An algorithm for the design of factorial experiments when the data are correlated

Since the development of methods for the analysis of experiments with dependent data, see for example Gleeson and Cullis (1987), the design of such experiments has been an area of active research. We investigate the design of factorial experiments, complete and fractional, for various dependency structures. An algorithm for generating optimal or near optimal designs is presented and shown to be useful across a wide range of dependency structures.     

A pragmatic approach to experimental design in industry

The importance of statistically designed experiments in industry has been well recognized. However, the use of 'design of experiments' is still not pervasive, owing in part to the inefficient learning process experienced by many non-statisticians. In this paper, the nature of design of experiments, in contrast to the usual statistical process control techniques, is discussed. It is then pointed out that for design of experiments to be appreciated and applied, appropriate approaches should be taken in training, learning and application. Perspectives based on the concepts of objective setting and design under constraints can be used to facilitate the experimenters' formulation of plans for collection, analysis and interpretation of empirical information. A review is made of the expanding role of design of experiments in the past several decades, with comparisons made of the various formats and contexts of experimental design applications, such as Taguchi methods and Six Sigma. The trend of development shows that, from the realm of scientific research to business improvement, the competitive advantage offered by design of experiments is being increasingly felt.     

A pragmatic approach to experimental design in industry

The importance of statistically designed experiments in industry has been well recognized. However, the use of 'design of experiments' is still not pervasive, owing in part to the inefficient learning process experienced by many non-statisticians. In this paper, the nature of design of experiments, in contrast to the usual statistical process control techniques, is discussed. It is then pointed out that for design of experiments to be appreciated and applied, appropriate approaches should be taken in training, learning and application. Perspectives based on the concepts of objective setting and design under constraints can be used to facilitate the experimenters' formulation of plans for collection, analysis and interpretation of empirical information. A review is made of the expanding role of design of experiments in the past several decades, with comparisons made of the various formats and contexts of experimental design applications, such as Taguchi methods and Six Sigma. The trend of development shows that, from the realm of scientific research to business improvement, the competitive advantage offered by design of experiments is being increasingly felt.     

A clinical application of expert system methodology

In recent years, several expert systems have been developed for practical applications in applied statistical methodologies. Existing expert systems in statistics have explored several areas, e.g. the determination of appropriate statistical tests, regression analysis, and determination of the ‘best’ experimental design for industrial screening experiments. We present here the DESIGN EXPERT which is a prototype expert system for the design of complex statistical experiments. It is intended for scientific investigators and statisticians who must design and analyze complex experiments, e.g. multilevel medical experiments with nested factors, repeated measures, and both fixed and random eflects. This system is ‘expert’ in the sense that it is capable of the following:(i) recognize specific types of complex experimental designs, based on the application of inference rules to non-technical information supplied by the user; (ii) encode the obtained and inferred information in a flexible general-purpose internal representation, for use by other program modules; (iii) generate analysis of variance tables for the recognized design and an appropriate BMDP runfile for data analysis, using the encoded information. DESIGN EXPERT is capable of recognizing randomized block designs, including lattice designs within embedded Latin squares, cross-over designs, split plots, nesting, repeated measures and covariates. It is written in an experimental programming language developed specifically for research in artificial intelligence.     

Mixture and mixture–process variable experiments for pharmaceutical applications

Many experiments in research and development in the pharmaceutical industry involve mixture components. These are experiments in which the experimental factors are the ingredients of a mixture and the response variable is a function of the relative proportion of each ingredient, not its absolute amount. Thus the mixture ingredients cannot be varied independently. A common variation of the mixture experiment occurs when there are also one or more process factors that can be varied independently of each other and of the mixture components, leading to a mixture–process variable experiment. We discuss the design and analysis of these types of experiments, using tablet formulation as an example. Our objective is to encourage greater utilization of these techniques in pharmaceutical research and development. Copyright © 2004 John Wiley & Sons Ltd.     

Direction and collinearity factors of wilks‘s a - a review

Wilks's A was factorized by Bartlett (1951) for testing the hypothesis of goodness of fit of a hypothetical discriminant function in the case of several groups. This test has applications in various areas such as Econometrics, contingency tables, growth curves, principal components analysis, design of experiments and so on. This paper gives a consolidated account of the research done in these areas on the application of factors of Wilks's A     

CONSTRUCTION OF CROSSOVER DESIGNS WITH CORRELATED ERRORS

Crossover experiments are widely used, particularly where a sequence of treatments is given to subjects. Correlations between observations on the same subject are therefore likely and should be considered in both the design and analysis of crossover experiments. This paper presents an algorithm for the generation of efficient crossover designs with autoregressive and linear variance structures. The algorithm has been implemented as a module in the experimental design generation package CycDesigN (Release 3.0; CycSoftware, Hamilton, New Zealand). Output from the algorithm is compared with earlier work. Some results are given from the analysis of a crossover experiment assuming correlated errors.     

