Statistical factorial experimental design techniques

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

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). 

Response surface methodology (RSM) is a method of optimization using statistical techniques based upon the special factorial designs of Box and Behenkini and Box and Wilson.I It is a scientific approach to determining optimum conditions which combines special experimental designs with Taylor first and second order equations. The RSM process determines the surface of the Taylor expansion curve which describes the response (yield, impurity level, etc.) The Taylor equation, which is the heart of the RSM method, has the form ... 

The philosophy of the factorial approach is attractive, so are there related techniques which are more appropriate to the special requirements of chemistry There is a number of other methods for experimental design but one that is becoming applied in several chemical applications is known as D-optimal design . The origin of the expression D-optimal is a bit of statistical jargon based on the determinant of the variance-covariance matrix. As will be seen in the next section on compound selection, a well-chosen set of experiments (or compounds) will have a wide spread in the... 

This model allows us to estimate a response inside the experimental domain defined by the levels of the factors and so we can search for a maximum, a minimum or a zone of interest of the response. There are two main disadvantages of the complete factorial designs. First, when many factors were defined or when each factor has many levels, a large number of experiments is required. Remember the expression number of experiments = replicates x Oevels) " (e.g. with 2 replicates, 3 levels for each factor and 3 factors we would need 2 x 3 = 54 experiments). The second disadvantage is the need to use ANOVA and the least-squares method to analyse the responses, two techniques involving no simple calculi. Of course, this is not a problem if proper statistical software is available, but it may be cumbersome otherwise. 

Optimization techniques may be classified as parametric statistical methods and nonparametric search methods. Parametric statistical methods, usually employed for optimization, are full factorial designs, half factorial designs, simplex designs, and Lagrangian multiple regression analysis [21]. Parametric methods are best suited for formula optimization in the early stages of product development. Constraint analysis, described previously, is used to simplify the testing protocol and the analysis of experimental results. 

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