
<li class="chapter" data-level="20.3" data-path="chap20.html"><a href="chap20.html#sec20-3"><i class="fa fa-check"></i><b>20.3</b> 模拟研究</a></li>
<li class="chapter" data-level="20.4" data-path="chap20.html"><a href="chap20.html#sec20-4"><i class="fa fa-check"></i><b>20.4</b> 结束语</a></li>
<li class="chapter" data-level="20.5" data-path="chap20.html"><a href="chap20.html#sec20-5"><i class="fa fa-check"></i><b>20.5</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="21" data-path="chap21.html"><a href="chap21.html"><i class="fa fa-check"></i><b>21</b> 案例研究：随机效应模型分析</a>
<ul>
<li class="chapter" data-level="21.1" data-path="chap21.html"><a href="chap21.html#sec21-1"><i class="fa fa-check"></i><b>21.1</b> 数据集</a></li>
<li class="chapter" data-level="21.2" data-path="chap21.html"><a href="chap21.html#sec21-2"><i class="fa fa-check"></i><b>21.2</b> 估计</a></li>
<li class="chapter" data-level="21.3" data-path="chap21.html"><a href="chap21.html#sec21-3"><i class="fa fa-check"></i><b>21.3</b> 模型构建</a></li>
<li class="chapter" data-level="21.4" data-path="chap21.html"><a href="chap21.html#sec21-4"><i class="fa fa-check"></i><b>21.4</b> 缩减模型</a></li>
<li class="chapter" data-level="21.5" data-path="chap21.html"><a href="chap21.html#sec21-5"><i class="fa fa-check"></i><b>21.5</b> 置信区间</a></li>
<li class="chapter" data-level="21.6" data-path="chap21.html"><a href="chap21.html#sec21-6"><i class="fa fa-check"></i><b>21.6</b> 使用 JMP 进行计算</a></li>
<li class="chapter" data-level="21.7" data-path="chap21.html"><a href="chap21.html#sec21-7"><i class="fa fa-check"></i><b>21.7</b> 结束语</a></li>
<li class="chapter" data-level="21.8" data-path="chap21.html"><a href="chap21.html#sec21-8"><i class="fa fa-check"></i><b>21.8</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="22" data-path="chap22.html"><a href="chap22.html"><i class="fa fa-check"></i><b>22</b> 混合模型的分析</a>
<ul>
<li class="chapter" data-level="22.1" data-path="chap22.html"><a href="chap22.html#sec22-1"><i class="fa fa-check"></i><b>22.1</b> 混合模型简介</a></li>
<li class="chapter" data-level="22.2" data-path="chap22.html"><a href="chap22.html#sec22-2"><i class="fa fa-check"></i><b>22.2</b> 混合模型随机效应部分的分析</a>
<ul>
<li class="chapter" data-level="22.2.1" data-path="chap22.html"><a href="chap22.html#sec22-2-1"><i class="fa fa-check"></i><b>22.2.1</b> 矩法</a></li>
<li class="chapter" data-level="22.2.2" data-path="chap22.html"><a href="chap22.html#sec22-2-2"><i class="fa fa-check"></i><b>22.2.2</b> 最大似然方法</a></li>
<li class="chapter" data-level="22.2.3" data-path="chap22.html"><a href="chap22.html#sec22-2-3"><i class="fa fa-check"></i><b>22.2.3</b> 残差最大似然法</a></li>
<li class="chapter" data-level="22.2.4" data-path="chap22.html"><a href="chap22.html#sec22-2-4"><i class="fa fa-check"></i><b>22.2.4</b> MINQUE 法</a></li>
</ul></li>
<li class="chapter" data-level="22.3" data-path="chap22.html"><a href="chap22.html#sec22-3"><i class="fa fa-check"></i><b>22.3</b> 混合模型固定效应部分的分析</a>
<ul>
<li class="chapter" data-level="22.3.1" data-path="chap22.html"><a href="chap22.html#sec22-3-1"><i class="fa fa-check"></i><b>22.3.1</b> 估计</a></li>
