Independence of observations

Two different types of scales can be used (cf. Belton and Stewart 2002, pp. 121-122). A local scale is defined with the best and worst existing alternatives forming the reference points for the bounds of the scale while a global scale is defined relative to absolute values for best and worst performance. Local scales are easier to define but global scales allow the decision maker to define objective weights independent of observed attribute values. 

The amount of EBT present in Showa Denko tryptophan varied markedly in the period 1987-89 (Figure 5), presumably reflecting alterations in the manufacturing conditions. It is likely that levels of all of the contaminants varied with time. These data are consistent with the hypothesis that a contami-nant(s) in tryptophan is responsible for EMS and for the sporadic cases of EE between 1986 and 1988. Recent statistical analyses of EBT, adjusted for serial autocorrelation (to take into account that sequential lots of tryptophan may be related), revealed that higher levels of EBT are still associated with EMS, but the association (p = 0.120) did not achieve statistical significance. Nonetheless, the results do not vindicate EBT as a cause of EMS because mis-classification of lots as case or control could weaken the association and the methods used to account for the lack of independence of observations over time probably reduce the power of the statistical analysis. 

One can expect the a priori (independent of observers) probability distribution Pip a) to vary on some characteristic scale, ApA determined by the underlying... 

In other words, two photons can never be detected at two points separated by an odd number of X/lr 2, despite the fact that one photon can be detected anywhere. The vanishing of G 2 (Ri, t R2, f2) for two photons at widely separated points Ri and R2 is an example of quantum-mechanical nonlocality, that the outcome of a detection measurement at Ri appears to be influenced by where we have chosen to locate the R2 detector. At certain positions R2 we can never detect a photon at Ri when there is a photon detected at R2, whereas at other position R2 it is possible. The photon correlation argument shows clearly that quantum theory does not in general describe an objective physical reality independent of observation [17],... 

Coronary heart disease and atherosclerosis are major contributors to morbidity and mortality in the United States and other developed countries. Epidemiological studies suggest that decreased mortality from coronary heart disease is associated with moderate consumption of alcohol, and especially of red wine [7], Numerous studies indicate that resveratrol inhibits platelet aggregation [8-10, 12, 16, 54, 55], alters eicosanoid synthesis [15, 55], modulates lipoprotein mechanisms [14, 56-58], inhibits vascular smooth muscle cell proliferation [59], and acts as an estrogen receptor agonist [60]. On the other hand, at least one earlier study indicated that it promoted atherosclerotic development, rather than protected against it, by a mechanism that appeared to be independent of observed... 

Independence of observation (as outlined in detail by Concordet and Toutain ), which may or may not be satisfied in every instance. 

Repeated observation is required to fully capture adaptive as well as rhythmic processes in organisms. Studies that use repeated measurements yield many benefits, in view of the importance of these time-dependent processes. However, traditional ANOVA approaches to repeated-measures data are fiaught with problems that can lead to an increase in the Type I error rate, losses in conceptual and statistical power, and overall inefficiency (Vasey Thayer, 1987). Importantly, traditional ANOVA is based on the assumption of the independence of observations. However, repeated observations of ongoing activity are frequently correlated with each other often in complex ways. This pattern of dependencies among observations is a source of information that is lost when using traditional ANOVA. The multivariate analysis of variance (MANOVA) qrproach takes these dependencies into account, but the multiple observations of the same DV are analogous to the multiple DVs discussed previously. 

Independence of observations. This is probably the most cited weaknesses of HMMs. While an observations depends on its state, and the state depends on the previous states, one observation is not statistically dependent on the previous one. To see effect of this, consider the probability of a sequence of observations at a single value. If we have a density with a mean of 0.5, we would then find that a sequence of observations of 0.3, 0.3, 0.3, 0.3... would have a certain probability, and as the Gaussian is symmetrical, this would be the same probability as a sequence of 0.7, 0.7, 0.7, O.7. But as the observations are independent of one another, this would have the same probability as a sequence which oscillates such as 0.3, 0.7, 0.3, 0.7... Such a pattern would be extremely imlikely in real speech, a fact not reflected in the model. 