Efficient factorial experiments when the data are spatially correlated

Factorial experiments with spatially arranged units occur in many situations, particularly in agricultural field trials. The design of such experiments when observations are spatially correlated is investigated in this paper. We show that having a large number of within-factor level changes in rows and columns is important for efficient and robust designs, and demonstrate how designs with these properties can be constructed.     

Construction of Balanced Incomplete Block Designs Using Cyclic Shifts

Balanced incomplete block designs (BIBDs) play important role in design of experiments, especially in field experiments. These designs ensure that treatments are compared with equal precision. Several methods are available in the literature to construct BIBDs but in this article some infinite series of these designs are presented by method of cyclic shifts. This method expresses some standard properties of a design just through examining the sets of shifts rather than studying the whole design.     

潜在成长模型在体育运动领域的应用

介绍了潜在成长模型的发展、类型和内容,通过分析、归纳、整理等,比较了潜在成长模型与传统t检验、方差分析、回归分析的差别,探讨了潜在成长模型研究设计的要求,通过台湾棒球职业球员薪酬成长模型说明。利用文献调查法,分析了LGM潜在成长模型在体育运动领域中应用的概况,举例说明体育运动领域应用LGM的情况,证实了未来潜在成长模型会在体育科学领域逐渐受到重视并得到快速发展。     

Cross-over trials in drug development: theory and practice

It is maintained that much research into the design and analysis of cross-over trials has been of little practical relevance to drug development. The point is illustrated using three topics: the AB/BA design, bioequivalence and multi-period designs in two treatments. It is suggested that statisticians should pay more attention to the work of fellow scientists, in particular, in the field of pharmacokinetics, and also that the philosophical–inferential base employed in examining cross-over trials has often been too narrow.     

Optimal Experiments for Time-Dependent Mineral Processes

Time dependence is an important characteristic of mineral processing plant data. This paper finds that the time dependence in the recovery data for an experiment at Bougainville Copper Limited (BCL) (Napier-Munn, 1995) can be described by an autoregressive-one process. The paper investigates the optimum form of experimental design for such data. Two intuitive approaches for the design of experiments involving time-dependent data have been disproved recently. Cheng & Steinberg (1991) showed that in some circumstances systematic experiments are preferable to replicated randomized block designs, and Saunders & Eccleston (1992) showed that rather than sampling at a frequency which ensures independent data, in some circumstances sampling intervals should be as small as possible. A third issue, raised in this paper, concerns the use of standard statistical tests when the data are serially correlated. It is shown that the simple paired t -test, suitably modified for time dependence, is appropriate and easily adapted to allow for a covariate and a sequential analysis. The results are illustrated using the BCL data and are already being used to design major experiments involving another mineral process.     

On totally balanced block designs for competition effects

Competition between neighbouring units in field experiments is a serious source of bias. The study of a competing situation needs construction of an environment in which it can happen and the competing units have to appear in a predetermined pattern. This paper describes methods of constructing incomplete block designs balanced for neighbouring competition effects. The designs obtained are totally balanced in the sense that all the effects, direct and neighbours, are estimated with the same variance. The efficiency of these designs has been computed as compared to a complete block design balanced for neighbours and a catalogue has also been prepared.     

Analysis of robust design experiments with time-dependent ordinal response characteristics: a quality improvement study from the horticulture industry

An approach to the analysis of time-dependent ordinal quality score data from robust design experiments is developed and applied to an experiment from commercial horticultural research, using concepts of product robustness and longevity that are familiar to analysts in engineering research. A two-stage analysis is used to develop models describing the effects of a number of experimental treatments on the rate of post-sales product quality decline. The first stage uses a polynomial function on a transformed scale to approximate the quality decline for an individual experimental unit using derived coefficients and the second stage uses a joint mean and dispersion model to investigate the effects of the experimental treatments on these derived coefficients. The approach, developed specifically for an application in horticulture, is exemplified with data from a trial testing ornamental plants that are subjected to a range of treatments during production and home-life. The results of the analysis show how a number of control and noise factors affect the rate of post-production quality decline. Although the model is used to analyse quality data from a trial on ornamental plants, the approach developed is expected to be more generally applicable to a wide range of other complex production systems.     

