Values variance

The variance p<7centa of the mean energy ia shown as a subscript to the variance value recorded for the BBK scheme. 

The variance diagram obtained for the example discussed before is quite simple. Clusters of pure variables are found at 30 degrees (var = 0.5853) and at 300 degrees (var = 0.4868) (see Fig. 34.36). The distance from the centre of the diagram to each point is proportional to the variance value. Neighbouring points are connected by solid lines. All values were scaled in such a way that the highest variance is full scale. As can be seen from Fig. 34.36, two clusters of pure variables are found. The... 

Er has dropped to five standard deviations, the optimum transmittance has dropped to 3.2, and then drops off quickly below that value. Surprisingly, the optimum value of transmittance appears to reach a minimum value, and then increase again as Er continues to decrease. It is not entirely clear whether this is simply appearance or actually reflects the correct description of the behavior of the noise in this regime, given the unstable nature of the variance values upon which it is based. In fact, originally these curves were computed only for values of Er equal to or greater than three due to the expectation that no reasonable results could be obtained at lower values of Er. However, when the unexpectedly smooth decrease in the optimum value of %T was observed down to that level, it seemed prudent to extend the calculations to still lower values, whereupon the results in Figure 45-11 were obtained. 

On the other hand, multiplicative patchwork scheme changes the sample variances by multiplying (1 + d) or (1 - d) by sample values. Accordingly, sample variance value of one subset increases while another subset decreases. In other words, multiplicative scheme scales the variance values up or down. Similarly, the scale-shift scheme stresses the fact of scaling sample variances due to multiplicative scheme (Yeo, 2003b). The ratio of resulting variances between two subsets is a clue to detect bit information embedded. 

Usual procedures for the selection of the common best basis are based on maximum variance criteria (Walczak and Massart, 2000). For instance, the variance spectrum procedure computes at first the variance of all the variables and arranges them into a vector, which has the significance of a spectrum of the variance. The wavelet decomposition is applied onto this vector and the best basis obtained is used to transform and to compress all the objects. Instead, the variance tree procedure applies the wavelet decomposition to all of the objects, obtaining a wavelet tree for each of them. Then, the variance of each coefficient, approximation or detail, is computed, and the variance values are structured into a tree of variances. The best basis derived from this tree is used to transform and to compress all the objects. 

Since the variance values depend on the measurement unit of variables, it becomes difficult to compare and impossible to combine information from variables of different nature, unless properly normalized column autoscaling is the transform most commonly applied. 

In fact, the space described by two or three PCs can be used to represent the objects (score plot), the original variables (loading plot), or both objects and variables (biplot). For instance, if the first two PCs (low-order) are drawn as axes of a Cartesian plane, we may observe in this plane a fraction of the information enclosed in the original multidimensional space which corresponds to the sum of the variance values explained by the two PCs. Since PCs are not intercorrelated variables, no duplicate information is shown in PC plots. 

It is interesting to remark that with an initial Boltzmann distribution, the probability density Px(t, jc) remains invariant over all time. Figure 4.4, in which the probability densities calculated at different times with Eq. (4.155) are reported, illustrates the temporal evolution of the expectation and variance values of X(t) for a 8(x - x0) initial condition. 

Variance value or variance measurement is in this case also determined by the well-known formula ... 

Variance values of trials are determined by application of expressions (2.125) and (2.126) ... 

Table 2.232 gives the variance values of replicated trials. Table 2.232 FRFE 24 1... 

The results of the principal component computations show a relatively high variance for PCI (77.5 % of total variance). This means that data points are mainly distributed along a single direction. For real chemical data this direction would hopefully correlate with a chemical or physical factor influencing the data structure. The high accumulated variance value of 97.8 % of total variance preserved by the first two principal components supports the assumption that a graph of the data... 

Based on published variability in pharmacokinetic studies of ethinylestradiol in lean subjects, taking confidence intervals of 80-125%, residual variance ranged between 10 and 33%. Based on these residual variance values, calculated samples sizes ranged between 6 and 30 (subjects). For example, based on a residual variance value of 17.5%, a sample size of 14 was calculated. 

