Incomplete split plot designs

We propose an incomplete split plot design where levels of one factor (say A) are applied to the wholeplots and levels of the other (say B) to subplots, and where the number of subplots in each wholeplot may be less than the number of levels of factor B.The t levels of factor A are arranged in a completely randomized design. The s levels of factor B are arranged in a connected and proper incomplete block design within each level of factor A, by considering the wholeplots as blocks.     

Two‐strata rotatability in split‐plot central composite designs

A rotatable design (Ann. Math. Stat. 1957; 28 :195–241) for k factors is one such that the prediction variance is purely a function of distance from the design center. Of special interest in this paper is the rotatable central composite design (CCD), which most software packages use as the typical default choice for a second‐order design. In many cases some factors are hard to change while others are easy to change, which creates a split‐plot experiment. This paper establishes that the split‐plot structure precludes the possibility of any second‐order design being rotatable in the traditional sense. As an alternative this paper proposes the two‐strata rotatable split‐plot CCD, where the resulting prediction variance is a function of the whole plot (WP) distance and the subplot (SP) distance separately instead of the sum of them. The resulting design is rotatable in the WP space when the SP factors are held fixed, and vice versa. In the special case where the WP variance component is zero, the two‐strata rotatable split‐plot CCD becomes the standard rotatable CCD. Copyright © 2009 John Wiley & Sons, Ltd.     

Efficiency measure,modelling and estimation in combined array designs

In off‐line quality control, the settings that minimize the variance of a quality characteristic are unknown and must be determined based on an estimated dual response model of mean and variance. The present paper proposes a direct measure of the efficiency of any given design‐estimation procedure for variance minimization. This not only facilitates the comparison of different design‐estimation procedures, but may also provide a guideline for choosing a better solution when the estimated dual response model suggests multiple solutions. Motivated by the analysis of an industrial experiment on spray painting, the present paper also applies a class of link functions to model process variances in off‐line quality control. For model fitting, a parametric distribution is employed in updating the variance estimates used in an iteratively weighted least squares procedure for mean estimation. In analysing combined array experiments, Engel and Huele (Technometrics, 1996; 39:365) used log‐link to model process variances and considered an iteratively weighted least squares leading to the pseudo‐likelihood estimates of variances as discussed in Carroll and Ruppert (Transformation and Weighting in Regression, Chapman & Hall: New York). Their method is a special case of the approach considered in this paper. It is seen for the spray paint data that the log‐link may not be satisfactory and the class of link functions considered here improves substantially the fit to process variances. This conclusion is reached with a suggested method of comparing ‘empirical variances’ with the ‘theoretical variances’ based on the assumed model. Copyright © 2003 John Wiley & Sons, Ltd.     

线性混合模型中方差分量的ANOVA估计的改进

讨论了在含三个方差分量的线性混合模型中,在均方误差意义下,方差分量的方差分析估计的改进,并把这一结果推广到一般的线性混合模型上,得到一个改进方差分析估计的简单方法.     

方差分析在复杂测量系统能力分析中的应用

测量系统分析是QS9000标准中的核心要素之一,主要用来评估测量系统对工序质量改进的保证程度。传统的测量系统能力分析主要采用极差分析或方差分析研究单台测量仪器组成的二因素交叉型简单测量系统,本文从企业的实际情况出发,采用方差分析法研究包含多台测量仪器的复杂测量系统,基于三因素套析因混合效应实验模型的方差分析和方差估计,提出了这种测量系统能力分析的方法,并给出了应用实例。     

随机效应模型中方差分量的经验Bayes检验问题

给出了双向分类随机效应模型中方差分量的Bayes检验的判决函数,利用核估计的方法,构造了相应的经验Bayes(EB)检验的判决函数．在适当的条件下证明了EB判决函数是渐近最优的且有收敛速度．给出了模型的特例和推广．最后,举出一个满足定理条件的例子．     

不同培养基对线虫质量影响的统计分析

本文运用方差分析和多重比较法，分析了由五种不同培养基所繁殖的Ｂｅｉｊｉｎｇ品系的芜菁夜蛾线虫在侵入率、运动能力及体长方面的差异性，从中确定了最佳培养基．为选择培养高质量线虫的营养条件提供了一定的理论依据。     

Planning accelerated life tests with random effects of test chambers

In accelerated life tests (ALTs), test units are often tested in multiple test chambers along with different stress conditions. The nonhomogeneity of test chambers precludes the complete randomized experiment and may affect the life‐stress relationship of the test product. The chamber‐to‐chamber variation should be taken into account for ALT planning so as to obtain more accurate test results. In this paper, planning ALTs under a nested experimental design structure with random test chamber effects is studied. First, by a 2‐phase approach, we illustrate to what extent different test chamber assignments to stress conditions may impact the estimation of unknown parameters. Then, D‐optimal test plans with 2 test chambers are considered. To construct the optimal design, we establish the generalized linear mixed model for failure‐time data and apply a quasi‐likelihood method, where test chamber assignments, as well as other decision variables that are required for planning ALTs, are simultaneously determined.     