Computer-aided unbalanced supersaturated designs involving interactions

Supersaturated designs (SSDs) are defined as fractional factorial designs whose experimental run size is smaller than the number of main effects to be estimated. While most of the literature on SSDs has focused only on main effects designs, the construction and analysis of such designs involving interactions has not been developed to a great extent. In this paper, we propose a backward elimination design-driven optimization (BEDDO) method, with one main goal in mind, to eliminate the factors which are identified to be fully aliased or highly partially aliased with each other in the design. Under the proposed BEDDO method, we implement and combine correlation-based statistical measures taken from classical test theory and design of experiments field, and we also present an optimality criterion which is a modified form of Cronbach's alpha coefficient. In this way, we provide a new class of computer-aided unbalanced SSDs involving interactions, that derive directly from BEDDO optimization.     

抽样调查应用与理论中的若干前沿问题

综述了近三四十年来抽样调查应用与理论的若干前沿热门问题,着重讨论抽样设计与推断方法、非抽样误差分析及小域估计等三个方向,同时指出中国抽样调查的实践与理论研究所面临的主要问题.     

Design issues for studies of infectious diseases

The design of infectious disease studies has received little attention because they are generally viewed as observational studies. That is, epidemic and endemic disease transmission happens and we observe it. We argue here that statistical design often provides useful guidance for such studies with regard to type of data and the size of the data set to be collected. It is shown that data on disease transmission in part of the community enables the estimation of central parameters and it is possible to compute the sample size required to make inferences with a desired precision. We illustrate this for data on disease transmission in a single community of uniformly mixing individuals and for data on outbreak sizes in households. Data on disease transmission is usually incomplete and this creates an identifiability problem for certain parameters of multitype epidemic models. We identify designs that can overcome this problem for the important objective of estimating parameters that help to assess the effectiveness of a vaccine. With disease transmission in animal groups there is greater scope for conducting planned experiments and we explore some possibilities for such experiments. The topic is largely unexplored and numerous open research problems in the area of statistical design of infectious disease data are mentioned.     

On the efficiency of some non-orthogonal split-plot×split-block designs with control treatments

Many split-plot×split-block (SPSB) type experiments used in agriculture, biochemistry or plant protection are designed to study new crop plant cultivars or chemical agents. In these experiments it is usually very important to compare test treatments with the so-called control treatments. It happens yet that experimental material is limited and it does not allow using a complete (orthogonal) SPSB design. In the paper we propose a non-orthogonal SPSB design for consideration. Two cases of the design are presented here, i.e. when its incompleteness is connected with a crossed treatment structure only or with a nested treatment structure only. It is assumed the factors' levels connected with the incompleteness of the design are split into two groups: a set of test treatments and a set of control treatments. The method of constructions involves applying augmented block designs for some factors' levels. In a modelling data obtained from such experiments the structure of experimental material and appropriate randomization scheme of the different kinds of units before they enter the experiment are taken into account. With respect to the analysis of the obtained randomization model the approach typical to the multistratum experiments with orthogonal block structure is adapted. The proposed statistical analysis of linear model obtained includes estimation of parameters, testing general and particular hypotheses defined by the (basic) treatment contrasts with special reference to the notion of general balance.     

Designs for two-colour microarray experiments

Summary.  Designs for two-colour microarray experiments can be viewed as block designs with two treatments per block. Explicit formulae for the A- and D-criteria are given for the case that the number of blocks is equal to the number of treatments. These show that the A- and D-optimality criteria conflict badly if there are 10 or more treatments. A similar analysis shows that designs with one or two extra blocks perform very much better, but again there is a conflict between the two optimality criteria for moderately large numbers of treatments. It is shown that this problem can be avoided by slightly increasing the number of blocks. The two colours that are used in each block effectively turn the block design into a row–column design. There is no need to use a design in which every treatment has each colour equally often: rather, an efficient row–column design should be used. For odd replication, it is recommended that the row–column design should be based on a bipartite graph, and it is proved that the optimal such design corresponds to an optimal block design for half the number of treatments. Efficient row–column designs are given for replications 3–6. It is shown how to adapt them for experiments in which some treatments have replication only 2.     

Multiphase experiments with at least one later laboratory phase. II. Nonorthogonal designs

Principles and laws that apply to nonorthogonal multiphase experiments are developed and illustrated using examples that are nonorthogonal but structure‐balanced, not structure, but first‐order, balanced or unbalanced, thus exposing the differences between the different design types. The design of such experiments using standard designs, a catalogue of designs and computer searches is exemplified. Factor–allocation diagrams are employed to depict the allocations in the examples, and used in producing the anatomies of designs or, when possible, the related skeleton‐analysis‐of‐variance tables, to assess the properties of designs. The formulation of mixed models based on them is also described. Tools used for structure‐balanced experiments are also shown to be applicable to those experiments that are not.