<li class="chapter" data-level="22.3.2" data-path="chap22.html"><a href="chap22.html#sec22-3-2"><i class="fa fa-check"></i><b>22.3.2</b> 置信区间的构建</a></li>
<li class="chapter" data-level="22.3.3" data-path="chap22.html"><a href="chap22.html#sec22-3-3"><i class="fa fa-check"></i><b>22.3.3</b> 假设检验</a></li>
</ul></li>
<li class="chapter" data-level="22.4" data-path="chap22.html"><a href="chap22.html#sec22-4"><i class="fa fa-check"></i><b>22.4</b> 最佳线性无偏预测</a></li>
<li class="chapter" data-level="22.5" data-path="chap22.html"><a href="chap22.html#sec22-5"><i class="fa fa-check"></i><b>22.5</b> 混合模型方程组</a></li>
<li class="chapter" data-level="22.6" data-path="chap22.html"><a href="chap22.html#sec22-6"><i class="fa fa-check"></i><b>22.6</b> 结束语</a></li>
<li class="chapter" data-level="22.7" data-path="chap22.html"><a href="chap22.html#sec22-7"><i class="fa fa-check"></i><b>22.7</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="23" data-path="chap23.html"><a href="chap23.html"><i class="fa fa-check"></i><b>23</b> 案例研究：混合模型</a>
<ul>
<li class="chapter" data-level="23.1" data-path="chap23.html"><a href="chap23.html#sec23-1"><i class="fa fa-check"></i><b>23.1</b> 双向混合模型</a></li>
<li class="chapter" data-level="23.2" data-path="chap23.html"><a href="chap23.html#sed23-2"><i class="fa fa-check"></i><b>23.2</b> 不均衡双向混合模型</a></li>
<li class="chapter" data-level="23.3" data-path="chap23.html"><a href="chap23.html#sec23-3"><i class="fa fa-check"></i><b>23.3</b> 不均衡双向数据集的 JMP 分析</a></li>
<li class="chapter" data-level="23.4" data-path="chap23.html"><a href="chap23.html#sec23-4"><i class="fa fa-check"></i><b>23.4</b> 结束语</a></li>
<li class="chapter" data-level="23.5" data-path="chap23.html"><a href="chap23.html#sec23-5"><i class="fa fa-check"></i><b>23.5</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="24" data-path="chap24.html"><a href="chap24.html"><i class="fa fa-check"></i><b>24</b> 分析裂区型设计的方法</a>
<ul>
<li class="chapter" data-level="24.1" data-path="chap24.html"><a href="chap24.html#sec24-1"><i class="fa fa-check"></i><b>24.1</b> 介绍</a>
<ul>
<li class="chapter" data-level="24.1.1" data-path="chap24.html"><a href="chap24.html#sec24-1-1"><i class="fa fa-check"></i><b>24.1.1</b> 示例 24.1：面包配方和烘焙温度</a></li>
<li class="chapter" data-level="24.1.2" data-path="chap24.html"><a href="chap24.html#sec24-1-2"><i class="fa fa-check"></i><b>24.1.2</b> 示例 24.2：在不同肥力条件下生长的小麦品种</a></li>
</ul></li>
<li class="chapter" data-level="24.2" data-path="chap24.html"><a href="chap24.html#sec24-2"><i class="fa fa-check"></i><b>24.2</b> 模型定义和参数估计</a></li>
<li class="chapter" data-level="24.3" data-path="chap24.html"><a href="chap24.html#sec24-3"><i class="fa fa-check"></i><b>24.3</b> 均值间比较的标准误</a></li>
<li class="chapter" data-level="24.4" data-path="chap24.html"><a href="chap24.html#sec24-4"><i class="fa fa-check"></i><b>24.4</b> 计算均值差标准误的一般方法</a>
<ul>
<li class="chapter" data-level="24.4.1" data-path="chap24.html"><a href="chap24.html#sec24-5"><i class="fa fa-check"></i><b>24.4.1</b> 通过一般对比进行比较</a></li>
</ul></li>
<li class="chapter" data-level="24.5" data-path="chap24.html"><a href="chap24.html#sec24-6"><i class="fa fa-check"></i><b>24.5</b> 其他示例</a>
<ul>
