英语翻译4.1 IntroductionThe objective of an experiment is often much more specific than merely determining whether or not all of the treatments give rise to similar responses.For example,a chemical experi-ment might be run primarily to dete

英语翻译4.1 IntroductionThe objective of an experiment is often much more specific than merely determining whether or not all of the treatments give rise to similar responses.For example,a chemical experi-ment might be run primarily to dete
英语翻译
4.1 Introduction
The objective of an experiment is often much more specific than merely determining whether or not all of the treatments give rise to similar responses.For example,a chemical experi-ment might be run primarily to determine whether or not the yield of the chemical process increases as the amount of the catalyst is increased.A medical experiment might be con-cerned with the efficacy of each of several new drugs as compared with a standard drug.A nutrition experiment may be run to compare high fiber diets with low fiber diets.Such treat-ment comparisons are formalized in Section 4.2.The purpose of this chapter is to provide confidence intervals and hypothesis tests about treatment comparisons and treatment means.We start,in Section 4.3,by considering a single treatment comparison or mean,and then,in Section 4.4,we develop the techniques needed when more than one treatment comparison or mean is of interest.The number of observations required to achieve confidence intervals of given lengths is calculated in Section 4.5.SAS commands for confidence intervals and hypothesis tests are provided in Section 4.6.
4.2 Contrasts
In Chapter 3,we defined a contrast to be a linear combination of the parameters τ1,τ2,...,τv of the form
∑ciτi,with　∑ci=0 .
For example,τu− τs is the contrast that compares the effects (as measured by the response variable) of treatments u and s.If τu− τs=0,then treatments u and s affect the response in exactly the same way,and we say that these treatments do not differ.Otherwise,the treatments do differ in the way they affect the response.We showed in Section 3.4 that for a completely randomized design and the one-way analysis of variance model (3.3.1),every contrast ∑ciτi is estimable with least squares estimate
∑ci τi=∑ci(µˆ + ˆτi)=∑ciyi.(4.2.1)
and corresponding least squares estimator　∑ciYi.The variance of the least squares
estimator is
Var(∑ciYi)=∑ci ²Var(Yi.)=∑ci²(σ2/ri)=σ2∑(ci²/ri).(4.2.2)
The first equality uses the fact that the treatment sample means Yi.involve different response variables,which in model (3.3.1) are independent.The error variance σ2is generally un-known and is estimated by the unbiased estimate msE,giving the estimated variance of thecontrast estimator as
Var(∑ciYi.)\x05=msE∑(ci²/ri)
The estimated standard error of the estimator is the square root of this quantity,namely.

英语翻译4.1 IntroductionThe objective of an experiment is often much more specific than merely determining whether or not all of the treatments give rise to similar responses.For example,a chemical experi-ment might be run primarily to dete
4.1简介
目的一个实验往往是更具体fi三仅仅确定是否所有的治疗产生了类似的反应.例如,一个化学实验可能是主要决定是否或不屈服的化学过程,增加催化剂用量的增加.医学实验可能涉及英法fi卡每几个新的药物相比,标准药物.营养实验可能是比较高的fi误码率低fi误码率饮食饮食.这样的处理比较正式的4.2节.本章的目的是提供一fi证据区间及假设试验比较治疗和治疗手段.我们开始,在4.3节,考虑一个单一的治疗比较平均,然后,在4.4部分,我们开发的技术时需要一个以上的治疗比较或是兴趣.若干意见要求达到节能fi密间隔在4.5节给出的长度计算.萨斯命令欺诈fi证据区间及假设检验提供4.6节.
4.2个对比
在3章,我们fi内德的对比是一个线性组合的参数τ1,τ2,.的.第五,τ形式
∑词τ我,与∑区间=0.
例如,你的τ−τ的对比和比较的影响（如测量反应变量）治疗你,如果你−ττ=0,那么你的治疗和影响的反应,在完全相同的方式,我们说,这些治疗并没有不同.否则,治疗不同的方式影响他们的反应.我们发现在3.4节,一个完全随机设计和单向方差分析模型（3）,每一个词的对比∑τ我是难能可贵的最小二乘估计
∑词τ我=∑词（µˆ+ˆτ我）=∑室.（2）
和相应的最小二乘估计∑室.差异的最小二乘法
估计是
无功（∑此役）=∑词²变种（彝族.）=∑词²（σ2 /日）=σ2∑（词²/日）.（图5）
该fi复位平等使用的事实,治疗手段yi.involve样品不同的反应变量,该模型（3）是独立的.误差方差是未知和σ一般估计的无偏估计,均方误差,给出估计方差对比估算
无功（∑此役.）=均方误差∑（词²/日）
估计标准误差的估计的平方根的数量,即.

