这个作业来自美国的关于用R语言对实验案例进行建模、方差分析以及回归分析的R语言代写,作业详情可扫码咨询客服
STA 466/566: Experimental Design Methods
1.1实验方法和范例(蒙哥马利1.1-1.2)
实验:一系列测试,目的是对系统的输入变量进行有目的的更改,以便
这些变化对输出变量的影响可以被观察和识别。
方差分析方法:如果您希望比较特定因素水平下的响应均值,则因素通常是分类的,或者离散因素是离散的。在这种情况下,将使用方差分析(ANOVA)模型
分析实验。
建模/回归/响应面方法:如果因素是定量的,则可以获得更多信息
通过像对回归中的定量预测变量那样对响应进行建模。允许您构建
使用低阶多项式的模型,然后可以将其用于预测和优化。优于
方差分析用于回答以下问题:这些量化因子中的哪些水平会产生最佳响应?
本课程的大部分内容将集中于经典的方差分析,但我们将密切关注回归
我们的ANOVA模型版本。我们还将考虑量化因素和
使用回归代替方差分析。
如果因子是分类的,则方差分析和回归(带有指标变量)是等效模型,但是如果
因素是定量的,您不能使用方差分析。
实验设计实例
例1:迈阿密的一个研究小组正在尝试对人类视网膜细胞进行基因改造。
判断某些人类干细胞是否正在变成视网膜细胞的一种方法是,其色素沉着减少。
考虑一个单因素实验来研究某些人类干细胞中色素沉着的损失。有
四种治疗方法进行比较。
实施例2:干汤混合物灌装过程的实验(Hare,质量技术杂志,1988年)。一个
公司希望将混合料的重量保持尽可能均匀。实验者认为
以下因素可能会影响混合过程:(A)蔬菜通过的混合器端口数量
加入油(1或3); (B)“混合器夹套”的温度(环境温度;冷却水的存在);
(C)混合时间(60秒; 80秒); (D)批次重量(1500磅; 2000磅); (E)之间的延迟
混合和包装(1天; 7天)。
示例3(观察性):体罚。 Straus,Sugarman和
Giles-Sims,由Oehlert描述。 1979年开始对14至21岁的女性进行大规模调查,
到1988年,这些妇女有1239名6至9岁的孩子。这些妇女在接受采访/测试
1988年和1990年。在其他情况下,他们被问及孩子的反社会行为,以及
有关打屁股的频率的问题。结果表明,打屁股的孩子更多
1988年通常在1990年有更多的反社会行为。打屁股会引起反社会行为吗?
相关与因果关系。在观察性研究中,我们通常无法得出结论:
变量导致响应发生变化;在实验中,我们可以。
Treatments: the different levels of a factor or different combinations of levels of several factors.
Nuisance factors: Sometimes there are factors in the experiment that explain some of the variation in the
response but are not a part of the treatment. They should be included in the analysis because they reduce
the amount of unexplained variability in the response. If these factors are discrete, they are called blocks. If
they are continuous, they are called covariates.
Experimental Unit: the object on which the treatments are applied; the Measurement Unit is the object
on which the response is actually measured. Often experimental and measurement units are the same, but
not always.
1.2 Some Basic Principles of Design (Montgomery 1.3)
Replication: independent repetition of a treatment.
Independent replication vs. repeated or nonindependent measurement.
1. Four subjects are assigned to a drug and four are assigned to a placebo. For each, three different blood
draws are taken and a measurement is obtained from each.
2. Four subjects are assigned to a drug and four are assigned to a placebo and a measurement is taken on
each.
3. Retinal cell example. The cells are grown in containers. Consider a version of the experiment with
four treatments, where each treatment is made by mixing up a set of compounds. Suppose four
mixtures are made, each consisting of a different treatment. Then, three samples are taken from the
mixes and administered to cells in separate containers. So a total of 12 containers are used (three for
each treatment).