MedicalStatisNotes.toc

\contentsline {section}{\numberline {1}简介与传送门}{1}{section.1}%
\contentsline {subsection}{\numberline {1.1}简介}{1}{subsection.1.1}%
\contentsline {subsubsection}{\numberline {1.1.1}软件准备}{2}{subsubsection.1.1.1}%
\contentsline {subsection}{\numberline {1.2}传送门}{2}{subsection.1.2}%
\contentsline {subsection}{\numberline {1.3}致谢}{3}{subsection.1.3}%
\contentsline {subsection}{\numberline {1.4}声明}{3}{subsection.1.4}%
\contentsline {section}{\numberline {2}第二章 计量资料的统计描述}{3}{section.2}%
\contentsline {subsection}{\numberline {2.1}描述统计}{3}{subsection.2.1}%
\contentsline {subsection}{\numberline {2.2}测试数据}{5}{subsection.2.2}%
\contentsline {subsection}{\numberline {2.3}数据输入和频率统计}{5}{subsection.2.3}%
\contentsline {subsubsection}{\numberline {2.3.1}读取数据，并将数据转换成单列形式}{5}{subsubsection.2.3.1}%
\contentsline {subsubsection}{\numberline {2.3.2}计算极差, max()/min()/range()}{5}{subsubsection.2.3.2}%
\contentsline {subsubsection}{\numberline {2.3.3}确定组段数和组距}{5}{subsubsection.2.3.3}%
\contentsline {subsubsection}{\numberline {2.3.4}计算频数分布}{6}{subsubsection.2.3.4}%
\contentsline {subsection}{\numberline {2.4}描述性统计的度量}{7}{subsection.2.4}%
\contentsline {subsubsection}{\numberline {2.4.1}算术平均值}{7}{subsubsection.2.4.1}%
\contentsline {subsubsection}{\numberline {2.4.2}几何平均值}{7}{subsubsection.2.4.2}%
\contentsline {subsubsection}{\numberline {2.4.3}中位数与百分位数}{7}{subsubsection.2.4.3}%
\contentsline {subsubsection}{\numberline {2.4.4}极差}{8}{subsubsection.2.4.4}%
\contentsline {subsubsection}{\numberline {2.4.5}四分位间距}{8}{subsubsection.2.4.5}%
\contentsline {subsubsection}{\numberline {2.4.6}方差与标准差}{8}{subsubsection.2.4.6}%
\contentsline {subsubsection}{\numberline {2.4.7}变异系数}{9}{subsubsection.2.4.7}%
\contentsline {subsubsection}{\numberline {2.4.8}其他的描述统计}{9}{subsubsection.2.4.8}%
\contentsline {paragraph}{\numberline {2.4.8.1}Summary}{9}{paragraph.2.4.8.1}%
\contentsline {paragraph}{\numberline {2.4.8.2}众数}{10}{paragraph.2.4.8.2}%
\contentsline {subsection}{\numberline {2.5}正态分布和标准正态分布}{10}{subsection.2.5}%
\contentsline {subsubsection}{\numberline {2.5.1}概率密度函数dnorm()}{11}{subsubsection.2.5.1}%
\contentsline {subsubsection}{\numberline {2.5.2}概率累积分布函数pnorm()}{11}{subsubsection.2.5.2}%
\contentsline {subsubsection}{\numberline {2.5.3}正态分位函数qnorm()}{12}{subsubsection.2.5.3}%
\contentsline {subsubsection}{\numberline {2.5.4}生成正态分布函数rnorm()}{12}{subsubsection.2.5.4}%
\contentsline {subsection}{\numberline {2.6}正态分布检验}{13}{subsection.2.6}%
\contentsline {subsubsection}{\numberline {2.6.1}直方图}{14}{subsubsection.2.6.1}%
\contentsline {subsubsection}{\numberline {2.6.2}概率密度图}{15}{subsubsection.2.6.2}%
\contentsline {subsubsection}{\numberline {2.6.3}QQ-plot}{15}{subsubsection.2.6.3}%
\contentsline {subsubsection}{\numberline {2.6.4}正态检验}{16}{subsubsection.2.6.4}%
