Experimental three-level

The three levels of water addition used in variation 8, i.e. 800 mL, 900 mL and 1 L, should be tried. As a result of this experiment it should be apparent which is the optimum level for this batch of flour. Experimenters are warned that wholemeal flour develops more slowly and will never rise as much as white flour. 

Fig. 1.15. Three-level calculations with full ID vibrational motion of the excitation of Hj as a function of wavelength. Also included are two independent sets of experimental data for wavelength scans from 490 to 520 nm...

The absorption spectra of Aspt, Ace-K, Caf and Na-Benz were recorded from 190 to 300 nm. The calibration set was generated by a three-level full factorial design (4).The absorbance valnes were recorded eveiy 5 nm. The calibration samples were measured in random order, so that experimental errors due to drift were not introduced. 

For theexample discussed here, the calibration sets for classes A and B are selected gs hically, and for class C are selected as the extremes and centers of each ofdie three levels in the experimental design. The selection results in 15 samples in each of the calibration sets and 12 in each of the validation sets. A score pS>t of all samples in class A is shown in Figure 4.69 with the calibration set samples indicated by X and the validation samples indicated by O. Similarly, SCO plots of clas.es B and C with calibration and validation samples identifiedsre shown in Figures 4.70 and 4.71, respectively. 

FIGURE 5.90. Concentration of component B versus concentration of component A in a three-level, full-factorial experimental design. 

Let us now consider an experimental arrangement where the subplot levels are assigned randomly in strips across each block of whole-plot levels. Such arrangements are frequently called strip-block designs. As an illustration of this arrangement, suppose that we have a whole-plot variable with three levels, a, a, and a, a subplot variable with two levels, b and... 

These limitations can be seen by comparing the experimental procedure for a three factor, three level star design, shown in Table 5.10, with the experimental procedure for a reflected saturated fractional design, which also tests three factors at three levels, shown in Table 5.11. 

The experimental scheme for a three level reflected saturated fractional design for seven factors is shown in Table 5.15 ( note that one factor was retained as a dummy factor to be used as an additional error check). The experimental order of the scheme was sorted on acid type as this required long equilibration times, this ordering loses some of the features of the initial design but is a compromise that can be justified on the fact that... 

Or, looking at the experimental design, we see three levels of xv This may lead to the question Is there curvature in the relationship of y with x Then an equation of one of the following forms might be helpful ... 

The most complete investigation of model response would establish a network of experimental cases throughout the area of interest. The more complete the coverage, obviously the more cases that will be required. For a system involving many variables the number of cases increases rapidly for example, in a system of six controllable variables an investigation at only two levels of each variable would require 26 = 64 cases. Examining three levels of each of the variables would require 36 = 729 cases. 

To provide a specific example of die method, near UV experiments have led to assignments of the vertical and adiabatic excitation energies for die I B PAg transition in A-diazene (HN=NH), where the Bg state is open-shell. Table 14.4 compares sum-method predictions at the UHF and BLYP levels of theory to diese experimental values, and also to published results at the MRCI level of theory. For diis system, die HF results are systematically too high, and the DFT too low (cf. the sum method prediction for A2 phenylnitrene in Table 14.1), but are competitive with the much more expensive MRCI results. Note that all three levels do quite well at predicting the difference in verdcal and adiabatic excitation energies. 

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. 

To determine Sb in marine sediments by ETAAS, a direct method was developed based on quantitating the analyte in the liquid phase of the slurries (prepared directly in autosampler cups). The variables influencing the extraction of Sb into the liquid phase and the experimental setup were set after a literature search and a subsequent multivariate optimisation procedure. After the optimisation, a study was carried out to assess robustness. Six variables were considered at three levels each (see Table 2.13). In addition, two noise factors were set after observing that two ions, which are currently present into marine sediments, might interfere in the quantitations. In order to evaluate robustness, a certified reference material was used throughout, BCR-CRM 277 Estuarine Sediment (guide value for Sb 3.5 0.4pgg ). Table 2.13 depicts the experimental setup. 

The design factors require 12 df so an Lig orthogonal array (with 15df) was selected. Hence we can study a factor at two levels and seven factors at three levels each. The matrix is adapted to our needs by discarding column 1 (designed for a variable with two levels) and column 7 (not needed in this example). This yields 3 df to calculate the residuals. Hence the experimental matrix is as presented in Table 2.14. 

For the second retention surface, data were collected according to a three-level, two-factor (density and temperature) experimental design. Each factor was assigned three different values (0.2,0.3 and 0.4 g/mL 75,100 and 125°C), and experiments were conducted at the nine combinations. Data were fit to the model by multiple regression, and these retention surfaces were used to calculate the response surface. 

The results presented show that three levels have to be distinguished when investigating attrition processes. The first one is the stress mode as derived from the process function which is essential to know if the attrition process is to be simulated successfully in a simple experimental setup. The second point is the material reaction to this stress mode, i.e. the material function which varies depending on material properties like storage and loss modulus as measured by DMA. Finally, the microscopic attrition mechanisms (see [18] for impact and [19,20] for sliding friction) describing the formation of attrition on a microscopic scale constitute the bottom level. 

Certain circumstances may force us to follow the opposite direction and to burden ourselves with additional experimental expense. Models of higher order may be unavoidable if the response variable follows a nonlinear function of the primary variables, or factor variables. Then one can utilize designs which take into account more than two levels of each factor. As an example, in 3" designs one has n factors with three levels each. 

Existing definitions of various detection and quantitation limits can be confusing to a non-laboratory person. Despite misleading similarities of these definitions, there is a logic and order to the basic concepts that they express. Various detection limits that we commonly refer to in our daily work (the IDLs, MDLs, and PQLs) are discussed in this chapter in the increasing order of magnitude of their numeric values. Some of these detection limits are determined experimentally and depend on the matrix and the method of preparation and analysis, while others may be arbitrary values selected by the laboratory or the data user. The relationship between these three levels of detection is approximately 1 5 10. 

---