Systematic influences

While a large magnitude correlation coefficient calculated for two variables indicates a strong association between them, it does not make any statement about a causal relationship. That is, it does not imply a cause-and-effect relationship. There may indeed be such a relationship between the variables, but this cannot be determined from knowledge of the correlation coefficient alone. It is entirely possible that a third variable is systematically influencing both variables and is responsible for the strong correlation that is evident between them. 

The result (Table 12, ax in eV) is nevertheless rather illuminating. The values of ax vary generally according to expected pattern, and are seemingly not systematically influenced by the charge of the acceptor. For hard ions, including the alkali and alkaline earth ions, ax is as a rule between 0 and 1 eV12). 

The external systematic influence is common in experimental research when the quality of the raw materials and of the chemicals undergo minor changes and/or when the first data were obtained in one experimental unit and the remaining measurements were carried out in a similar but not identical apparatus. 

In these situations, we cannot start the analysis of data without separating the effect of the external systematic influence from the unprocessed new data. In other words, we must separate the variations due to the actions of some factors with systematic influences from the original data. For this purpose, the methods of Latin squares and of effects of unification of factors have been developed in the plan of experiments. 

The correct use of the Latin squares method imposes a completely random order of execution of the experiments. As far as the experiment required in the box table is randomly chosen and as a single value of the process response is introduced into the box, we guarantee the random spreading of the effect produced by the factor which presents a systematic influence. 

The method of the effects of the unification of factors considers that, for a fixed plan of experiments, we can produce different groups where each contains experiments presenting the same systematic influence [5.8, 5.13, 5.23, 5.35, 5.36]. To introduce this method, we can consider the case of a process with three factors analyzed with a CFE 2 plan of experiments. In our example, we will take into account the systematic influence of a new factor D. To begin this analysis, we will use the initial plan with eight experiments with the condition to separate these experiments into two blocks or groups ... 

The justification for our consideration showing that the action of a factor with systematic influence is concentrated in the relation which binds the blocks (frequently named contrast) is sustained by the following observations ... 

A division into four blocks made from two unification relations, is also possible with a CEE 2 plan where the systematic influence of one or more factors is considered. If interactions AB and AC give the unification relations, then, by using the block division procedure used above (Table 5.63), the following blocks will be obtained ... 

In this division example, if interactions AB and AC influence the process response, we can conclude that the displacement of the process response contains the effect of a systematic influence. 

The examples where a CFE 2 plan has been divided into two or four blocks are not explicit enough to develop the idea that the relations of the unification of blocks are selected randomly. In the next example, a CFE 2 plan is developed with the purpose being to show the procedures to select the unification relations of inter-blocks. In this plan, the actions showing a systematic influence will be divided into two blocks or into four blocks with, respectively, eight experiments or four experiments per block. We start this new analysis by building the CFE 2 plan. Table 5.64 contains this CFE 2 plan and also gives the division of the two blocks when we use the ABCD interaction as a unification relation. 

Three different qualities of alcohol have been used recycled, distilled or rectified. It is easy to observe that the quality of the alcohol introduces a systematic influence towards factor B in the esterification reaction. Indeed, the development of the experimental research is made with a plan with four blocks. The ABC and BCD have the contrasts considered for the blocks division. For the experiments grouped in block Ej, the first type of alcohol has been used. Distilled alcohol is the reactant used in the experiments of the second block (E2) and the rectified alcohol for the experiments of the last two blocks (E3, E4). Table 5.66 presents the initial data where the division of the blocks is not visible. 

At this point, we have to verify the eorreetness of the selection of the unification relations. When S sSint we can conclude that our selection for the unification relations is good in this case, we can also note that the calculations have been made without errors. Otherwise, if computation errors have not been detected, we have to observe that the selected interactions for the unification of blocks are strong and then they carmot be used as unification interactions. In this case, we have to carry out a new experimental research with a new plan. However, part of the experiments realized in the previous plan can be recuperated. Table 5.68 contains the synthesis of the analysis of the variances for the current example of an esterification reaction. We observe that, for the evolution of the factors, the molar ratio of reactants (B) prevails, whereas all other interactions, except interaction AC (temperature-reaction time), do not have an important influence on the process response (on the reaction conversion). This statement is sustained by all zero hypotheses accepted and reported in Table 5.68. It should be mentioned that the alcohol quality does not have a systematic influence on the esterification reaction efficiency. Indeed, the reaction can be carried out with the cheapest alcohol. As a conclusion, the analysis of the variances has shown that conversion enhancement can be obtained by increasing the temperature, reaction time and, catalyst concentration, independently or simultaneously. 

Accuracy by Comparison. For drug substance, the only possibility of a quantitative assessment of accuracy is the comparison to the results of another analytical procedure or to a reference (if established with other procedures and/or additional characterization). This can be performed statistically with a r-test (see statistical textbooks or corresponding software). However, the shortcomings of these statistical tests (or better the justification of their use) are especially important here. It must be taken into consideration that two independent analytical procedures most probably differ in their specificity. This may lead to a systematic influence on the results (Table 2). If the effect can be quantified, the means should be corrected before performing the statistical comparison. If a... 

If the calculated value of F exceeds the critical value, it is probable that the data cannot be represented by the expression under examination. However, before turning to other rate expressions, the data of the replicate experiments should be examined to make sure that no hidden or incompletely controlled factors systematically influence the values of k i obtained. The procedure is described in the next section. 

Will the properties of the solvent have a systematic influence on yield and selectivity ... 

The cause of the scatter is the non-systematic influence of the substituent on the microscopic environment of the transition structure. The linear free energy relationship between product state XpyH (Equation 22) and the transition structure (Xpy. .. PO32 . . . isq) will be modulated by second-order non-systematic variation because the microscopic environment of the reaction centre in the standard (XpyH ) differs slightly from that (Xpy-PO ) in the reaction under investigation giving rise to specific substituent effects. These effects are mostly small. An unusually dramatic intervention of the microscopic medium effect may be found in Myron Bender s extremely scattered Hammett dependence of the reaction of cyclodextrins with substituted phenyl acetates.22 The cyclodextrin reagent complexes the substrate and interacts... 

Cooper et al. reported that solid-state 23Na NMR is useful for observing the sodium cation in sulfonated polystyrene ionomers (NaSPS).44 Three NMR peaks were detected, corresponding to isolated ion pairs, aggregated ions and hydrated ions (Fig. 14). The distributions of these three types of sodium cations are systematically influenced by hydration treatment, sulfonation level and neutralization level. Fully dried NaSPS at low ion content shows that the isolated and aggregated sodium ions in NaSPS are available for hydration. As the sulfonation level increases, the fraction of sodium ions held in isolated ion pairs decreases while the fraction of ionic species in the ionic aggregates increases. This coincides with a shift in the peak position of the aggregated sodium ions to low frequency, indicative of increased quadrupolar interactions. 

No systematic influence of GASLAB measurements on CMDL flasks has been detected. Figure 4 shows the results of the ICP flask comparisons for CO2 and for S C. Compared to cylinder intercomparisons, the precision on the ICP comparisons is low (individual measurements) but the frequency is high. The CO, results are startling. The Australian calibration scale was established to within 0.01 ppm at ambient CO, mixing ratios by repeated analysis of 10 cylinders initially characterized by CMDL. Return of a subset of the cylinders after two years confirmed this agreement to within a few hundredths of a ppm, as have comparisons of other cylinders. Despite this agreement in calibration scales (see also Fig. 2b, Australia), there is a consistent mean difference (CSIRO-CMDL) in the ICP flasks of 0.17 0.17 ppm. 

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