\contentsline {section}{\numberline {3}第三章 总体均数的估计与假设检验}{17}{section.3}%
\contentsline {subsection}{\numberline {3.1}推论统计}{18}{subsection.3.1}%
\contentsline {subsubsection}{\numberline {3.1.1}参数估计与假设检验}{18}{subsubsection.3.1.1}%
\contentsline {subsubsection}{\numberline {3.1.2}统计量与标准误}{18}{subsubsection.3.1.2}%
\contentsline {subsection}{\numberline {3.2}\emph {t} 分布}{19}{subsection.3.2}%
\contentsline {subsubsection}{\numberline {3.2.1}概率密度函数dt()}{20}{subsubsection.3.2.1}%
\contentsline {subsubsection}{\numberline {3.2.2}概率累积分布函数pt()}{20}{subsubsection.3.2.2}%
\contentsline {subsubsection}{\numberline {3.2.3}求置信区间的qt()}{21}{subsubsection.3.2.3}%
\contentsline {subsubsection}{\numberline {3.2.4}指定t分布函数rt()}{22}{subsubsection.3.2.4}%
\contentsline {subsubsection}{\numberline {3.2.5}参数估计}{23}{subsubsection.3.2.5}%
\contentsline {paragraph}{\numberline {3.2.5.1}总体均数可信区间}{23}{paragraph.3.2.5.1}%
\contentsline {subsubsection}{\numberline {3.2.6}假设检验}{24}{subsubsection.3.2.6}%
\contentsline {paragraph}{\numberline {3.2.6.1}假设检验的步骤}{25}{paragraph.3.2.6.1}%
\contentsline {subsection}{\numberline {3.3}\emph {t} 检验的分类及应用}{28}{subsection.3.3}%
\contentsline {subsubsection}{\numberline {3.3.1}\emph {t}检验与Z检验}{28}{subsubsection.3.3.1}%
\contentsline {subsubsection}{\numberline {3.3.2}单样本\emph {t}检验}{29}{subsubsection.3.3.2}%
\contentsline {subsubsection}{\numberline {3.3.3}配对样本\emph {t}检验}{32}{subsubsection.3.3.3}%
\contentsline {subsubsection}{\numberline {3.3.4}两种独立样本t检验}{34}{subsubsection.3.3.4}%
\contentsline {paragraph}{\numberline {3.3.4.1}总体方差相等的\emph {t}检验}{35}{paragraph.3.3.4.1}%
\contentsline {paragraph}{\numberline {3.3.4.2}\emph {t'}检验}{36}{paragraph.3.3.4.2}%
\contentsline {paragraph}{\numberline {3.3.4.3}参数估计与假设检验的联系}{37}{paragraph.3.3.4.3}%
\contentsline {subsubsection}{\numberline {3.3.5}两样本方差齐性检验}{38}{subsubsection.3.3.5}%
\contentsline {subsection}{\numberline {3.4}变量转换}{40}{subsection.3.4}%
\contentsline {subsubsection}{\numberline {3.4.1}对数变换}{42}{subsubsection.3.4.1}%
\contentsline {section}{\numberline {4}第四章 多个样本均数比较的方差分析}{46}{section.4}%
\contentsline {subsection}{\numberline {4.1}\emph {F}分布}{46}{subsection.4.1}%
\contentsline {subsection}{\numberline {4.2}\emph {F}检验的分类、原理及应用}{48}{subsection.4.2}%
\contentsline {subsubsection}{\numberline {4.2.1}分类}{48}{subsubsection.4.2.1}%
\contentsline {subsubsection}{\numberline {4.2.2}原理}{48}{subsubsection.4.2.2}%
\contentsline {paragraph}{\numberline {4.2.2.1}\emph {F}检验的原理示例}{51}{paragraph.4.2.2.1}%
\contentsline {paragraph}{\numberline {4.2.2.2}\emph {F}检验的前提和应用}{52}{paragraph.4.2.2.2}%
\contentsline {subparagraph}{\numberline {4.2.2.2.1}前提}{52}{subparagraph.4.2.2.2.1}%
\contentsline {subparagraph}{\numberline {4.2.2.2.2}应用}{52}{subparagraph.4.2.2.2.2}%
