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1、Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024多个样本均数比较的方差分析多个样本均数比较的方差分析 s前章介绍了两样本均数比较的t检验。在医学科学研究中，常常要通过多个样本均数比较来推断各处理组间是否存在差别，此时若多次重复使用t-test ，会使犯第类错误（假阳性错误）的概率增大，且脱离了原先的实验设计，将多个样本均数的同时比较转变为两个样本均数的多次比较。若采用实验设计所对应的方差分析同时分析多个样本均数的差别，则可避免以上问题。 Thursda
2、y, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024第一节 方差分析的基本思想和应用条件 s方差分析（analysis of variance, ANOVA）的理论依据是F分布，故又称F检验。在处理实验设计资料时，主要用于推论多个处理组处理效应的差别。s下面结合例11-1的试验结果，介绍方差分析的基本思想及其应用条件。 Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August
3、 8, 2024202420242024s例例11-1 为了解烫伤后不同时期切痂对肝脏三磷酸腺苷（简写为ATP）的影响，将30只雄性大鼠随机分成3组, 每组10只：A组为烫伤对照组，B组为烫伤后24小时(休克期)切痂组，C组为烫伤后96小时（非休克期）切痂组。全部动物统一在烫伤后168小时处死并测量其肝脏的ATP含量，结果见表11-1。这一问题的解决可以归结为三组ATP总体均数差别的比较。如果三组ATP的总体均数存在差别，则推论B组和C组的处理对ATP有影响。 Thursday, Thursday, Thursday, Thursday, August 8, August 8, August
4、8, August 8, 2024202420242024Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8,
5、 2024202420242024Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 20242024202
6、42024方差分析的应用条件s各组样本是相互独立的随机样本且来自正态总体。s各组总体方差相等，即方差齐性（homoscedasticity）。s上述两个条件与两均数比较的t检验的应用条件是相同的。实际上，当组数为2时，方差分析与两均数比较的t检验是等价的，且对同一资料有。Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024第二节 完全随机设计资料的方差分析s完全随机设计（completely random design）只设计一个处理因素（该因素有两个或两
7、个以上水平），采用完全随机的方法直接将受试对象分配到各个处理水平组。各处理水平组例数可以相等亦可以不等。以例11-1为例，先将30只大鼠按体重大小编号，从附表15中第10行第6列、第7列向下开始取2位的随机数，即63，73，65，。随机数排出序号后，序号110为A组，序号1120为B组，序号2130为C组。 Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024Thursday, Thursday, Thursday, Thursday, August 8,
8、 August 8, August 8, August 8, 2024202420242024Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024Thursday, Thursday, Thursday, Thursday, August 8, August 8, A
9、ugust 8, August 8, 2024202420242024s方差分析的结果只能说明多组间是否有差别，有时我们更关心哪两组间有差别(如本例更关心两个切痂组的ATP含量是否有差别)。这时可进行多个均数的两两比较，详见本章第四节。Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024第三节 随机区组设计资料的方差分析 s随机区组设计（随机区组设计（randomized block design）亦亦称配伍组设计或单位组设计，是配对设计的扩展。称配伍组设
10、计或单位组设计，是配对设计的扩展。具体做法是首先将受试对象按可能影响试验结果具体做法是首先将受试对象按可能影响试验结果的属性分组（非随机分组），如按动物的性别、的属性分组（非随机分组），如按动物的性别、体重分组，按病人的年龄、职业、病情分组等。体重分组，按病人的年龄、职业、病情分组等。分组的原则是属性相同或相近的分在同一组内，分组的原则是属性相同或相近的分在同一组内，共形成共形成b个区组，再分别将各区组内的受试对象个区组，再分别将各区组内的受试对象随机分配到各处理组。其设计特点是：每个区组随机分配到各处理组。其设计特点是：每个区组的受试对象数与处理组数相等，区组内的受试对的受试对象数与处理组数
11、相等，区组内的受试对象生物学特性较均衡，可减少试验误差，提高统象生物学特性较均衡，可减少试验误差，提高统计假设检验的效率。计假设检验的效率。Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024s例例11-4（续例11-3） 根据表11-6的试验结果，检验甲、乙、丙、丁不同浓度的血水草总生物碱对小鼠体内的尾蚴存活率的影响。（注：这里的小鼠体内的尾蚴存活率是测量指标，不同于第四章计数资料统计指标的“率”）Thursday, Thursday, Thursday
12、, Thursday, August 8, August 8, August 8, August 8, 2024202420242024Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024注意问题s在实际工作中，一般只对试验的研究因素感兴趣，即注重处理组间差别的假设检
13、验，必要时也可对区组间的差别进行假设检验。本例，区组间的总体均数有差别，说明小鼠体重（或各区组的试验条件）对小鼠体内尾蚴存活率有影响。 Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024第四节 多个均数间的两两比较s经方差分析，若各组的均数差别无统计学意义，则不需要作进一步的统计处理，但是当方差分析结果为 时，只说明k组总体均数不相同或不全相同，不能说明各组总体均数间有差别。如果要分析哪两组间均数有差别，需进行多个均数间的两两比较（multiple co
14、mparison）。在进行两两比较时若仍用两均数比较t检验，将会增加第一类错误的概率，把本来无差别的两个总体均数判为有差别。 Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024SNK-q检验sSNK为Student-Newman-Keuls三人姓氏的缩写，检验统计量
15、为q ，亦称q检验，适用于多个均数的两两比较，常用于探索性研究。 q的计算公式如下Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024LSD-t检验s即最小显著差异（least significant difference）t检验。适用于某一对或几对在专业上有特殊价值的均数间差别的比较。 Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 20242
16、02420242024三、Dunnett-t检验s适用于k-1个实验组与一个对照组均数差别的多重比较，检验统计量为Dunnett-t值， Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024第六节 重复测量数据的方差分析* s对于临床上常见的重复测量数据（repeated measurement data），也称监测数据（monitoring data），即每个患者的临床观察结果是多次重复测量结果的连线（见图11-2），统计分析的目的是比较这些连线变化趋势的特征。Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024Thursday, Thursday, Thursday, Thursday, August 8, August 8, August 8, August 8, 2024202420242024