<li class="chapter" data-level="24.5.1" data-path="chap24.html"><a href="chap24.html#sec24-6-1"><i class="fa fa-check"></i><b>24.5.1</b> 示例 24.3：水分和肥料</a></li>
<li class="chapter" data-level="24.5.2" data-path="chap24.html"><a href="chap24.html#sec24-6-2"><i class="fa fa-check"></i><b>24.5.2</b> 示例 24.4：具有裂区误差的回归</a></li>
<li class="chapter" data-level="24.5.3" data-path="chap24.html"><a href="chap24.html#sec24-6-3"><i class="fa fa-check"></i><b>24.5.3</b> 示例 24.5：混乱的裂区设计</a></li>
<li class="chapter" data-level="24.5.4" data-path="chap24.html"><a href="chap24.html#sec24-6-4"><i class="fa fa-check"></i><b>24.5.4</b> 示例 24.6：裂-裂区设计</a></li>
</ul></li>
<li class="chapter" data-level="24.6" data-path="chap24.html"><a href="chap24.html#sec24-7"><i class="fa fa-check"></i><b>24.6</b> 样本量和功效考虑</a></li>
<li class="chapter" data-level="24.7" data-path="chap24.html"><a href="chap24.html#sec24-8"><i class="fa fa-check"></i><b>24.7</b> 使用 JMP 进行计算：示例 24.7</a></li>
<li class="chapter" data-level="24.8" data-path="chap24.html"><a href="chap24.html#sec24-9"><i class="fa fa-check"></i><b>24.8</b> 结束语</a></li>
<li class="chapter" data-level="24.9" data-path="chap24.html"><a href="chap24.html#sec24-10"><i class="fa fa-check"></i><b>24.9</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="25" data-path="chap25.html"><a href="chap25.html"><i class="fa fa-check"></i><b>25</b> 分析条区型设计的方法</a>
<ul>
<li class="chapter" data-level="25.1" data-path="chap25.html"><a href="chap25.html#sec25-1"><i class="fa fa-check"></i><b>25.1</b> 条区设计和模型的描述</a></li>
<li class="chapter" data-level="25.2" data-path="chap25.html"><a href="chap25.html#sec25-2"><i class="fa fa-check"></i><b>25.2</b> 推断技术</a></li>
<li class="chapter" data-level="25.3" data-path="chap25.html"><a href="chap25.html#sec25-3"><i class="fa fa-check"></i><b>25.3</b> 示例：氮与灌溉</a></li>
<li class="chapter" data-level="25.4" data-path="chap25.html"><a href="chap25.html#sec25-4"><i class="fa fa-check"></i><b>25.4</b> 示例：含裂区的条区 1</a></li>
<li class="chapter" data-level="25.5" data-path="chap25.html"><a href="chap25.html#sec25-5"><i class="fa fa-check"></i><b>25.5</b> 示例：含裂区的条区 2</a></li>
<li class="chapter" data-level="25.6" data-path="chap25.html"><a href="chap25.html#sec25-6"><i class="fa fa-check"></i><b>25.6</b> 示例：含裂区的条区 3</a></li>
<li class="chapter" data-level="25.7" data-path="chap25.html"><a href="chap25.html#sec25-7"><i class="fa fa-check"></i><b>25.7</b> 示例：含裂区的条区 4</a></li>
<li class="chapter" data-level="25.8" data-path="chap25.html"><a href="chap25.html#sec25-8"><i class="fa fa-check"></i><b>25.8</b> 条-条区的设计与分析：基于 JMP7</a></li>
<li class="chapter" data-level="25.9" data-path="chap25.html"><a href="chap25.html#sec25-9"><i class="fa fa-check"></i><b>25.9</b> 结束语</a></li>
<li class="chapter" data-level="25.10" data-path="chap25.html"><a href="chap25.html#sec25-10"><i class="fa fa-check"></i><b>25.10</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="26" data-path="chap26.html"><a href="chap26.html"><i class="fa fa-check"></i><b>26</b> 分析重复测量实验的方法</a>
<ul>
<li class="chapter" data-level="26.1" data-path="chap26.html"><a href="chap26.html#sec26-1"><i class="fa fa-check"></i><b>26.1</b> 模型指定和理想条件</a></li>
