Testing for lack of fit in blocked and split-plot response surface designs

Textbooks on response surface methodology emphasize the importance of lack-of-fit tests when fitting response surface models, and stress that, to be able to test for lack of fit, designed experiments should have replication and allow for pure-error estimation. In this paper, we show how to obtain pure-error estimates and how to carry out a lack-of-fit test when the experiment is not completely randomized, but a blocked experiment, a split-plot experiment, or any other multi-stratum experiment. Our approach to calculating pure-error estimates is based on residual maximum likelihood (REML) estimation of the variance components in a full treatment model. It generalizes the one suggested by Vining et al. (2005) in the sense that it works for a broader set of designs and for replicates other than center point replicates. Our lack-of-fit test also generalizes the test proposed by Khuri (1992) for data from blocked experiments because it exploits replicates other than center point replicates and works for split-plot and other multi-stratum designs as well. We provide analytical expressions for the test statistic and the corresponding degrees of freedom, and demonstrate how to perform the lack-of-fit test in the SAS procedure MIXED. We re-analyze several published data sets and discover a few instances in which the usual response surface model exhibits significant lack of fit

BLOCKING FACTORIAL DESIGNS IN GREENHOUSE EXPERIMENTS

Experiments in greenhouses usually have to be conducted with very limited resources. This makes it particularly important to control the between plot variation by appropriate use of blocking. Many greenhouse experiments are naturally laid out in a pattern that makes a class of designs known as semi-Latin squares useful. Their properties have been studied recently by a number of authors and this work is reviewed. Often, the experimental treatments will have a factorial structure. An example of a 23 structure is used to show how factorial treatments can be assigned to treatment labels to ensure that the appropriate information is obtained from the experiment

Factorial and response surface designs robust to missing observations

Made available in DSpace on 2018-11-26T17:35:05Z (GMT). No. of bitstreams: 0 Previous issue date: 2017-09-01Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Compound optimum design criteria which allow pure error degrees of freedom may produce designs that break down when even a single run is missing, if the number of experimental units is small. The inclusion, in the compound criteria, of a measure of leverage uniformity is proposed in order to produce designs that are more robust to missing observations. By appropriately choosing the weights of each part of the criterion, robust designs are obtained that are also highly efficient in terms of other properties. Applications to various experimental setups show the advantages of the new methods. (C) 2016 Elsevier B.V. All rights reserved.USP UFSCar, Programa Interinst Posgrad Estat, Sao Carlos, SP, BrazilKings Coll London, Dept Math, London, EnglandUniv Estadual Paulista, Dept Bioestat, IB, Botucatu, SP, BrazilUniv Estadual Paulista, Dept Bioestat, IB, Botucatu, SP, BrazilFAPESP: 2014/01818-

Professor Gopal Kanji\u27s Retirement as Editor of Journal of Applied Statistics

(First paragraph) This. issue of Journal of Applied Statistics marks the first in its history which does not fall under the editorship of its founder Professor Gopal Kanji. Following his retirement from the role we would like to use this editorial to outline the history and development of the Journal and pay tribute to the many achievements of Gopal’s career