Experimental design accuracy

Bob is particularly concerned that, although analytical chemistry forms a major part of the UK chemical industry s efforts, it is still not considered by many to be a subject worthy of special consideration. Consequently, experimental design is often not employed when it should be and safeguards to ensure accuracy and precision of analytical measurements are often lacking. He would argue that although the terms accuracy and precision can be defined by rote, their meanings, when applied to analytical measurements, are not appreciated by many members of the scientific community. 

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. 

Experimental design A number of formal procedures whereby the effect of experimental variables on the outcome of an experiment may be assessed. These may be used to assess the optimum conditions for an experiment and to maximize the accuracy and precision obtained. 

Bzik, T. J., Henderson, P. B., and Hobbs, J. R, Increasing the Precision and Accuracy of Top-Loading Balances Application of Experimental Design, Anal. Chem. 70, 1998, 58-63. 

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. 

We present a general approach for estimating relative permeability and capillary pressure functions from displacement experiments. The accuracy with which these functions are estimated will depend on the information content of the measurements, and hence on the experimental design. We determine measures of the accuracy with which the functions are estimated, and use these measures to evaluate different experimental designs. In addition to data measured during conventional displacement experiments, we show that the use of multiple injection rates and saturation distributions measured with MRI can substantially increase the accuracy of estimates of multiphase flow functions. 

Displacement experiments can be relatively complex and time-consuming, so the experimental design can be a critical issue. Using suitable system and parameter identification methods, we obtain the best estimates of properties from the available data. It is most desirable to have some measures of the accuracy with which the properties are estimated. If that level of accuracy is less than desired, one can consider other ways of conducting the experiments so that additional information about the properties may be obtained. 

The analysis is based on a chosen set of properties. While the accuracy will depend on those particular properties, global features can often be readily identified. We demonstrate the assessment of experimental design in the next subsection. 

Our approach was demonstrated by determining multiphase flow functions from displacement experiments. Spatially resolved porosity and permeability distributions can be incorporated to mitigate errors encountered by assuming that the properties are uniform. We developed measures of the accuracy of the estimates and demonstrated improved experimental designs for obtaining more accurate estimates of the flow functions. One of the candidate experimental designs incorporated MRI measurements of saturation distributions conducted during the dynamic experiments. 

Several methods are available for measuring enteric CH4 production, and the selection of the most appropriate method is based on several factors such as cost, level of accuracy, and experimental design [29, 30]. 

The reliability of multispecies analysis has to be validated according to the usual criteria selectivity, accuracy (trueness) and precision, confidence and prediction intervals and, calculated from these, multivariate critical values and limits of detection. In multivariate calibration collinearities of variables caused by correlated concentrations in calibration samples should be avoided. Therefore, the composition of the calibration mixtures should not be varied randomly but by principles of experimental design (Deming and Morgan [1993] Morgan [1991]). 

Sections on matrix algebra, analytic geometry, experimental design, instrument and system calibration, noise, derivatives and their use in data analysis, linearity and nonlinearity are described. Collaborative laboratory studies, using ANOVA, testing for systematic error, ranking tests for collaborative studies, and efficient comparison of two analytical methods are included. Discussion on topics such as the limitations in analytical accuracy and brief introductions to the statistics of spectral searches and the chemometrics of imaging spectroscopy are included. 

We have presented a statistical experimental design and a protocol to use in evaluating laboratory data to determine whether the sampling and analytical method tested meets a defined accuracy criterion. The accuracy is defined relative to a single measurement from the test method rather than for a mean of several replicate test results. Accuracy here is the difference between the test result and the "true value, and thus, must combine the two sources of measurement error ... 

In order to overcome, or at least minimise, such drawbacks we can resort to the use of chemometric techniques (which will be presented in the following chapters of this book), such as multivariate experimental design and optimisation and multivariate regression methods, that offer great possibilities for simplifying the sometimes complex calibrations, enhancing the precision and accuracy of isotope ratio measurements and/or reducing problems due to spectral overlaps. 

Figure 18.2 diagrams the workflow of a typical BE-AES experiment. There are two major experimental steps (1) buffer equilibration and (2) ICP-AES concentration determination. Both sample preparation (i.e., buffer exchange) and sample concentration determination (i.e., AES) must be successfully completed in order to make meaningful measurements. To maximize the utility of BE-AES, experimental design must carefully balance practical issues such as the availability and behavior of the nucleic acid being studied with the desire to get high precision and accuracy in the final measurements. 

The thermal conductivity is a property of any given material, and its value must be determined experimentally. For solids, the effect of temperature on thermal conductivity is relatively small at normal temperatures. Because the conductivity varies approximately linearly with temperature, adequate design accuracy can be obtained by employing an average value of thermal conductivity based on the arithmetic-average temperature of the given material. Values of thermal conductivities for common materials at various temperatures are listed in the Appendix. 

Our concern with the treatment of experimental data does not end when we have obtained a numerical result for the quantity of interest. We must also answer the question How good is the numerical result Without an answer to this question, the numerical result may be next to nseless. The expression of how good the result may be is usually couched in terms of its accuracy, i.e., a statement of the degree of the uncertainty of the resnlt. A related question, often to be asked before the experiment is begun, is How good does the resnlt need to be The answer to this question may influence important decisions as to the experimental design, equipment, and degree of effort required to achieve the desired accuracy. 

These experimental designs are known as balanced incomplete blocks. They are balanced because each treatment occurs to exactly the same extent they are incomplete because no block contains the full number of treatments. They suffer from the restriction that balanced arrangements are not possible for all experimental set-ups. Broadly speaking, if we fix the number of treatments that we wish to compare, and if the number of experiments per batch (or block ) is also fixed, then the number of replication of each treatment is thereby determined. This is the principal disadvantage of these designs the number of replications they require may be greater than we think are necessary to attain sufficient accuracy. 

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