<li class="chapter" data-level="26.2" data-path="chap26.html"><a href="chap26.html#sec26-2"><i class="fa fa-check"></i><b>26.2</b> 时间的裂区分析</a>
<ul>
<li class="chapter" data-level="26.2.1" data-path="chap26.html"><a href="chap26.html#sec26-2-1"><i class="fa fa-check"></i><b>26.2.1</b> 示例 26.1：药物对心率的影响</a></li>
<li class="chapter" data-level="26.2.2" data-path="chap26.html"><a href="chap26.html#sec26-2-2"><i class="fa fa-check"></i><b>26.2.2</b> 示例 26.2：一个复杂的舒适度实验</a></li>
<li class="chapter" data-level="26.2.3" data-path="chap26.html"><a href="chap26.html#sec26-2-3"><i class="fa fa-check"></i><b>26.2.3</b> 示例 26.3：家庭态度</a></li>
</ul></li>
<li class="chapter" data-level="26.3" data-path="chap26.html"><a href="chap26.html#sec26-3"><i class="fa fa-check"></i><b>26.3</b> 使用 SAS-Mixed 程序的数据分析</a>
<ul>
<li class="chapter" data-level="26.3.1" data-path="chap26.html"><a href="chap26.html#sec26-3-1"><i class="fa fa-check"></i><b>26.3.1</b> 示例 26.1</a></li>
<li class="chapter" data-level="26.3.2" data-path="chap26.html"><a href="chap26.html#sec26-3-2"><i class="fa fa-check"></i><b>26.3.2</b> 示例 26.2</a></li>
<li class="chapter" data-level="26.3.3" data-path="chap26.html"><a href="chap26.html#sec26-3-3"><i class="fa fa-check"></i><b>26.3.3</b> 示例 26.3</a></li>
</ul></li>
<li class="chapter" data-level="26.4" data-path="chap26.html"><a href="chap26.html#sec26-4"><i class="fa fa-check"></i><b>26.4</b> 结束语</a></li>
<li class="chapter" data-level="26.5" data-path="chap26.html"><a href="chap26.html#sec26-5"><i class="fa fa-check"></i><b>26.5</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="27" data-path="chap27.html"><a href="chap27.html"><i class="fa fa-check"></i><b>27</b> 不满足理想条件时重复测量实验的分析</a>
<ul>
<li class="chapter" data-level="27.1" data-path="chap27.html"><a href="chap27.html#sec27-1"><i class="fa fa-check"></i><b>27.1</b> 介绍</a></li>
<li class="chapter" data-level="27.2" data-path="chap27.html"><a href="chap27.html#sec27-2"><i class="fa fa-check"></i><b>27.2</b> MANOVA 法</a></li>
<li class="chapter" data-level="27.3" data-path="chap27.html"><a href="chap27.html#sec27-3"><i class="fa fa-check"></i><b>27.3</b> <span class="math inline">\(p\)</span> 值调整法</a></li>
<li class="chapter" data-level="27.4" data-path="chap27.html"><a href="chap27.html#sec27-4"><i class="fa fa-check"></i><b>27.4</b> 混合模型法</a>
<ul>
<li class="chapter" data-level="27.4.1" data-path="chap27.html"><a href="chap27.html#sec27-4-1"><i class="fa fa-check"></i><b>27.4.1</b> 最大似然法</a></li>
<li class="chapter" data-level="27.4.2" data-path="chap27.html"><a href="chap27.html#sec27-4-2"><i class="fa fa-check"></i><b>27.4.2</b> 受限最大似然法</a></li>
</ul></li>
<li class="chapter" data-level="27.5" data-path="chap27.html"><a href="chap27.html#sec27-5"><i class="fa fa-check"></i><b>27.5</b> 总结</a></li>
<li class="chapter" data-level="27.6" data-path="chap27.html"><a href="chap27.html#sec27-6"><i class="fa fa-check"></i><b>27.6</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="28" data-path="chap28.html"><a href="chap28.html"><i class="fa fa-check"></i><b>28</b> 案例研究：重复测量的复杂例子</a>
<ul>
<li class="chapter" data-level="28.1" data-path="chap28.html"><a href="chap28.html#sec28-1"><i class="fa fa-check"></i><b>28.1</b> 复杂舒适度实验</a></li>
