Effective multiplication factor

One can also use the dummy factor effects in a similar way for the interpretation of Plackett-Burman designs. One then uses a formula analogous to equation (20). Instead of using the multiple-factor effects in the formula one uses the dummy factor effects ... 

The practice of estabHshing empirical equations has provided useflil information, but also exhibits some deficiencies. Eor example, a single spray parameter, such as may not be the only parameter that characterizes the performance of a spray system. The effect of cross-correlations or interactions between variables has received scant attention. Using the approach of varying one parameter at a time to develop correlations cannot completely reveal the tme physics of compHcated spray phenomena. Hence, methods employing the statistical design of experiments must be utilized to investigate multiple factors simultaneously. 

The number of active sites is a multiplicative factor in the rate of the main reaction. See for example Equations (10.11) and (10.16). Thus, the decline in reaction rate can be modeled using a time-dependent effectiveness. A reasonable functional form for the time-dependent effectiveness factor is... 

On the basis of hydrodynamic arguments first suggested by Brady, Johnson et al. [186] proposed that the hydrodynamic and steric effects that influence the diffusivity of a macromolecule in a fibrous medium can be separated into two multiplicative factors. The overall functional dependence is of the form... 

At first these effects of activators may appear complicated, requiring multiple factors to explain the total response, but reference to the kinetic model for channel gating (Figure 2) clarifies the complexity. Activators may produce spontaneous opening... 

Aluminium toxicity is a major stress factor in many acidic soils. At soil pH levels below 5.0, intense solubilization of mononuclear A1 species strongly limits root growth by multiple cytotoxic effects mainly on root meristems (240,241). There is increasing evidence that A1 complexation with carboxylates released in apical root zones in response to elevated external Al concentration is a widespread mechanism for Al exclusion in many plant species (Fig. 10). Formation of stable Al complexes occurs with citrate, oxalate, tartarate, and—to a lesser extent— also with malate (86,242,243). The Al carboxylate complexes are less toxic than free ionic Al species (244) and are not taken up by plant roots (240). This explains the well-documented alleviatory effects on root growth in many plant species by carboxylate applications (citric, oxalic, and tartaric acids) to the culture media in presence of toxic Al concentrations (8,244,245) Citrate, malate and oxalate are the carboxylate anions reported so far to be released from Al-stressed plant roots (Fig. 10), and Al resistance of species and cultivars seems to be related to the amount of exuded carboxylates (246,247) but also to the ability to maintain the release of carboxylates over extended periods (248). In contrast to P deficiency-induced carboxylate exudation, which usually increases after several days or weeks of the stress treatment (72,113), exudation of carboxylates in response to Al toxicity is a fast reaction occurring within minutes to several hours... 

Many mechanisms involve reversible steps which are rapid (and therefore in virtual equilibrium) followed by the critical rds. In these cases, the equilibrium constant for each of the rapid steps appears as a multiplicative factor in the rate law. The effective activation energy is the sum of the enthalpies of the equilibrium steps and the activation energy of the rds. 

For current densities below JPS the photocurrent in aqueous HF is found to be increased by a factor of 2 or even up to a factor of 4 for small photocurrent densities [Br2, Mai, Pel]. This effect is shown in Fig. 4.13. For non-aqueous HF electrolytes factors between 2 and 3 are observed. For further reduction of the illumination intensity the multiplication factor approaches infinity, because of the illu-... 

When one tries to rationalize the effect of the solvent on any type of chemical reactivity, considerable problems are encountered due to the multiple factors responsible for the solute/solvent interaction.2 7 One of the common ways to take into account the solvent effect is to consider it in terms of polarity (or polarizability) of the solvent. However, this concept is vague and difficult to define precisely. A first tentative... 

Another possible reason for public interest in herbal medications is that they provide some autonomy from medical professionals. Multiple factors contribute to a person s satisfaction with medical care (Siahpush et al. 1999 Sixma et al. 1998 Kaptchuk and Eisenberg 1998). One cause of dissatisfaction results from the traditionally passive role of the patient. Independent of its efficacy, alternative medicine provides an individual with a greater range of explanations and treatment options for their illnesses. The psychological appeal of more options is sufficient to draw individuals to consult alternative medicine, especially in cases where modern medicine has not been effective. 

The effects of multiple factors tend to produce a normal distribution. 

The coefficient of multiple determination, / is a measure of how much of SS, is accounted for by the factor effects. 

Figure 9.4 Relationships among SS, SS and SS for calculating both the coefficient of multiple determination, R, and the variance-ratio for the significance of the factor effects,...

Evaluation of approach to predict the contribution of multiple cytochrome P450s in drug metabolism using relative activity factor effects of the differences in expression levels of NADPH-cytochrome P450 reductase and cytochrome b(5) in the expression system and the differences in the marker activities. Journal of Pharmaceutical Sciences, 91, 952—963. 

Although it has become obvious that a fluorine atom in position 6 is the best substituent for antimicrobial activity, the reasons for this effect remain unclear. A comparative study of numerous quinolones seems to indicate that this F-substitution in position 6 affords both a better affinity with gyrase (2-17 times) and the best cell penetration (1-70 times).The presence of this fluorine lowers the basicity of the nitrogen-containing substituent in position 7, and this fact could play a role. However, there are multiple factors to take into account and interpretations must be carefully considered. Thus, replacing the fluorine atom by a chlorine in pefloxacin does not affect the activity on the enzyme, but a decrease of the bacterial activity is observed. This shows the importance of the pharmacokinetic factors. ... 

As many as 10% of children have a medication-responsive psychiatric disorder (Riddle et ah, 1998) and there has been a dramatic increase in the use of psychotropic medication to treat mental disorders in youth (Rappley et ah, 1999). Multiple factors account for this increase, including scientific advances in fields such as epidemiology, nosology, neuroscience, drug development, and clinical measurements, and efforts to educate the public about the benefits of early, effective treatment. Despite large gaps between research and practice, many medications are used in children on the basis of a small amount of scientific data. Factors that contribute to this situation are societal desires for rapid, effective treatment, acceptance of medication as a therapeutic modality, and a reimbursement climate in which there is increased pressure for brief treatment. Clearly there is a need to balance clinical and administrative pressures with a resort to treatment based on the best available data. 

Using the effects of multiple-factor interactions from full or fractional factorial designs. Multiple-factor interactions (e.g. three- and four-factor interactions) are considered to have a negligible effect. It is then considered that these higher-order interaction effects measure differences arising from experimental error [31]. 

ExjXjXjj are the effects of the multiple-factor interactions and XjXjX]f... 

The equations used to estimate (SE)g from negligible effects can be explained as follows. The mean effect of the multiple-factor interactions or of the dummies is expected to be zero. The variance of these effects can then be calculated as ... 

Multiple-factor interaction effects can be used to determine a critical effect value for the interpretation of full and fractional factorial designs [29] ... 

The error term can be approximated in different ways. A first possibility is that, analogous to the above, it is estimated from the multiple-factor interactions (two-, three-factor interactions, etc.) for (fractional) factorial designs [29]. In the example of Table 3.19 the sums of squares of the interactions AB, AC, BC and ABC are summed giving a MS error with 4 degrees of freedom. From this iSmain effects. The ANOVA table and equation (20) give of course the same results. 

---