Factors main effects

These full factorial designs can give values for all main effect and all interaction effects between these three factors main effects and interactions are shown in Table 5.6. 

Goal Rank process factors (main effects)... 

Block 1 Perform a 2 fraction factorial design plus 2 center points. Estimate the factor main effects (Srst-order effects) and the overall curvature effect. 

Environmental Factor Main effect Direct consequence on polymer Biotic effects... 

The result of studies performed in the laboratory in the search for additivity rules from the subs ce k>rmula are shown below. This study was carried out using multiple linear r ression, the software being limited to the analysis of the main effects of fourteen factors, the study had to be subdivided into grou/x of compounds starting with hydrocarbons. 

In some cases interactions are improbable and information on them is not needed. Then reduced variants of three-way ANOVA can be applied by which the effects of the main factors can be estimated more reliable (see Dunn and Clark [1974] Graf et al. [1987] Sachs [1992]). Concentrating on the main effects, the design of the experiments can be aimed at a minimum number of observations. 

Because the experimental expenditure increases strongly with the increasing number of influence factors, fractional factorial design FFD (partial factorial design) is applied in such cases. It is not possible to evaluate all the interactions by FFDs but only the main effects. 

Because of the way the data was created, we can rely on the calibration statistics as an indicator of performance. There is no need to use a validation set of data here. Validation sets are required mainly to assess the effects of noise and intercorrelation. Our simulated data contains no noise. Furthermore, since we are using only one wavelength or one factor, intercorrelation effects are not operative, and can be ignored. Therefore the final test lies in the values obtained from the sets of calibration results, which are presented in Table 27-1. 

The factorial approach to the design of experiments allows all the tests involving several factors to be combined in the calculation of the main effects and their interactions. For a 23 design, there are 3 main effects, 3 two-factor interactions, and 1 three-factor interaction. Yates algorithm can be used to determine the main effects and their interactions (17). The data can also be represented as a multiple linear regression model... 

The photochemistry of conjugated polyenes has played a central role in the development of modern molecular photochemistry, due in no small part to its ultimate relevance to the electronic excited state properties of vitamins A and D and the visual pigments, as well as to pericyclic reaction theory. The field is enormous, tremendously diverse, and still very active from both experimental and theoretical perspectives. It is also remarkably complex, primarily because file absorption spectra and excited state behavior of polyene systems are strongly dependent on conformation about the formal single bonds in the polyene chain, which has the main effect of turning on or off various pericyclic reactions whose efficiencies are most strongly affected by conformational factors. 

Thus, since Sps will be relatively insensitive to the items inside the logarithmic term, the main effect of this correction is to increase the value of Sps or Jp by the factor [1 + (2/.i/Pp) ]. 

FIGURE 15 An example of a main effect plot.The average responses at low level and high level of the factors are plotted. 

FIGURE 15 Example of a main effect plot (for the critical resolution) clearly showing the extent of the effects relative to each other. Factor temperature appears to be the most important factor on the resolution. Reprinted with permission from reference 18. 

In references 82-86, the results were treated statistically. Main effects and standard errors were calculated. In references 83, 85, and 86 also a graphical interpretation by means of bar plots was performed. Both positive and negative effects were seen on these plots, but all effects between levels [—1,0] are negative, while all those between [0,4-1] are positive. Possibly, the length of the bars represents the absolute value of the factor effects, and all effects for the interval [—1,0] seem to be given a negative sign, while all those for [0,4-1] a positive. However, the above are assumptions since no details were provided. In references 83 and 86, critical effects are drawn on the bar plots. 

In the classical factorial design literature, a factor effect is defined as the difference in average response between the experiments carried out at the high level of the factor and the experiments carried out at the low level of the factor. Thus, in a 2 full factorial design, the main effect of A would be calculated as ... 

The first column of Table 14.3 gives the response notation (or, equivalently, the factor combination). The next eight columns list the eight factor effects of the model the three main effects (A, B, and C), the three two-factor interactions (AB, AC, and BC), the single three-factor interaction (ABC), and the single offset term (MEAN, analogous to PJ in the equivalent linear model). 

The classical main effects of factors B and C can also be calculated in this manner ... 

The economics of the situation are desirable for factors B and C - lighter pressure would produce less wear on the machine and maintenance costs would be less the lighter weight packaging material would presumably cost less. However, an analysis of the main effects of B and C is insufficient in this example the interaction effects must also be examined. The three-factor interaction ABC is small. The AB and AC interactions are small. But the BC interaction is very large, larger than the largest main effect. 

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