<li class="chapter" data-level="28.2" data-path="chap28.html"><a href="chap28.html#sec28-2"><i class="fa fa-check"></i><b>28.2</b> 家庭态度实验</a></li>
<li class="chapter" data-level="28.3" data-path="chap28.html"><a href="chap28.html#sec28-3"><i class="fa fa-check"></i><b>28.3</b> 多地点研究</a></li>
<li class="chapter" data-level="28.4" data-path="chap28.html"><a href="chap28.html#sec28-4"><i class="fa fa-check"></i><b>28.4</b> 练习</a></li>
</ul></li>
<li class="chapter" data-level="29" data-path="chap29.html"><a href="chap29.html"><i class="fa fa-check"></i><b>29</b> 交叉设计的分析</a>
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<li class="chapter" data-level="29.1" data-path="chap29.html"><a href="chap29.html#sec29-1"><i class="fa fa-check"></i><b>29.1</b> 定义，假设和模型</a></li>
<li class="chapter" data-level="29.2" data-path="chap29.html"><a href="chap29.html#sec29-2"><i class="fa fa-check"></i><b>29.2</b> 两时期/两处理交叉设计</a></li>
<li class="chapter" data-level="29.3" data-path="chap29.html"><a href="chap29.html#sec29-3"><i class="fa fa-check"></i><b>29.3</b> 具有两个以上时期的交叉设计</a></li>
<li class="chapter" data-level="29.4" data-path="chap29.html"><a href="chap29.html#sec29-4"><i class="fa fa-check"></i><b>29.4</b> 具有两种以上处理的交叉设计</a></li>
<li class="chapter" data-level="29.5" data-path="chap29.html"><a href="chap29.html#sec29-5"><i class="fa fa-check"></i><b>29.5</b> 小结</a></li>
</ul></li>
<li class="chapter" data-level="30" data-path="chap30.html"><a href="chap30.html"><i class="fa fa-check"></i><b>30</b> 嵌套设计的分析</a>
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<li class="chapter" data-level="30.1" data-path="chap30.html"><a href="chap30.html#sec30-1"><i class="fa fa-check"></i><b>30.1</b> 定义，假设和模型</a>
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<li class="chapter" data-level="30.1.1" data-path="chap30.html"><a href="chap30.html#sec30-1-1"><i class="fa fa-check"></i><b>30.1.1</b> 示例 30.1：公司和杀虫剂</a></li>
<li class="chapter" data-level="30.1.2" data-path="chap30.html"><a href="chap30.html#sec30-1-2"><i class="fa fa-check"></i><b>30.1.2</b> 示例 30.2：舒适度实验回顾</a></li>
<li class="chapter" data-level="30.1.3" data-path="chap30.html"><a href="chap30.html#sec30-1-3"><i class="fa fa-check"></i><b>30.1.3</b> 示例 30.3：咖啡价格示例回顾</a></li>
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<li class="chapter" data-level="30.2" data-path="chap30.html"><a href="chap30.html#sec30-2"><i class="fa fa-check"></i><b>30.2</b> 参数估计</a>
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<li class="chapter" data-level="30.2.1" data-path="chap30.html"><a href="chap30.html#sec30-2-1"><i class="fa fa-check"></i><b>30.2.1</b> 示例 30.1：继续</a></li>
<li class="chapter" data-level="30.2.2" data-path="chap30.html"><a href="chap30.html#sec30-2-2"><i class="fa fa-check"></i><b>30.2.2</b> 示例 30.2：继续</a></li>
<li class="chapter" data-level="30.2.3" data-path="chap30.html"><a href="chap30.html#sec30-2-3"><i class="fa fa-check"></i><b>30.2.3</b> 示例 30.3：继续</a></li>
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<li class="chapter" data-level="30.3" data-path="chap30.html"><a href="chap30.html#sec30-3"><i class="fa fa-check"></i><b>30.3</b> 假设检验和置信区间的构建</a>