4.1简介
实验的目的不仅仅是决定并非所有的治疗是否会引起类似的反应往往更加具体。例如，一个化学实验可能主要运行以决定是否或不是化学过程的产量增加催化剂用量增加。医学实验可能与一些新的药物的疗效比标准药物浓度关注。可以运行比较低纤维饮食，高纤维饮食营养实验。这样的处理比较正式的第4.2节。本章的目的是提供有关治疗比较和治疗means.we开始的置信区间和假设检验，在4.3节，考虑一个单一的...

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4.1简介
实验的目的不仅仅是决定并非所有的治疗是否会引起类似的反应往往更加具体。例如，一个化学实验可能主要运行以决定是否或不是化学过程的产量增加催化剂用量增加。医学实验可能与一些新的药物的疗效比标准药物浓度关注。可以运行比较低纤维饮食，高纤维饮食营养实验。这样的处理比较正式的第4.2节。本章的目的是提供有关治疗比较和治疗means.we开始的置信区间和假设检验，在4.3节，考虑一个单一的治疗比较，或意味着，然后在4.4节中，我们开发时需要更多的技巧多个治疗比较或平均利益。在4.5节须达到给定长度的置信区间的观测数计算。在第4.6节提供的置信区间和假设检验的SAS命令。
4.2对比
在第三章中，我们定义了一个对比参数τ1，τ2，是一个线性组合。 。 。 ，τv的形式
σciτi，与Σci= 0。
例如，τuτs是比较U和S的治疗效果（响应变量的测量）的对比。 τu-τs如果= 0，则U和S在完全相同的方式影响的反应，和我们说，这些治疗并无不同的治疗方法。否则，处理不同的方式影响他们的响应。我们发现，在3.4节，完全随机设计方差模型（3.3.1）单向分析，每一个的对比Σciτi是难能可贵的，与最小二乘估计
σciτi=Σci（μ+τi）=Σciyi。 （4.2.1）
和相应的至少估计Σciyi平方。最小二乘方差
估计是
VAR（Σciyi）=Σci“VAR（yi.）=Σci平方英哩（σ2/ri）=σ2Σ（CI平方米/ RI）。 （4.2.2）
第一平等使用的事实，处理样品意味着yi.involve不同的反应变量，在模型（3.3.1）是独立的。误差方差σ2is一般未知，估计是无偏估计的MSE，给人的thecontrast估计的估计方差作为
VAR（Σciyi.）=mseΣ（CI平方米/ RI）
估计标准误差估计是这个数量的平方根，即

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4.1 Introduction
The objective of an experiment is often much more specific than merely determining whether or not all of the treatments give rise to similar responses. For example, a chemic...

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4.1 Introduction
The objective of an experiment is often much more specific than merely determining whether or not all of the treatments give rise to similar responses. For example, a chemical experi-ment might be run primarily to determine whether or not the yield of the chemical process increases as the amount of the catalyst is increased. A medical experiment might be con-cerned with the efficacy of each of several new drugs as compared with a standard drug. A nutrition experiment may be run to compare high fiber diets with low fiber diets. Such treat-ment comparisons are formalized in Section 4.2. The purpose of this chapter is to provide confidence intervals and hypothesis tests about treatment comparisons and treatment means.We start, in Section 4.3, by considering a single treatment comparison or mean, and then, in Section 4.4, we develop the techniques needed when more than one treatment comparison or mean is of interest. The number of observations required to achieve confidence intervals of given lengths is calculated in Section 4.5. SAS commands for confidence intervals and hypothesis tests are provided in Section 4.6.
4.2 Contrasts
In Chapter 3, we defined a contrast to be a linear combination of the parameters τ1, τ2, . . . , τv of the form
∑ciτi, with　∑ci=0 .
For example, τu− τs is the contrast that compares the effects (as measured by the response variable) of treatments u and s. If τu− τs=0, then treatments u and s affect the response in exactly the same way, and we say that these treatments do not differ. Otherwise, the treatments do differ in the way they affect the response. We showed in Section 3.4 that for a completely randomized design and the one-way analysis of variance model (3.3.1), every contrast ∑ciτi is estimable with least squares estimate
∑ci τi=∑ci(µˆ + ˆτi)=∑ciyi. (4.2.1)
and corresponding least squares estimator　∑ciYi. The variance of the least squares
estimator is
Var(∑ciYi)=∑ci ²Var(Yi.)=∑ci²(σ2/ri)=σ2∑(ci²/ri). (4.2.2)
The first equality uses the fact that the treatment sample means Yi.involve different response variables, which in model (3.3.1) are independent. The error variance σ2is generally un-known and is estimated by the unbiased estimate msE, giving the estimated variance of thecontrast estimator as
Var(∑ciYi.)=msE∑(ci²/ri)
The estimated standard error of the estimator is the square root of this quantity, namely。

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