英语语调性别差异的统计分析

本文主要采用语料库语言学的研究方法,选取IViE语料库中英国剑桥地区6男6女共12位母语朗读者的不同句型的单句和段落朗读中的相关句型,从英语语调的核心声学参数调核音高入手,分析男女朗读者在5种不同句子类型(陈述句、陈述疑问句、一般疑问句、特殊疑问句和感叹句)上的异同。我们针对408句声音语料,利用先进的计算机语音分析软件获取研究数据,再通过严格的统计分析,以定量分析的方式考察英语不同句型的调核音高差异程度和调核音高的性别差异,分析英国英语语调在调核音高上的性别差异和特点。     

活性染料废水脱色正交试验设计与分析

使用正交试验设计方法设计出试验方案,对总体数据用方差分析等方法对选择方案进行期望评估,从而避免了常规试验中由于随机误差导致的判断失误,达到了试验效率非常高的效果.     

Simultaneous optimal estimates of fixed effects and variance components in the mixed model

For a general linear mixed model with two variance components, a set of simple conditions is obtained, under which, (i) the least squares estimate of the fixed effects and the analysis of variance (ANOVA) estimates of variance components are proved to be uniformly minimum variance unbiased estimates simultaneously; (ii) the exact confidence intervals of the fixed effects and uniformly optimal unbiased tests on variance components are given; (iii) the exact probability expression of ANOVA estimates of variance components taking negative value is obtained.     

An improved two‐stage variance balance approach for constructing partial profile designs for discrete choice experiments

In many discrete choice experiments set up for product innovation, the number of attributes is large, which results in a substantial cognitive burden for the respondents. To reduce the cognitive burden in such cases, Green suggested in the early '70s the use of partial profiles that vary only the levels of a subset of the attributes. In this paper, we present two new methods for constructing Bayesian ‐optimal partial profile designs for estimating main‐effects models. They involve alternative generalizations of Green's approach that makes use of balanced incomplete block designs and take into account the fact that attributes may have differing numbers of levels. We refer to our methods as variance balance I and II because they vary an attribute with a larger number of levels more often than an attribute with fewer levels to stabilize the variances of the individual part‐worth estimates. The two variance balance methods differ in the way attributes with differing numbers of levels are weighted. Both methods provide statistically more efficient partial profile designs for differing numbers of attribute levels than another generalization of Green's approach that does not weight the attributes. This method is called attribute balance. We show results from an actual experiment in software development demonstrating the usefulness of our methods. Copyright © 2014 John Wiley & Sons, Ltd.     

A new estimate of the parameters in linear mixed models

In linear mixed models, there are two kinds of unknown parameters: one is the fixed effect, the other is the variance component. In this paper, new estimates of these parameters, called the spectral decomposition estimates, are proposed, Some important statistical properties of the new estimates are established, in particular the linearity of the estimates of the fixed effects with many statistical optimalities. A new method is applied to two important models which are used in economics, finance, and mechanical fields. All estimates obtained have good statistical and practical meaning.     

正交表交互作用的广义方差分析

本文给出“正交表的多指标效应与单指标效应的交互列一致”的结论 ,并据此结合实例给出了交互作用的“广义方差分析”法     

AHP的检验方法及其比较分析

介绍了目前较有影响的三种ＡＨＰ一致性检验算法,并对其作了比较分析,最后提出了一种检验算法的选择准则     

幂变换在多元线性回归中的应用

幂变换是多元线性回归分析中数据预处理的有效办法之一.以胰岛素注射治疗糖尿病为例,探讨幂变换实用的条件、研究方法及研究结论,并将幂变换处理后的变量,用于线性回归分析,研究医学问题.具体就是通过对变量数据描述性分析了解数据的特点,相关分析及聚类分析确定胰岛素初始剂量的重要影响因素,幂变换对数据进行预处理,继而进行回归分析,并对比变换前初步回归分析的结果,确定最终以尿蛋白分类标准,RI用量与血糖的对数之间的线性回归模型.     

服装主观热感觉的统计分析

本文用多因子方差分析模型和多重比较分析了服装穿着时的主观热感觉与服装品种、环境条件、穿着者的活动状态与籍贯之间的关系。通过主成分回归建立了用生理指标预测主观热感觉的模型，从而得出一种定量地评价服装属性的方法。     

析因试验中交互作用分析的SAS技术

本文剖析了析因试验中交互作用的意义 ,并介绍了用 SAS软件对达显著的交互作用继续分析的两种方法 .此两法具有重要的实用价值 .     

医学显性致死试验平均死胎率比较的统计分析

负二项分布方法可用作比较显性致死试验中平均死胎率的差异 ,本文对传统的负二项分布方法进行了描述 ,同时提出两种非参数方法 ,且就以上的方法的不足进行了比较 ,例子显示利用文中的一种非参数方法—L法更为合理     

均衡随机分组设计的研究

均衡随机分组设计是一种把随机抽样设计与显著性检验相结合的试验设计方法.试验设计可以避免完全随机抽样(或完全随机分组)设计可能会造成所分组间存在较大差异的缺点,保证所分组或样本间具有均衡性,确保抽样的科学性和可比性,以增强对处理效果反应的灵敏度,提高试脸的准确度.