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<li class="chapter" data-level="30.3.1" data-path="chap30.html"><a href="chap30.html#sec30-3-1"><i class="fa fa-check"></i><b>30.3.1</b> 示例 30.1：继续</a></li>
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<li class="chapter" data-level="30.4" data-path="chap30.html"><a href="chap30.html#sec30-4"><i class="fa fa-check"></i><b>30.4</b> 使用 JMP 进行分析</a></li>
<li class="chapter" data-level="30.5" data-path="chap30.html"><a href="chap30.html#sec30-5"><i class="fa fa-check"></i><b>30.5</b> 结束语</a></li>
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<h1><span class="header-section-number">第 16 章</span> 分析三向和高阶处理结构<a href="chap16.html#chap16" class="anchor-section" aria-label="Anchor link to header"></a></h1>
<blockquote>
<p>“Statistics are the triumph of the quantitative method, and the quantitative method is the victory of sterility and death” - Hilaire Belloc</p>
</blockquote>
<p>在第 <a href="chap7.html#chap7">7</a> - <a href="chap15.html#chap15">15</a> 章中，我们讨论了双向处理结构的分析。这 <a href="chap9.html#chap9">9</a> 章中给出的方法和结果可以推广到更复杂的处理结构；随着处理结构复杂性的增加，这种分析只会变得稍微复杂一些。我们通过具体分析三向处理结构来说明泛化方法。</p>
<p>在第 <a href="chap16.html#sec16-1">16.1</a> 节中，我们给出了分析高阶处理结构时应遵循的一般策略。第 <a href="chap16.html#sec16-2">16.2</a> 节讨论了均衡和不均衡处理结构的分析。对不均衡实验的讨论包括每个处理组合至少观测一次的情况和一些处理组合缺失的情况。</p>
<div id="sec16-1" class="section level2 hasAnchor" number="16.1">
<h2><span class="header-section-number">16.1</span> 一般策略<a href="chap16.html#sec16-1" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>假设处理 <span class="math inline">\(T_i,B_j,C_k\)</span> 同时应用于同一实验单元。设 <span class="math inline">\(\mu_{ijk}\)</span> 表示对处理组合 <span class="math inline">\((T_i,B_j,C_k)\)</span> 的预期响应，<span class="math inline">\(i=1,2,\cdots,t;j=1,2,\cdots,b;k=1,2,\cdots,c\)</span>. 这些处理组合之间不存在三向相互作用的前提是</p>
<p><span class="math display">\[(\mu_{ijk}-\mu_{i^{\prime}jk}-\mu_{ij^{\prime}k}+\mu_{i^{\prime}j^{\prime}k})-(\mu_{ijk^{\prime}}-\mu_{i^{\prime}jk^{\prime}}-\mu_{ij^{\prime}k^{\prime}}+\mu_{i^{\prime}j^{\prime}k^{\prime}})=0\quad\mathrm{for~all~}i,i^{\prime},j,j^{\prime},k,\mathrm{and~}k^{\prime}\]</span></p>
<p>这意味着对于所有 k 和 k’ 值，因素 C 在 k 水平上的 T × B 交互作用与因素 C 在 k’ 水平上的 T × B 交互作用相同。类似地，T × C 交互作用在因素 B 的所有水平上都是相同的，以及 B × C 交互作用在因素 T 的所有水平上都是相同的。无交互作用陈述的等价表达为</p>
<ol style="list-style-type: decimal">
<li><span class="math inline">\(\mu_{ijk}-\bar{\mu}_{ij\cdot}-\bar{\mu}_{i\cdot k}-\bar{\mu}_{\cdot jk}+\bar{\mu}_{i\cdot\cdot}+\bar{\mu}_{\cdot j\cdot}+\bar{\mu}_{\cdot\cdot k}-\bar{\mu}_{\cdot\cdot\cdot}=0\quad\text{ for all }i,j,\mathrm{~and~}k\)</span></li>
<li>存在参数 <span class="math inline">\(\mu,\tau_1,\tau_2,\cdots,\tau_t,\beta_1,\beta_2,\cdots,\beta_b,\xi_1,\xi_2,\ldots,\xi_c,\gamma_{11},\gamma_{12},\cdots,\gamma_{tb},\eta_{11},\eta_{12},\cdots,\eta_{tc},\theta_{11},\theta_{12},\cdots,\theta_{bc}\)</span> 使得
<span class="math display">\[\mu_{ijk}=\mu+\tau_i+\beta_j+\xi_k+\gamma_{ij}+\eta_{ik}+\theta_{jk}\quad\text{for all }i,j,\mathrm{~and~}k\]</span></li>
</ol>
<p>也就是说，<span class="math inline">\(\mu_{ijk}\)</span> 可以用主效应和双因素交互效应来描述。<strong>在分析三向处理结构时，第一步也是最重要的一步是确定是否存在三因素交互作用，尽管实验者可能对此不感兴趣</strong>。如果没有三因素交互作用，那么第二步是确定是否存在任何双因素交互作用。如果也没有双因素交互作用，那么可以分析每个主效应。如果存在三因素交互作用，实验者应该在所选的第三个处理因素（通常是最不感兴趣的因素）的每个水平上分析两个处理因素的双向处理结构。显然，这些双向分析可以通过让每个处理成为所选的第三个处理来进行。使用统计计算包可以获得的分析类型与可用于双向处理结构的分析类型相似。</p>