The chosen sample size reflects (i) the formal sample size calculation (using a residual variance value of 17.5%) based on the pharmacokinetics of ethinylestradiol in lean subjects, (ii) published sample sizes in other studies of this type of study ranged between 12 and 34, (iii) that this study will include overweight and obese subjects, a population who have been suggested to show a higher variability in their pharmacokinetics and in their menstrual cycles, and finally (iv) the plan not to replace dropouts. 

Thus far, only differences in accuracy have been discussed. The variance values owing to differences among triplicate analyses provide some precision. Among all formulations and concentrations, the mean squares obtained from the analyses of variance were 0.07, 0.13, 0.07, 0.53, and 1.48. The last two values are for ester and acid recovery from Florida muck, respectively. Therefore, residue recovery from muck, in addition to being the least accurate and sensitive, is also the least precise. 

For each activity, there is information about the subject matter to be processed, a necessary work tool, a skill profile of possible persons to execute the activity, input and output information of the activity, and a duration distribution. The distribution of the duration includes an expected value and a variance value. The distribution of the time consumption (e.g., Gaussian, right- or left-skewed /3-distribution) may also be used for the calculation of possible buffer times. For the execution of an activity, a qualified person and, if necessary, adequate tools are selected to achieve the goal of the activity. As a result, the net for the representation of the execution of a single activity builds the link between the partial models of the work tool and the employee (Person Net and Tool Net, see below). 

The results of all experiments were expressed as mean SD. Levels of significance were determined using analysis of variance. Values of p<0.05 were regarded as significant. 

The statistical treatment involves tests, e.g. to assess the conformity of the distributions of individual results and of laboratory means to normal distributions (Kolmogorov-Smimov-Lilliefors tests), to detect outlying values in the population of individual results and in the population of laboratory means (Nalimov test), to assess the overall consistency of the variance values obtained in the participating laboratories (Bartlett test), and to detect outlying values in the laboratory variances (s ) (Cochran test). One-way analysis of variance (F-test) may be used to compare and estimate... 

The calculation as applied above for y, the estimated population mean for random sampling, may be applied to each stratum and these individual values used to get a population mean based on all stratum values. Similarly the calculation for S. the estimated population variance for random sampling, may be applied to each stratum and an analogous procedure used to get an overall variance based on all stratum values. If unequal samples are taken from the various strata, the overall population mean and variance values that represent the entire stratified population must be obtained on a weighted average basis see Section 3. 

The experimental variance, S, obtained from these samples is of little value unless it can be related to limiting variance values. If the assumptions are made that the mixtu re is a two-component system, and that the component particles differ only in colour, then these limiting values can be predicted with the help of the binomial theorem. The binomial theorem is applicable for the particular cases where the value of y, is either 0 or I. This condition is applicable in two limiting cases. 

The index will have a zero value for a completely segregated mixture and increase to unity for a fully randomized mixture. A criticism of the Lacey index is that it is insensitive to mixture quality. Even a very bad mixture will have a variance value much closer to than to So. and as a result practical values of the Lacey index are restricted to the range of 0.75 to 1.0. 

As welt as providing essential limiting variance values, equations (2.1) and (2.2) indicate how the mixture quality will be affected by the scale of scrutiny, or sample size. The variance, and hence the quality, of a completely s regated mixture is independent of the scale of scrutiny. If a fully randomized mixture is attainable then the quality of that mixture is inversely proportional to the number of particles in the sample. In this case a reduction in the particle size of the mixture will increase the number of particles in each Hxed weight sample and produce a predictable improvement in the attainable mixture quality. For a randomized mixture, equation (2.2) quantifles the effect of changes in the scale of scrutiny on mixture quality. Between these extremes of mixture types there is no infallible guide as to the relationship between scale of scrutiny and mixture quality. 

The equations (2.1) and (2.2) defining the limiting variance values S and were based on the assumption that a two-component, equi-sized particulate system was being analysed. Real systems are unlikely to be so obliging ... 

Equations (2.2), (2.5) and (2.6) for random variance presuppose that all the individual particles within the mixture can move independently of their neighbours. It will be seen in Chapter 5 that for cohesive powder systems the structure of the powder mixture can prevent independent movement of individual particles and that these limiting variance values have to be modified. 

If sample bias has been avoided the second distribution curve will peak at the true sample variance of the mixture, and the standard deviation of the estimates of variance, or standard error of the variance, s.e. (5 ), can be calculated. The area under this second curve can be used to express the probability of certain variance values occurring when the mixture is sampled. 

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