Theoretical models of the film viscosity lead to values about 10 times smaller than those often observed [113, 114]. It may be that the experimental phenomenology is not that supposed in derivations such as those of Eqs. rV-20 and IV-22. Alternatively, it may be that virtually all of the measured surface viscosity is developed in the substrate through its interactions with the film (note Fig. IV-3). Recent hydrodynamic calculations of shape transitions in lipid domains by Stone and McConnell indicate that the transition rate depends only on the subphase viscosity [115]. Brownian motion of lipid monolayer domains also follow a fluid mechanical model wherein the mobility is independent of film viscosity but depends on the viscosity of the subphase [116]. This contrasts with the supposition that there is little coupling between the monolayer and the subphase [117] complete explanation of the film viscosity remains unresolved. 

Relaxations in the double layers between two interacting particles can retard aggregation rates and cause them to be independent of particle size [101-103]. Discrepancies between theoretical predictions and experimental observations of heterocoagulation between polymer latices, silica particles, and ceria particles [104] have promptetl Mati-jevic and co-workers to propose that the charge on these particles may not be uniformly distributed over the surface [105, 106]. Similar behavior has been seen in the heterocoagulation of cationic and anionic polymer latices [107]. 

Another point in connection with Eq. XII-5 is that both the yielding and the shear will involve mainly the softer material, so that li is given by a ratio of properties of the same substance. This ratio should be nearly independent of the nature of the metal itself since s and P tend to vary together in agreement with the observation that for most frictional situations, the coefficient of friction lies between about O.S and 1.0. Also, temperature should not have much effect on n, as is observed. 

The existence of this situation (for nonporous solids) explains why the ratio test discussed above and exemplified by the data in Table XVII-3 works so well. Essentially, any isotherm fitting data in the multilayer region must contain a parameter that will be found to be proportional to surface area. In fact, this observation explains the success of Ae point B method (as in Fig. XVII-7) and other single-point methods, since for any P/P value in the characteristic isotherm region, the measured n is related to the surface area of the solid by a proportionality constant that is independent of the nature of the solid. 

The existence of a characteristic isotherm (or of a r-plot) gives a very important piece of information about the adsorption potential, at least for polar solids for which the observation holds. The direct implication is that film thickness f, or alternatively n/n is determined by P/I independent of the nature of the adsorbent. We can thus write... 

Sing (see Ref. 207 and earlier papers) developed a modification of the de Boer r-plot idea. The latter rests on the observation of a characteristic isotherm (Section XVII-9), that is, on the conclusion that the adsorption isotherm is independent of the adsorbent in the multilayer region. Sing recognized that there were differences for different adsorbents, and used an appropriate standard isotherm for each system, the standard isotherm being for a nonporous adsorbent of composition similar to that of the porous one being studied. He then defined a quantity = n/nx)s where nx is the amount adsorbed by the nonporous reference material at the selected P/P. The values are used to correct pore radii for multilayer adsorption in much the same manner as with de Boer. Lecloux and Pirard [208] have discussed further the use of standard isotherms. 

It is important to recognize that thennodynamic laws are generalizations of experimental observations on systems of macroscopic size for such bulk systems the equations are exact (at least within the limits of the best experimental precision). The validity and applicability of the relations are independent of the correchiess of any model of molecular behaviour adduced to explain them. Moreover, the usefiilness of thennodynamic relations depends cmcially on measurability, unless an experimenter can keep the constraints on a system and its surroundings under control, the measurements may be worthless. 

One may now consider how changes can be made in a system across an adiabatic wall. The first law of thermodynamics can now be stated as another generalization of experimental observation, but in an unfamiliar form the M/ork required to transform an adiabatic (thermally insulated) system, from a completely specified initial state to a completely specifiedfinal state is independent of the source of the work (mechanical, electrical, etc.) and independent of the nature of the adiabatic path. This is exactly what Joule observed the same amount of work, mechanical or electrical, was always required to bring an adiabatically enclosed volume of water from one temperature 0 to another 02. 