<p>图 <a href="chap16.html#fig:figure16-1">16.1</a> 显示了分析三向处理结构的一般策略。这种策略也可应用于四向和高阶处理结构。如果对所有处理组合进行相同次数的观测，则可以使用许多不同类型的统计软件来分析结果数据。</p>
<div class="figure" style="text-align: center"><span style="display:block;" id="fig:figure16-1"></span>
<img src="figure/figure%2016.1.png" alt="三因素实验的分析策略" width="648" />
<p class="caption">
图 16.1: 三因素实验的分析策略
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<div id="sec16-2" class="section level2 hasAnchor" number="16.2">
<h2><span class="header-section-number">16.2</span> 均衡和不均衡实验<a href="chap16.html#sec16-2" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>如果观测到所有处理组合，但观测次数不相等，则可以使用 III 型分析。如果每种处理组合都至少观测一次，那么所有的主效应和交互作用假设仍然可以得到检验，并且回答的问题与在处处完全均衡时回答的问题相同。</p>
<p>如果某些处理组合缺失，那么就像第 <a href="chap13.html#chap13">13</a> 章中的情况一样，无法检验涉及缺失处理组合的假设。实验者应该在感兴趣的处理之间指定她自己的 IV 型假设。这种假设可以通过使用第 <a href="chap1.html#chap1">1</a> 章中描述的矩阵程序或通过许多统计计算包中可用的 Contrast 语句进行检验。</p>
<p>第 <a href="chap17.html#chap17">17</a> 章中的示例演示了可能需要的一些步骤，以便获得对缺失处理组合数据的完整分析。</p>
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<div id="sec16-3" class="section level2 hasAnchor" number="16.3">
<h2><span class="header-section-number">16.3</span> I 型和 II 型分析<a href="chap16.html#sec16-3" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>第 <a href="chap10.html#chap10">10</a> 章描述了双向处理结构实验的 I 型和 II 型分析。这两种分析都使用模型比较程序为每个效应产生平方和。I 型分析序贯式地 (sequentially) 拟合模型，每个效应都会针对模型中之前的所有其他效应进行调整。在第 II 型分析中，针对相同或更低水平的所有其他效应调整每个效应的平方和。考虑由下式给出的三向模型</p>
<p><span class="math display">\[\begin{aligned}y_{ijk\ell}&=\mu+T_i+B_j+(TB)_{ij}+C_k+(TC)_{ik}+(BC)_{jk}+(TBC)_{ijk}+\varepsilon_{ijk\ell}\\&\mathrm{for~}i=1,2,\ldots,t,~j=1,2,\ldots,b;~k=1,2,\ldots,c;~\mathrm{and}~\ell=1,2,\ldots,n_{ijk}\end{aligned}\]</span></p>
<p>假设对于所有 <span class="math inline">\(i,j,k\)</span> 有 <span class="math inline">\(n_{ijk}>0\)</span>. 也就是说，每个三向单元格至少观测一次。表 <a href="chap16.html#tab:table16-1">16.1</a> 显示了使用第 <a href="chap10.html#chap10">10</a> 章中描述的缩减符号的 I 型和 II 型平方和及其相应的自由度。</p>
<table>
<caption>
<span id="tab:table16-1">表 16.1: </span>在每个单元格中至少有一次观测的三向实验的 I 型和 II 型平方和
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x
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<img src="table/table%2016.1.png">
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<div id="sec16-4" class="section level2 hasAnchor" number="16.4">
<h2><span class="header-section-number">16.4</span> 结束语<a href="chap16.html#sec16-4" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>本章讨论了三向及高阶处理结构实验的分析。给出了一个流程图，提供了分析此类实验的一般策略。</p>
<p>首先研究最高阶交互作用效应是很重要的。许多实验者避免考虑高阶交互作用，因为他们通常不太确定如何处理这些交互作用。应该避免这种诱惑。尽管经验告诉我们，非常高阶的交互作用很少是有意义的，但无论何时，都必须处理它们。第 <a href="chap8.html#chap8">8</a> 章中讨论的技术可以推广到三向和更高阶的处理结构，并有助于确定哪些处理组合导致了交互作用。交点的原因可能是研究中确定的最重要的信息。</p>
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<div id="sec16-5" class="section level2 hasAnchor" number="16.5">
<h2><span class="header-section-number">16.5</span> 练习<a href="chap16.html#sec16-5" class="anchor-section" aria-label="Anchor link to header"></a></h2>
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