Experimental design linear effects

This model is capable of estimating both linear and non-linear effects observed experimentally. Hence, it can also be used for optimization of the desired response with respect to the variables of the system. Two popular response surface designs are central composite designs and Box-Behnken designs. Box-Behnken designs were not employed in the experimental research described here and will therefore not be discussed further, but more information on Box-Behnken designs can be obtained from reference [15]. 

Designing a stability study is based on a factorial design of experiments where a systemic procedure is used to determine the effect on the response variable of various factors and factor combinations. A linear model is used to represent the relationship between the factors and factor combinations with the response variable. Once the experimental design is established, the assays are conducted and stability data are saved to finally estimate the shelf life period. 

In setting the number of levels to be studied of any one variable factor, the type of effects which it is likely to have on the functional properties to be studied is very important. If its effects are known to be linear and that factor is of secondary Importance to the researcher, then two levels (one at each end of some practical range of levels) may be sufficient. If, on the other hand, it is known that the effects of this factor are curvilinear and/or discontinuous at some point, then at least three levels should be included in the experimental design. If the Interaction of a factor with other factors is known to be significant, then this too could be sufficient reason to Include more than two levels of that factor in the design. 

From the technical viewpoint, the matrix inversion (ClC) 1 in Equation 8.27 can be very unstable if any two of the analyte concentrations in the calibration data are highly correlated with one another. This translates into 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 addition, the CLS model assumes perfect linearity and additivity of the spectral contributions from each of the analytes in the sample. In many practical cases in PAC, there can be significant non-linearity of analyzer responses and strong spectral interaction effects between analytes,... 

The variables in the experimental space are continuous. The relations between the settings of the experimental variables and the observed response can reasonably be assumed to be cause-effect relations. The appropriate method for establishing quantitative relation is to use multiple linear regression for fitting response surface models to observed data. For this purpose, an experimental design with good statistical properties is essential. 

In this section, three categories of experimental design are considered for method validation experiments. An important quality of the design to be used is balance. Balance occurs when the levels each factor (either a fixed effects factor or a random effects variance component) are assigned the same number of experimental trials. Lack of balance can lead to erroneous statistical estimates of accuracy, precision, and linearity. Balance of design is one of the most important considerations in setting up the experimental trials. From a heuristic view this makes sense, we want an equivalent amount of information from each level of the factors. 

In the experimental designs we saw in the preceding chapters, each factor was studied at only two levels. Because of this economy, we had to be content with a hmited form of the function describing the effects of the factors on the response. Consider, for example, the variation in reaction yield with temperature discussed in Chapter 3. The average yields observed with catalyst A are 59% at 40 °C, and 90% at 60 °C, as given in Table 3.1. We can see in Fig. 5.1a that these two pairs of values are compatible with an infinite number of functions. In Chapter 3, we fitted a model with a linear part and an interaction term to the response values, but we had no guarantee that this was the correct model. To clarify this situation, more information is needed. 

Since there is increasing recognition that hormonal effects are essentially of a vectorial rather than linear nature, it is essential that cells and tissues be analyzed for more than one hormone at a time. This will call for an increasing use of new experimental designs. Hormonal action takes place in a matrix and this needs to be recognized when measurements are being made and reported. 

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