Statistical factorial experimental design

Key words Toxicity testing, pre-clinical development, inbred strain, drug development, factorial experimental designs, statistics, signal/noise ratio. 

Cropley made general recommendations to develop kinetic models for compUcated rate expressions. His approach includes first formulating a hyperbolic non-linear model in dimensionless form by linear statistical methods. This way, essential terms are identified and others are rejected, to reduce the number of unknown parameters. Only toward the end when model is reduced to the essential parts is non-linear estimation of parameters involved. His ten steps are summarized below. Their basis is a set of rate data measured in a recycle reactor using a sixteen experiment fractional factorial experimental design at two levels in five variables, with additional three repeated centerpoints. To these are added two outlier... 

A two levels of full factorial experimental design with three independent variables were generated with one center point, which was repeated[3]. In this design, F/P molar ratio, Oh/P wt%, and reaction temperature were defined as independent variables, all receiving two values, a high and a low value. A cube like model was formed, with eight comers. One center point (repeated twice) was added to improve accuracy of the design. Every analysis results were treated as a dependent result in the statistical study. 

Evaluation of Bonded-Phase Extraction Techniques Using a Statistical Factorial Experimental Design... 

A factorial experimental design formulations x packaging materials x storage temperature x evaluation times, with two repetitions were used. The physical, chemical, physicochemical and sensorial alterations were evaluated and their means compared by Tukey s test at the 5% level of probability or by statistical models (Cochram Cox, 1992). 

Other experimental designs have been developed and involve more than two levels, and also involve the use of replicates used to evaluate the statistical error. Fractional factorial experimental designs use part of the full factorial experimental design and cut down the number of trials needed. 

C. Daniel, App/ications of Statistics to lndustria/Experimentation, ]oE Wiley Sons, Inc., New York, 1976. This book is based on the personal experiences and insights of the author, an eminent practitioner of industrial appHcations of experimental design. It provides extensive discussions and concepts, especially in the areas of factorial and fractional factorial designs. "The book should be of use to experimenters who have some knowledge of elementary statistics and to statisticians who want simple explanations, detailed examples, and a documentation of the variety of outcomes that may be encountered." Some of the unusual features are chapters on "Sequences of fractional repHcates" and "Trend-robust plans," and sections entided, "What is the answer (what is the question )," and "Conclusions and apologies."... 

Any experimental design that is intended to determine the effect of a parameter on a response must be able to differentiate a real effect from normal experimental error. One usual means of doing this determination is to run replicate experiments. The variations observed between the replicates can then be used to estimate the standard deviation of a single observation and hence the standard deviation of the effects. However, in the absence of replicates, other methods are available for ascertaining, at least in a qualitative way, whether an observed effect may be statistically significant. One very useful technique used with the data presented here involves the analysis of the factorial by using half-normal probability paper (19). 

Although factorial designs are very useful for studying multiple variables at various levels, typically they will not be applicable to cosolvent solubility studies because of the constraint that all of the components must add to 100%. Forthis reason, mixtures of experimental designs are typically used. The statistical theory behind mixture designs has been extensively published [81-85], There... 

A complete design of experimental research, which includes all eight design points, is one of the best-known statistical experimental designs, the so-called full factorial design. 

The electrochemically available concentrations of Cd, Cu, and Zn, as a measure of the free ions, were analyzed for their dependence on pH and on different concentrations of calcium and fulvic acid (fa) by differential pulse anodic stripping voltammetry. A statistical experimental design in the form of a full 23-factorial plan was used to minimize... 

The experimental design was a 2x2x3 factorial with 4 Replicates plus two extra replicates per sample. Except for the four replicates, run In adjacent pairs, the order of all the runs was randomized. This resulted In 51 total runs for analysis In the statistical design. 

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