Simple experimental design

A simple example, focusing on the analytical procedure, will illustrate the type of experimental design used to investigate three key factors in an HPLC method. Detailed discussion of experimental designs for robustness testing can be found in Morgan and Hendriks et Riley and Rosanske provide an 

Consider an HPLC method for the separation of 11 priority pollutant phenols using an isocratic system. The aqueous mobile phase contains acetic acid, methanol and citric acid. From preliminary studies, it was established that the mobile phase composition was critical to ensure maximum resolution and to minimise tailing. The overall response factor, CRF, was measured by summing the individual resolutions between pairs of peaks. Hence, the CRF will increase as analytical performance improves. 

The data for this example are taken from ref. 26 in the bibliography. Many experimental designs are available but a simple full factorial is taken by way of example. A full factorial design is where all combinations of the factors are experimentally explored. This is usually limited from practical consideration to low values. To simplify the matter further no replication was used. 

The design chosen is a full factorial 2 with two levels of each of the three factors, acetic acid concentration, methanol concentration and citric acid concentration. The low ( —) and high ( + ) levels of each are shown in Table I. 

These extreme levels were established during the preliminary method development work. 

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Methane emission from ruminants can be estimated by using the ERUCT technique (Emissions from Ruminants Using a Calibrated Tracer). The tracer can either be isotopic or nonisotopic. Isotopic tracer techniques generally require simple experimental designs and relatively straightforward calculations [31]. Isotopic methods involve the use of (3H-)CH4 or (14C-)CH4 and ruminally cannulated animals. 

Figure 34-2 Simple experimental design for Youden/Steiner comparison of two Methods (data shown in Table 34-2).

Where possible, stick to simple experimental designs, where the results can be expressed as a 2 x 2 contingency table. The interpretation of the outcome will then be unambiguous. 

Statistics users (and those who teach statistics users) should stop worrying about calculation methods and concentrate on the issues that surround statistical procedures. There is no need for anybody to shy away from statistical testing for fear of hard sums. For simple experimental designs (as advocated later in this chapter), numbercrunching is no longer an issue - widely available statistical packages will look after that. 

Define critical process variables and response parameters using simple experimental designs. 

Finally, the QCM can not only be used in a sensory mode but also as an actuator. It has been recently shown by Dultsev and coworkers [57] that virus particles deposited on the resonator surface may be displaced by increasing the shear amplitude of the resonator. Thus, it seems plausible that the resistance of cell-substrate interactions to lateral shear forces may be inferred from QCM measurements when the shear amplitude is increased to invasive magnitudes. The ease of the measurement, which can be automated and multiplexed, the rather simple experimental design, as well as the unique experimental access to the interface between living cells and technical substrates is very likely to create growing interest within the cell culture community for these new experimental options. 

Potential factors that affect a given objective function are best selected by the domain expert in a particular analytical field. The test for significance of the factors influence should be performed on the basis of a simple experimental design, a screening design, by means of statistical tests. Factors should not be kept or eliminated solely for subjective reasons. 

The experimental design for respiratory exposure necessarily depends on several assumptions and disparate pieces of available data. The excretion kinetics of the pesticide employed must be known. If the total dose is excreted by small animals in 24-48 hr., the same may also be true of humans, and a simple experimental design may suffice. If the dose Is excreted over a period of a week, a simple design correlating dose with the Immediate effect on urine will not correctly assess respiratory exposure. The difficulty with longer sampling periods, occasioned by longer excretion kinetics, derives from the variation normally observed in the urinary exposure estimation for field experiments. It Is not... 

The development of Remote Field Eddy Current probes requires experience and expensive experiments. The numerical simulation of electromagnetic fields can be used not only for a better understanding of the Remote Field effect but also for the probe lay out. Geometrical parameters of the prohe can be derived from calculation results as well as inspection parameters. An important requirement for a realistic prediction of the probe performance is the consideration of material properties of the tube for which the probe is designed. The experimental determination of magnetization curves is necessary and can be satisfactory done with a simple experimental setup. 

D. R. Cox, P/anning of Experiments,]ohxi Wiley Sons, Inc., New York, 1958. This book provides a simple survey of the principles of experimental design and of some of the most usehil experimental schemes. It tries "as far as possible, to avoid statistical and mathematical technicalities and to concentrate on a treatment that will be intuitively acceptable to the experimental worker, for whom the book is primarily intended." As a result, the book emphasizes basic concepts rather than calculations or technical details. Chapters are devoted to such topics as "Some key assumptions," "Randomization," and "Choice of units, treatments, and observations."... 

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."... 

