Information in experiments and sufficiency

We define measures of information contained in an experiment which are by-products of the parametric measures of Fisher, Vajda, Mathai and Boekee and the non-parametric measures of Bhattacharyya, Rényi, Matusita, Kagan and Csiszár. We use these measures to compare sufficient experiments according to Blackwell's definition. In particular, we prove that if δ_X and δ_Y are two experiments and δ_X≥δ_Y then l_X≥l_y for all of the above measures.     

Symmetry in mixture experiments

Two types of symmetry can arise when the proportions of mixture components are constrained by upper and lower bounds. These two types of symmetry are shown to be useful for blocking first-order designs, as well as for finding the centroid of the experimental region. Orthogonal blocking of first-order mixture designs provides a method of including process variables in the mixture experiment, with the mixture terms orthogonal to the process factors. Symmetric regions are used to develop spherical and rotatable response surface designs for mixtures. The central composite design and designs based on the icosahedron and the dodecahedron are given for four-component mixtures. The uniform shell designs are three-level designs when applied to mixture experiments.     

Outliers in incomplete multiresponse experiments

Identification of outlier vectors in block designs for incomplete multiresponse experiments has been considered. Design is composed of two sets of experimental units. Different numbers of response variables are observed from these two sets. Cook-statistic has been developed for identification of outliers. The developed statistic has been illustrated with a real-life data set. It has been shown that presence of outliers can distort the overall conclusion from an experiment.     

Combining p-values in large-scale genomics experiments

In large-scale genomics experiments involving thousands of statistical tests, such as association scans and microarray expression experiments, a key question is: Which of the L tests represent true associations (TAs)? The traditional way to control false findings is via individual adjustments. In the presence of multiple TAs, p-value combination methods offer certain advantages. Both Fisher's and Lancaster's combination methods use an inverse gamma transformation. We identify the relation of the shape parameter of that distribution to the implicit threshold value; p-values below that threshold are favored by the inverse gamma method (GM). We explore this feature to improve power over Fisher's method when L is large and the number of TAs is moderate. However, the improvement in power provided by combination methods is at the expense of a weaker claim made upon rejection of the null hypothesis - that there are some TAs among the L tests. Thus, GM remains a global test. To allow a stronger claim about a subset of p-values that is smaller than L, we investigate two methods with an explicit truncation: the rank truncated product method (RTP) that combines the first K-ordered p-values, and the truncated product method (TPM) that combines p-values that are smaller than a specified threshold. We conclude that TPM allows claims to be made about subsets of p-values, while the claim of the RTP is, like GM, more appropriately about all L tests. GM gives somewhat higher power than TPM, RTP, Fisher, and Simes methods across a range of simulations.     

Individual control treatment in split-plot experiments

The paper deals with experiments laid out in a complete or an incomplete split-plot design in which one control (standard) treatment occurs in addition to the usual treatments. Usually the control (standard) treatment has been treated as one specific factor level. In this paper, in contrast to others in this area, the control (standard) may not be strictly connected with treatment combinations. The new incomplete split-plot designs with control satisfy all generally accepted methodological requirements, with special reference to the problems of randomisation. Moreover, tools are described which allow checking of the general balance or efficiency of the design, as well as performance of experiments with inference.     

Loss of efficiency in spoilt experiments

For a wide class of experimental designs, the loss of efficiency that results from missing data is shown to be an approximately linear function of the number of missing data.     

Smoothing fertility trends in agricultural field experiments

Fertility trend within blocks and local variations are the major obstacles to estimate cultivar contrasts in agricultural field trials. This paper examines methods of smoothing fertility trends in field trials using the P-spline. We begin by smoothing trend within block and for each block, and proceeds to demonstrate how it can be extended to smooth trends in trials with two-dimensional setting. We propose simultaneous modelling of trends and local variation. We use Papadakis [J.S. Papadakis, Comparison de differentes methds d'expermentation phytotechnique, Rev. Argen. Agronom. 7 (1940), pp. 297–362.] and kriged covariate to model local variation. We emphasize on the benefit of using P-spline to compromise between parametric and non-parametric approaches. Data sets from wheat and barley trials, designed as randomized complete block design and row-column, are analyzed. We set out a simple strategy of choosing between additive model and two-dimensional setting. We explore different estimation methods and offer some generalizations. The results show importance of the P-spline in modelling trend and the need to choose between additive and two-dimensional settings.     

Post-hoc selection of covariates in randomized experiments

Monte Carlo methods are used to compere a number of adaptive strategies for deciding which of several covariates to incorporate into the analysis of a randomized experiment.Sixteen selection strategies in three categories are considered: 1)select covariates correlated with the response, 2)select covariates with means differing across groups, and 3)select covariates with means differing across groups that are also correlated with the response. The criteria examined are the type I error rate of the test for equality of adjusted group means and the variance of the estimated treatment effect. These strategies can result in either inflated or deflated type I errors, depending on the method and the population parameters. The adaptive methods in the first category some times yieldpoint estimates of the treatment effect more precise than estimators derive dusing either all or none of the covariates.     

Rotation designs for experiments in high-bias situations

Many experiments in the physical and engineering sciences study complex processes in which bias due to model inadequacy dominates random error. A noteworthy example of this situation is the use of computer experiments, in which scientists simulate the phenomenon being studied by a computer code. Computer experiments are deterministic: replicate observations from running the code with the same inputs will be identical. Such high-bias settings demand different techniques for design and prediction. This paper will focus on the experimental design problem introducing a new class of designs called rotation designs. Rotation designs are found by taking an orthogonal starting design D and rotating it to obtain a new design matrix D_R=DR, where R is any orthonormal matrix. The new design is still orthogonal for a first-order model. In this paper, we study some of the properties of rotation designs and we present a method to generate rotation designs that have some appealing symmetry properties.     