\contentsline {subsubsection}{\numberline {4.2.3}单因子方差分析}{52}{subsubsection.4.2.3}%
\contentsline {subsubsection}{\numberline {4.2.4}双因子方差分析}{55}{subsubsection.4.2.4}%
\contentsline {subsubsection}{\numberline {4.2.5}拉丁方设计资料的方差分析}{59}{subsubsection.4.2.5}%
\contentsline {subsubsection}{\numberline {4.2.6}两阶段交叉设计资料的方差分析}{61}{subsubsection.4.2.6}%
\contentsline {subsection}{\numberline {4.3}方差分析的诊断图}{63}{subsection.4.3}%
\contentsline {subsection}{\numberline {4.4}多个样本均数间的多重比较}{65}{subsection.4.4}%
\contentsline {subsection}{\numberline {4.5}多样本方差齐性检验}{71}{subsection.4.5}%
\contentsline {subsubsection}{\numberline {4.5.1}Bartlett's 检验}{71}{subsubsection.4.5.1}%
\contentsline {subsubsection}{\numberline {4.5.2}Levene's 检验}{72}{subsubsection.4.5.2}%
\contentsline {section}{\numberline {5}第五章 计数资料的统计描述}{73}{section.5}%
\contentsline {subsection}{\numberline {5.1}常用相对数}{73}{subsection.5.1}%
\contentsline {subsubsection}{\numberline {5.1.1}强度相对数}{73}{subsubsection.5.1.1}%
\contentsline {subsubsection}{\numberline {5.1.2}结构相对数}{74}{subsubsection.5.1.2}%
\contentsline {subsubsection}{\numberline {5.1.3}相对比}{74}{subsubsection.5.1.3}%
\contentsline {subsubsection}{\numberline {5.1.4}应用相对数的注意点}{74}{subsubsection.5.1.4}%
\contentsline {subsection}{\numberline {5.2}率的标准化}{75}{subsection.5.2}%
\contentsline {subsubsection}{\numberline {5.2.1}标准化率的计算}{76}{subsubsection.5.2.1}%
\contentsline {subsection}{\numberline {5.3}动态数列及其指标分析}{76}{subsection.5.3}%
\contentsline {subsubsection}{\numberline {5.3.1}绝对增长量}{77}{subsubsection.5.3.1}%
\contentsline {subsubsection}{\numberline {5.3.2}发展速度与增长速度}{77}{subsubsection.5.3.2}%
\contentsline {subsubsection}{\numberline {5.3.3}平均发展速度与平均增长速度}{77}{subsubsection.5.3.3}%
\contentsline {section}{\numberline {6}第六章 计数资料的统计描述}{78}{section.6}%
\contentsline {subsection}{\numberline {6.1}二项分布}{78}{subsection.6.1}%
\contentsline {subsubsection}{\numberline {6.1.1}二项分布的性质}{79}{subsubsection.6.1.1}%
\contentsline {paragraph}{\numberline {6.1.1.1}均数与标准差}{79}{paragraph.6.1.1.1}%
\contentsline {paragraph}{\numberline {6.1.1.2}二项分布的图像}{79}{paragraph.6.1.1.2}%
\contentsline {paragraph}{\numberline {6.1.1.3}与其他分布的关系}{80}{paragraph.6.1.1.3}%
\contentsline {subsubsection}{\numberline {6.1.2}二项分布的应用}{80}{subsubsection.6.1.2}%
\contentsline {paragraph}{\numberline {6.1.2.1}总体率的估计}{80}{paragraph.6.1.2.1}%
\contentsline {subparagraph}{\numberline {6.1.2.1.1}精确法/直接法}{80}{subparagraph.6.1.2.1.1}%
\contentsline {subparagraph}{\numberline {6.1.2.1.2}正态近似法}{81}{subparagraph.6.1.2.1.2}%
\contentsline {paragraph}{\numberline {6.1.2.2}样本率与总体率的比较}{83}{paragraph.6.1.2.2}%
\contentsline {subparagraph}{\numberline {6.1.2.2.1}直接法}{83}{subparagraph.6.1.2.2.1}%
\contentsline {subparagraph}{\numberline {6.1.2.2.2}正态近似法}{84}{subparagraph.6.1.2.2.2}%
