Title 



Optimum design of experiments for statistical inference : discussion
 
Author 



 
Abstract 



One attractive feature of optimum design criteria, such as D and Aoptimality, is that they are directly related to statistically interpretable properties of the designs that are obtained, such as minimizing the volume of a joint confidence region for the parameters. However, the assumed relationships with inferential procedures are valid only if the variance of experimental units is assumed to be known. If the variance is estimated, then the properties of the inferences depend also on the number of degrees of freedom that are available for estimating the error variance. Modified optimality criteria are defined, which correctly reflect the utility of designs with respect to some common types of inference. For fractional factorial and response surface experiments, the designs that are obtained are quite different from those which are optimal under the standard criteria, with many more replicate points required to estimate error.The optimality of these designs assumes that inference is the only purpose of running the experiment, but in practice interpretation of the point estimates of parameters and checking for lack of fit of the treatment model assumed are also usually important.Thus, a compromise between the new criteria and others is likely to be more relevant to many practical situations. Compound criteria are developed, which take account of multiple objectives, and are applied to fractional factorial and response surface experiments. The resulting designs are more similar to standard designs but still have sufficient residual degrees of freedom to allow effective inferences to be carried out. The new procedures developed are applied to three experiments from the food industry to see how the designs used could have been improved and to several illustrative examples. The design optimization is implemented through a simple exchange algorithm.   
Language 



English
 
Source (journal) 



Journal of the Royal Statistical Society: series C: applied statistics.  London  
Publication 



London : 2012
 
ISSN 



00359254
 
Volume/pages 



61:3(2012), p. 369401
 
ISI 



000302866200007
 
Full text (Publisher's DOI) 


  
