THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Response surface methodology (RSM) as a tool for optimization in analytical chemistry

Summary. A general class of statistical models for a univariate response variable is presented which we call the generalized additive model for location, scale and shape (GAMLSS). The model assumes independent observations of the response variable y given the parameters, the explanatory variables and the values of the random effects. The distribution for the response variable in the GAMLSS can be selected from a very general family of distributions including highly skew or kurtotic continuous and discrete distributions. The systematic part of the model is expanded to allow modelling not only of the mean (or location) but also of the other parameters of the distribution of y, as parametric and/or additive nonparametric (smooth) functions of explanatory variables and/or random-effects terms. Maximum (penalized) likelihood estimation is used to fit the (non)parametric models. A Newton–Raphson or Fisher scoring algorithm is used to maximize the (penalized) likelihood. The additive terms in the model are fitted by using a backfitting algorithm. Censored data are easily incorporated into the framework. Five data sets from different fields of application are analysed to emphasize the generality of the GAMLSS class of models.

https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.1467-9876.2005.00510.x

Generalized additive models for location, scale and shape

http://irep.iium.edu.my/28632/4/Santanu_J_Food_Eng%2D2013.pdf

Techniques for extraction of bioactive compounds from plant materials: A review

Generalized Linear Models (2nd ed.)

In designed experiments and in particular longitudinal studies, the aim may be to assess the effect of a quantitative variable such as time on treatment effects. Modelling treatment effects can be complex in the presence of other sources of variation. Three examples are presented to illustrate an approach to analysis in such cases. The first example is a longitudinal experiment on the growth of cows under a factorial treatment structure where serial correlation and variance heterogeneity complicate the analysis. The second example involves the calibration of optical density and the concentration of a protein DNase in the presence of sampling variation and variance heterogeneity. The final example is a multienvironment agricultural field experiment in which a yield-seeding rate relationship is required for several varieties of lupins. Spatial variation within environments, heterogeneity between environments and variation between varieties all need to be incorporated in the analysis. In this paper, the cubic smoothing spline is used in conjunction with fixed and random effects, random coefficients and variance modelling to provide simultaneous modelling of trends and covariance structure. The key result that allows coherent and flexible empirical model building in complex situations is the linear mixed model representation of the cubic smoothing spline. An extension is proposed in which trend is partitioned into smooth and non-smooth components. Estimation and inference, the analysis of the three examples and a discussion of extensions and unresolved issues are also presented.

The analysis of designed experiments and longitudinal data by using smoothing splines. Discussion. Authors' reply

http://soiaefrutta.com/wp-content/uploads/2013/06/A.3.2-Enzyme-extraction-soybean.pdf

Combined effect of operational variables and enzyme activity on aqueous enzymatic extraction of oil and protein from soybean.

Many processes in the biological industries are studied using response surface methodology. The use of biological materials, however, means that run-to-run variation is typically much greater than that in many experiments in mechanical or chemical engineering and so the designs used require greater replication. The data analysis which is performed may involve some variable selection, as well as fitting polynomial response surface models. This implies that designs should allow the parameters of the model to be estimated nearly orthogonally. A class of three-level response surface designs is introduced which allows all except the quadratic parameters to be estimated orthogonally, as well as having a number of other useful properties. These subset designs are obtained by using two-level factorial designs in subsets of the factors, with the other factors being held at their middle level. This allows their properties to be easily explored. Replacing some of the two-level designs with fractional replicates broadens the class of useful designs, especially with five or more factors, and sometimes incomplete subsets can be used. It is very simple to include a few two- and four-level factors in these designs by excluding subsets with these factors at the middle level. Subset designs can be easily modified to include factors with five or more levels by allowing a different pair of levels to be used in different subsets.

Response Surface Designs for Experiments in Bioprocessing

When selecting variables in multiple-regression studies, the model with the lowest value of Mallows's C p -statistic is often chosen. It is shown here that when the estimate of σ 2 comes from the full model an adjusted C p , V p , has the property that E(C p ) = p. It is suggested that a procedure be adopted which involves testing whether the model with minimum C p is really better than a simpler model. Tables approximating the null distribution of the test statistics are given.

The Interpretation of Mallows's CP-Statistic

There has been much recent interest in supersaturated designs and their application in factor screening experiments. Supersaturated designs have mainly been constructed by using the E(s 2 )-optimality criterion originally proposed by Booth and Cox in 1962. However, until now E(s 2 )-optimal designs have only been established with certainty for n experimental runs when the number of factors m is a multiple of n - 1, and in adjacent cases where m = q(n - 1) + r (|r| ≤ 2, q an integer). A method of constructing E(s 2 )-optimal designs is presented which allows a reasonably complete solution to be found for various numbers of runs n including n = 8, 12, 16, 20, 24, 32, 40, 48, 64.

Steven G. Gilmour

Papers

The analysis of designed experiments and longitudinal data by using smoothing splines. Discussion. Authors' reply

Combined effect of operational variables and enzyme activity on aqueous enzymatic extraction of oil and protein from soybean.

Response Surface Designs for Experiments in Bioprocessing

The Interpretation of Mallows's CP-Statistic

A general method of constructing E(s2)-optimal supersaturated designs