The reactant P is again taken as a pool chemical, so the first step has a constant rate. The rate of the second step depends on the concentration of the intennediate A and on the temperature T and this step is taken as exothennic. (In the simplest case, is taken to be independent of T and the first step is thennoneutral.) Again, the steady state is found to be nnstable over a range of parameter values, with oscillations being observed. 

Once the basic work has been done, the observed spectrum can be calculated in several different ways. If the problem is solved in tlie time domain, then the solution provides a list of transitions. Each transition is defined by four quantities the mtegrated intensity, the frequency at which it appears, the linewidth (or decay rate in the time domain) and the phase. From this list of parameters, either a spectrum or a time-domain FID can be calculated easily. The spectrum has the advantage that it can be directly compared to the experimental result. An FID can be subjected to some sort of apodization before Fourier transfomiation to the spectrum this allows additional line broadening to be added to the spectrum independent of the sumilation. 

In a coupled spin system, the number of observed lines in a spectrum does not match the number of independent z magnetizations and, fiirthennore, the spectra depend on the flip angle of the pulse used to observe them. Because of the complicated spectroscopy of homonuclear coupled spins, it is only recently that selective inversions in simple coupled spin systems [23] have been studied. This means that slow chemical exchange can be studied using proton spectra without the requirement of single characteristic peaks, such as methyl groups. 

Additives, whether hydrophobic solutes, other surfactants or polymers, tend to nucleate micelles at concentrations lower than in the absence of additive. Due to this nucleating effect of polymers on micellization there is often a measurable erne, usually called a critical aggregation concentration or cac, below the regular erne observed in the absence of added polymer. This cac is usually independent of polymer concentration. The size of these aggregates is usually smaller than that of free micelles, and this size tends to be small even in the presence of added salt (conditions where free micelles tend to grow in size). 

If one is interested in the probability that mh be observed when is measured regardless of what bond length r is involved, then it is appropriate to integrate this expression over the r-variable about which one does not care. This, in effect, sums contributions from all r-values to obtain a result that is independent of the r variable. As a result, the probability reduces to ... 

A quantitative correlation between rate and equilibrium constants for the different metal ions is absent. The observed rate enhancements are a result of catalysis by the metal ions and are clearly not a result of protonation of the pyridyl group, since the pH s of all solutions were within the region where the rate constant is independent of the pH (Figure 2.1). 

For the last two compounds, first-order rates were observed towards the end of the reactions, enabling the reactivities of these compounds relative to that of water to be estimated (table 2.1). The nitration of 2-mesitylethanesulphonate anion was independent of the concentration of the aromatic over 80 % of its course, and because the final part of the reaction did not obey a truly first-order law its reactivity could not be estimated. 

Nitration at a rate independent of the concentration of the compound being nitrated had previously been observed in reactions in organic solvents ( 3.2.1). Such kinetics would be observed if the bulk reactivity of the aromatic towards the nitrating species exceeded that of water, and the measured rate would then be the rate of production of the nitrating species. The identification of the slow reaction with the formation of the nitronium ion followed from the fact that the initial rate under zeroth-order conditions was the same, to within experimental error, as the rate of 0-exchange in a similar solution. It was inferred that the exchange of oxygen occurred via heterolysis to the nitronium ion, and that it was the rate of this heterolysis which limited the rates of nitration of reactive aromatic compounds. 

The observation of nitration at a rate independent of the concentration and the nature of the aromatic means only that the effective nitrating species is formed slowly in a step which does not involve the aromatic. The fact that the rates of zeroth-order nitration under comparable conditions in solutions of nitric acid in acetic acid, sulpholan and nitromethane differed by at most a factor of 50 indicated that the slow step in these three cases was the same, and that the solvents had no chemical involvement in this step. The dissimilarity in the rate between these three cases and nitration with acetyl nitrate in acetic anhydride argues against a common mechanism, and indeed it is not required from evidence about zeroth-order rates alone that in the latter solutions the slow step should involve the formation of the nitronium ion. 

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