\contentsline {paragraph}{\numberline {6.1.2.3}两样本率的比较(正态近似)}{85}{paragraph.6.1.2.3}%
\contentsline {paragraph}{\numberline {6.1.2.4}非遗传疾病的家族聚集性}{87}{paragraph.6.1.2.4}%
\contentsline {paragraph}{\numberline {6.1.2.5}群检验}{87}{paragraph.6.1.2.5}%
\contentsline {subsection}{\numberline {6.2}泊松分布}{88}{subsection.6.2}%
\contentsline {subsubsection}{\numberline {6.2.1}泊松分布的性质}{89}{subsubsection.6.2.1}%
\contentsline {paragraph}{\numberline {6.2.1.1}均数与标准差}{89}{paragraph.6.2.1.1}%
\contentsline {paragraph}{\numberline {6.2.1.2}泊松分布的图像}{89}{paragraph.6.2.1.2}%
\contentsline {subsubsection}{\numberline {6.2.2}泊松分布的应用}{89}{subsubsection.6.2.2}%
\contentsline {paragraph}{\numberline {6.2.2.1}总体均数的区间估计}{89}{paragraph.6.2.2.1}%
\contentsline {subparagraph}{\numberline {6.2.2.1.1}直接法}{89}{subparagraph.6.2.2.1.1}%
\contentsline {subparagraph}{\numberline {6.2.2.1.2}正态近似法}{91}{subparagraph.6.2.2.1.2}%
\contentsline {paragraph}{\numberline {6.2.2.2}样本均数与总体均数的比较}{91}{paragraph.6.2.2.2}%
\contentsline {subparagraph}{\numberline {6.2.2.2.1}直接法}{91}{subparagraph.6.2.2.2.1}%
\contentsline {subparagraph}{\numberline {6.2.2.2.2}正态近似法}{92}{subparagraph.6.2.2.2.2}%
\contentsline {paragraph}{\numberline {6.2.2.3}两样本均数的比较(正态近似)}{93}{paragraph.6.2.2.3}%
\contentsline {subsection}{\numberline {6.3}负二项分布}{95}{subsection.6.3}%
\contentsline {subsubsection}{\numberline {6.3.1}负二项分布的性质}{95}{subsubsection.6.3.1}%
\contentsline {paragraph}{\numberline {6.3.1.1}均数与标准差}{95}{paragraph.6.3.1.1}%
\contentsline {paragraph}{\numberline {6.3.1.2}负二项分布的图像}{96}{paragraph.6.3.1.2}%
\contentsline {paragraph}{\numberline {6.3.1.3}与其他分布的关系}{96}{paragraph.6.3.1.3}%
\contentsline {subsubsection}{\numberline {6.3.2}负二项分布的参数估计}{96}{subsubsection.6.3.2}%
\contentsline {subsubsection}{\numberline {6.3.3}负二项分布的应用}{98}{subsubsection.6.3.3}%
\contentsline {paragraph}{\numberline {6.3.3.1}拟合优度检验}{98}{paragraph.6.3.3.1}%
\contentsline {paragraph}{\numberline {6.3.3.2}两样本均数比较}{98}{paragraph.6.3.3.2}%
\contentsline {section}{\numberline {7}第七章 \(\chi ^2\)检验}{99}{section.7}%
\contentsline {subsection}{\numberline {7.1}卡方分布}{99}{subsection.7.1}%
\contentsline {subsubsection}{\numberline {7.1.1}概率密度函数}{100}{subsubsection.7.1.1}%
\contentsline {subsection}{\numberline {7.2}卡方检验}{100}{subsection.7.2}%
\contentsline {subsubsection}{\numberline {7.2.1}卡方独立性检验的基本思想}{101}{subsubsection.7.2.1}%
\contentsline {subsubsection}{\numberline {7.2.2}四格资料表的卡方检验}{101}{subsubsection.7.2.2}%
\contentsline {paragraph}{\numberline {7.2.2.1}四格资料表的卡方检验的校正公式}{104}{paragraph.7.2.2.1}%
\contentsline {subsubsection}{\numberline {7.2.3}配对的四格资料表的卡方检验}{107}{subsubsection.7.2.3}%
\contentsline {subsubsection}{\numberline {7.2.4}四格资料表的Fisher确切概率法}{110}{subsubsection.7.2.4}%
\contentsline {subsection}{\numberline {7.3}行列资料表的卡方检验}{114}{subsection.7.3}%