When a reaction has many participants, which may be the case even of apparently simple processes like pyrolysis of ethane or synthesis of methanol, a factorial or other experimental design can be made and the data subjected to a re.spon.se. suiface analysis (Davies, Design and Analysis of Industrial Experiments, Oliver Boyd, 1954). A quadratic of this type for the variables X, Xo, and X3 is... 

The Fourier transform of a pure Lorentzian line shape, such as the function equation (4-60b), is a simple exponential function of time, the rate constant being l/Tj. This is the basis of relaxation time measurements by pulse NMR. There is one more critical piece of information, which is that in the NMR spectrometer only magnetization in the xy plane is detected. Experimental design for both Ti and T2 measurements must accommodate to this requirement. 

Method development is not always, therefore, a simple task since there are a substantial number of parameters that may influence the final results that are obtained. As a consequence of the number of parameters that may be involved, formal experimental design procedures are increasingly being utilized, indeed are essential, to determine the experimental conditions that give optimum analytical performance. 

When an analytical method is being developed, the ultimate requirement is to be able to determine the analyte(s) of interest with adequate accuracy and precision at appropriate levels. There are many examples in the literature of methodology that allows this to be achieved being developed without the need to use complex experimental design simply by varying individual factors that are thought to affect the experimental outcome until the best performance has been obtained. This simple approach assumes that the optimum value of any factor remains the same however other factors are varied, i.e. there is no interaction between factors, but the analyst must be aware that this fundamental assumption is not always valid. 

As an analytical method becomes more complex, the number of factors is likely to increase and the likelihood is that the simple approach to experimental design described above will not be successful. In particular, the possibility of interaction between factors that will have an effect on the experimental outcome must be considered and factorial design [2] allows such interactions to be probed. 

From the foregoing discussion it may seem that a complex experimental design must be carried out before any analysis is attempted. While it is certainly a necessity/advantage that the analyst has some understanding of the effect that a parameter is likely to have on the experimental outcome, many analyses, particularly those involving mixtures containing relatively few components at relatively high concentrations, will be accomplished successfully on the basis of a simple study of selected experimental variables. 

Method development is important. LC-MS performance, probably more than any other technique involving organic mass spectrometry, is dependent upon a range of experimental parameters, the relationship between which is often complex. While it is possible (but not always so) that conditions may be chosen fairly readily to allow the analysis of simple mixtures to be carried out successfully, the widely variable ionization efficiency of compounds with differing structures often makes obtaining optimum performance for the study of all components of a complex mixture difficult. In such cases, the use of experimental design should be seriously considered. 

This paper explores how models may be developed to account for the relationship between the stable isotope composition of a body tissue of an organism and its diet. The main approach taken is to express this relationship as an explicit equation, or a DIFF , and then to show how the values of such a DIFF can be evaluated from published experimental data. These values can be expected to have a much wider meaning than a simple encapsulation of a particular experimental design. As a main example, we show how the values may be used to constract a metabolic model in which the synthesis of non-essential amino acid for collagen construction can be treated. A second example is to show how the evaluation, in terms of diet, of the spacing between collagen and carbonate 6 C may be put on a rigorous basis. 

As an example for precise parameter estimation of dynamic systems we consider the simple consecutive chemical reactions in a batch reactor used by Hosten and Emig (1975) and Kalogerakis and Luus (1984) for the evaluation of sequential experimental design procedures of dynamic systems. The reactions are... 

With the conventional experimental design, information about spatial variations of the permeability is not available. With MRI, we can obtain information within the sample, so that we may determine the spatial distribution of the permeability. Clearly, the computational procedure required to estimate the entire distribution will not be as simple as that reflected by Eq. 4.1.7. We will use the principles of system and parameter identification, discussed in the following section, to determine the various macroscopic properties from experiments. 

This technique is readily adaptable for use with the generalized additive physical approach discussed in Section 3.3.3.2. It is applicable to systems that give apparent first-order rate constants. These include not only simple first-order irreversible reactions but also irreversible first-order reactions in parallel and reversible reactions that are first-order in both the forward and reverse directions. The technique provides an example of the advantages that can be obtained by careful planning of kinetics experiments instead of allowing the experimental design to be dictated entirely by laboratory convention and experimental convenience. 

A simple statistical test for the presence of systematic errors can be computed using data collected as in the experimental design shown in Figure 34-2. (This method is demonstrated in the Measuring Precision without Duplicates sections of the MathCad Worksheets Collabor GM and Collabor TV found in Chapter 39.) The results of this test are shown in Tables 34-9 and 34-10. A systematic error is indicated by the test using... 

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