Correlated experimental designs

Figure 15.2 Factor combinations for the highly correlated experimental design of Equation 15.5.

Austel, V. (1995). Experimental Design in Synthesis Planning and Structure-Property Correlations. Experimental Design. In Chemometrics Methods in Molecular Design - Vol. 2 (van de Waterbeemd, H., ed.), VCH Publishers, New York (NY), pp. 49-62. 

Kelkar and McCarthy (1995) proposed another method to use the feedforward experiments to develop a kinetic model in a CSTR. An initial experimental design is augmented in a stepwise manner with additional experiments until a satisfactory model is developed. For augmenting data, experiments are selected in a way to increase the determinant of the correlation matrix. The method is demonstrated on kinetic model development for the aldol condensation of acetone over a mixed oxide catalyst. 

The existing series of substituent constants has been developed by analysis of experimental data. Separation of the various components has usually depended on correlation analysis designed to identify the contributions from various components of... 

Boundary layer similarity solution treatments have been used extensively to develop analytical models for CVD processes (2fl.). These have been useful In correlating experimental observations (e.g. fi.). However, because of the oversimplified fiow description they cannot be used to extrapolate to new process conditions or for reactor design. Moreover, they cannot predict transverse variations In film thickness which may occur even In the absence of secondary fiows because of the presence of side walls. Two-dimensional fully parabolized transport equations have been used to predict velocity, concentration and temperature profiles along the length of horizontal reactors for SI CVD (17,30- 32). Although these models are detailed, they can neither capture the effect of buoyancy driven secondary fiows or transverse thickness variations caused by the side walls. Thus, large scale simulation of 3D models are needed to obtain a realistic picture of horizontal reactor performance. 

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]). 

Because variables in models are often highly correlated, when experimental data are collected, the xrx matrix in Equation 2.9 can be badly conditioned (see Appendix A), and thus the estimates of the values of the coefficients in a model can have considerable associated uncertainty. The method of factorial experimental design forces the data to be orthogonal and avoids this problem. This method allows you to determine the relative importance of each input variable and thus to develop a parsimonious model, one that includes only the most important variables and effects. Factorial experiments also represent efficient experimentation. You systematically plan and conduct experiments in which all of the variables are changed simultaneously rather than one at a time, thus reducing the number of experiments needed. 

Correll MA, Broward-Partin SM, Hansen DK, Behlow HW, Lewis MM, Rose JQ, Thompson TN (2000) Achievement of higher throughput in the Caco-2 absorption screen using a simplified experimental design. AAPS PharmSci 2(4) abstract. 

Fig. 14.7 Correlation ofVolSurf descriptors with human serum albumin binding affinity. Two submodels indicate their predictive ability to external test sets. Ten compounds were removed by either experimental design on PCA scores (A) or literature proposals (B). Model A 0.558,...

From the technical viewpoint, the matrix inversion (C C) in Equation 12.36 can be very unstable if any two of the analyte concentrations in the calibration standards happen to be highly correlated to one another. This translates to the need for careful experimental design in the preparation of calibration standards for CLS modeling, which is particularly challenging because multiple constituents must be considered. In addi-... 

Both the time of analysis and experimental design may affect the results. An explanation for the increase in adenylates under the conditions of our experiment is still needed. Since both ATP alone and total adenylate concentrations have increased, it does not appear that a shift in phosphorylation can account for the increases. The decrease in photosynthesis and increase in adenylates occur during the same time period and both factors return to normal after 21 hr. From previous research we know that the photosynthetic levels of ozonated pinto bean foliage decrease immediately after ozone exposure even when symptoms do not develop ( ). This does not hold true for the adenylate or respiration responses. Therefore, it appears that the ozone-initiated increase in adenylates is not correlated directly to the photosynthetic response. The increase in respiration persists when adenylate content and photosynthetic rates have returned to normal. Impaired mitochondrial function appears to be a secondary response more closely related to symptom development. 

The steric parameter must be as nearly independent as possible of electrical and transport effects. It must of course be realized that a small subset of badly chosen groups will frequently show a statistically significant relationship between steric and electrical parameters or between steric and transport parameters. Often this can ge avoided by proper experimental design. In some cases the nature of the problem makes it impossible to achieve independence of steric parameters. Correlations of amino acid bioactivities which are restricted to the amino acids that are common constituents of protein are an example of a data set whose members cannot be conveniently varied. 

The Bonferoni method with OVAT rests on the assumption that the variables analysed are independent. This is, however, seldom true. In fact, the chance that variables are independent and uncorrelated is very small unless it is possible to have full control over the variables in an experiment. If this is the case, it is possible to choose an experimental design that makes the intervariable correlations zero vide infra). 

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