Embedded experiments in repeated and overlapping surveys

Summary.  Statistical agencies make changes to the data collection methodology of their surveys to improve the quality of the data collected or to improve the efficiency with which they are collected. For reasons of cost it may not be possible to estimate the effect of such a change on survey estimates or response rates reliably, without conducting an experiment that is embedded in the survey which involves enumerating some respondents by using the new method and some under the existing method. Embedded experiments are often designed for repeated and overlapping surveys; however, previous methods use sample data from only one occasion. The paper focuses on estimating the effect of a methodological change on estimates in the case of repeated surveys with overlapping samples from several occasions. Efficient design of an embedded experiment that covers more than one time point is also mentioned. All inference is unbiased over an assumed measurement model, the experimental design and the complex sample design. Other benefits of the approach proposed include the following: it exploits the correlation between the samples on each occasion to improve estimates of treatment effects; treatment effects are allowed to vary over time; it is robust against incorrectly rejecting the null hypothesis of no treatment effect; it allows a wide set of alternative experimental designs. This paper applies the methodology proposed to the Australian Labour Force Survey to measure the effect of replacing pen-and-paper interviewing with computer-assisted interviewing. This application considered alternative experimental designs in terms of their statistical efficiency and their risks to maintaining a consistent series. The approach proposed is significantly more efficient than using only 1 month of sample data in estimation.     

Some extremal problems in designing discriminating experiments

This paper is devoted to some properties of local T-optimaj. designs fox discriminating between two rival regression models. It is demonstrated that the problem of searching for an optimal design is closely connected with the problem of searching for a Tchebycheff extremal basis. The question raised concerns the number of supporting points in an optimal design.     

The problem of confounding in two-factor experiments

The problem of confounding in an axb experiment is studied without indexing the set of levels of each factor a priori by an algebraic object. General arithmetic restrictions on a and b are derived, leading to a'geometric reformulation of the problem when a or b is prime. This reformulation reduces to the problem of the existence of a generalized Hadamard matrix of specified order.     

The problem of confounding in two-factor experiments

The problem of confounding in an axb experinent is studied without indexing the set of levels of each factor a prior by an algebraic object. General arithmetic restrictions on a and b are derived, leading to a geometric reformulation of the problem when a or b is prime. This reformulation reduces to the problem of the existence of a generalized Hadamard matrix of specified order.     

Minimally changed run sequences in factorial experiments

Randomization of run sequences in factorial experiments may result in large number of changes in factor levels which will make the experimentation expensive, time-consuming and difficult. Experiments in which it is difficult to change the levels of factor(s) use of minimally changed run sequences may often be preferable to a random run sequence. In the present paper, we have developed method for obtaining minimally changed run sequences for factorial experiments. The general expression of factor-wise number of level changes for the developed minimally changed run sequences has also been obtained. A relationship has been established between the time count effect of a lower order factorial with minimally changed run sequences and that of a higher order factorial with minimally changed run sequences obtained through the lower order minimally changed run sequences. For providing a readymade solution to the end users, a SAS macro has also been developed for generating these minimally changed run sequences along with its parameters.     

Confounding in mixed factorial experiments through isomorphisms

The derivation of a simpie mexhoa for confounding in mixed factorial experiments from an isomorphism of finite abelian groups is presented. The theoretical bases of confounding procedures that use modular arithmetic for such experiments are compared.     

The random fatigue-limit model in multi-factor experiments

The Random Fatigue-Limit (RFL) model in Pascual and Meeker (1999a) was motivated by the need to describe fatigue life of certain materials. The RFL model describes the relationship between lifetime (measured in cycles) and a single factor, often the applied stress on the material. It has been found to be particularly useful for modeling high-cycle fatigue (HCF), that is, lifetimes that exceed 10 million cycles. Outputs from this model can be used as input for system models for lifetimes of jet engines for design purposes. Understanding how well parts hold up as a function of stress and other environmental variables would be valuable to engineers designing new and better engines. In this article, we show how the RFL model can be extended from single factor (single stress) to multi-factor situations. We fit the proposed model extensions to available data and describe methods to assess the adequacy of the fits.     

Factorial experiments in the analysis of assembly systems

Assembly systems are a key tool for mass production and are increasingly being implemented in the manufacturing industry. Since the performance of such systems depends on the levels of many design variables, they are not well understood. In this paper, the performance of free transfer automatic assembly systems with closed inspection and repair loops is studied via factorial experiments of a simulated system. Five factors were identified that affect the throughput of the system: buffer size, number of pallets in the system, number of repair stations, repair time of jammed assembly machines, and subcomponent defect rate. Initially, two levels of each factor were considered, so that a full 2 5 factorial design of the experiment was used to study the system. Next, to develop a deeper understanding of the linear or non-linear effect of each factor, additional levels were investigated. Finally, a predictive model is proposed. Engineers and system designers can use this predictive model to estimate the performance of the system, given a combination of levels of each of the five factors that we studied.     

Subset selection for normal means in multi-factor experiments

The procedure of Gupta [1956], [1965] for selecting a random sized subset of k ≧ 2 normal populations which contains the population with the largest population mean when the populations have a common variance is generalized to multi-factor experiments. Two-factor experiments with equal replication on each factor-level combination are discussed in detail. The cases of zero and non-zero interactions between factor levels are considered. For the two-factor, zero interaction case with a common number of observations at each factor-level combination, a table of constants necessary to implement the procedure is provided for experiments having selected levels per factor; the constants are equi-coordinate upper percentage points of a multivariate Student t distribution.