\contentsline {subsubsection}{\numberline {7.3.1}多个样本率的比较(\(R \times 2\)表)}{114}{subsubsection.7.3.1}%
\contentsline {subsubsection}{\numberline {7.3.2}样本构成比的比较(\(2 \times C\)表)}{115}{subsubsection.7.3.2}%
\contentsline {subsubsection}{\numberline {7.3.3}双向无序分组资料的关联性检验}{117}{subsubsection.7.3.3}%
\contentsline {subsubsection}{\numberline {7.3.4}双向有序分组资料的线性趋势检验}{119}{subsubsection.7.3.4}%
\contentsline {subsubsection}{\numberline {7.3.5}卡方检验的注意事项与选择思路}{123}{subsubsection.7.3.5}%
\contentsline {paragraph}{\numberline {7.3.5.1}注意事项}{123}{paragraph.7.3.5.1}%
\contentsline {paragraph}{\numberline {7.3.5.2}选择思路}{124}{paragraph.7.3.5.2}%
\contentsline {subsubsection}{\numberline {7.3.6}多个样本率的多重比较}{125}{subsubsection.7.3.6}%
\contentsline {paragraph}{\numberline {7.3.6.1}卡方分割法}{125}{paragraph.7.3.6.1}%
\contentsline {subsection}{\numberline {7.4}Cochran-Mantel-Haenszel卡方统计量检验}{128}{subsection.7.4}%
\contentsline {subsection}{\numberline {7.5}频数分布的拟合优度检验}{132}{subsection.7.5}%
\contentsline {subsubsection}{\numberline {7.5.1}观察数据的无分布预期}{132}{subsubsection.7.5.1}%
\contentsline {subsubsection}{\numberline {7.5.2}观察数据的有预期分布}{135}{subsubsection.7.5.2}%
\contentsline {section}{\numberline {8}第八章 秩转换的非参数检验}{137}{section.8}%
\contentsline {subsection}{\numberline {8.1}Wilcoxon符号秩检验}{139}{subsection.8.1}%
\contentsline {subsubsection}{\numberline {8.1.1}Wilcoxon符号秩检验的原理与过程}{139}{subsubsection.8.1.1}%
\contentsline {subsubsection}{\numberline {8.1.2}单组样本与总体的中位数的Wilcoxon符号秩检验}{141}{subsubsection.8.1.2}%
\contentsline {subsubsection}{\numberline {8.1.3}配对样本差值的中位数和0比较}{142}{subsubsection.8.1.3}%
\contentsline {paragraph}{\numberline {8.1.3.1}配对的等级资料的中位数和0比较}{144}{paragraph.8.1.3.1}%
\contentsline {paragraph}{\numberline {8.1.3.2}正态近似法}{144}{paragraph.8.1.3.2}%
\contentsline {subsection}{\numberline {8.2}Wilcoxon秩和检验}{144}{subsection.8.2}%
\contentsline {subsubsection}{\numberline {8.2.1}Wilcoxon秩和检验的原理与过程}{145}{subsubsection.8.2.1}%
\contentsline {subsubsection}{\numberline {8.2.2}连续型资料的两样本比较}{145}{subsubsection.8.2.2}%
\contentsline {subsubsection}{\numberline {8.2.3}非连续型资料的两样本比较}{147}{subsubsection.8.2.3}%
\contentsline {subsection}{\numberline {8.3}完全随即设计多个样本比较的Kruskal-Wallis H 检验}{150}{subsection.8.3}%
\contentsline {subsubsection}{\numberline {8.3.1}原始数据的多个样本比较}{150}{subsubsection.8.3.1}%
\contentsline {subsubsection}{\numberline {8.3.2}频数表资料和登记资料的多个样本比较}{152}{subsubsection.8.3.2}%
\contentsline {subsection}{\numberline {8.4}多个独立样本两两比较的Nemenyi法检验}{154}{subsection.8.4}%
\contentsline {subsection}{\numberline {8.5}随机区组设计多个相关样本的Friedman M 检验}{156}{subsection.8.5}%
\contentsline {subsubsection}{\numberline {8.5.1}多个相关样本的两两比较}{157}{subsubsection.8.5.1}%
\contentsline {section}{\numberline {9}双变量回归与相关}{159}{section.9}%