Variance percentage

The error of the AAS determination of chromium in river water with a determined mean concentration of 4.8 (ig L 1 is acceptable for this particular environmental purpose. The highest variance percentage arises as a result of centrifugation. The sampling error arising from river inhomogeneity is relatively small in this particular environmental situation. 

The director of pharmacy uses an expense report prepared on a monthly or weekly basis. In this report, all pharmacy department expenses are categorized into at least five major sections. Each expense is also given a unique code so that not only the pharmacy department but also the hospitals central accounting office can access and monitor expenses. The expense report indicates the amount budgeted for each expense, the actual expense incurred, the variance between budgeted and incurred expenses, and the variance percentage. Table 15-10 shows an abbreviated, simplified expense report for the pharmacy department of a large tertiary-care hospital. 

Factor Eigenvalue Percentage of variance Percentage of accumulated variance... 

Table 2. Percentage error for LN compared to reference Langevin trajectories (at 0.5 fs) for energy means and associated variances for BPTI over 60 ps at 7 = 20 ps At = 0.5 fs, Atm = 3 fe, and At — k2Atm, where hz ranges from 1 for LN 1 to 96 for LN 96.

While none of these kinds of variances can be precisely estimated you should consider them (and others you identify) in terms of their potential impact, and build an appropriate contingency percentage into estimates of... 

Though the kinetic results above can be rationalised by reasonable premises, one experimental observation is markedly at variance and this is that the percentage of orr/io-benzoylation of toluene is constant under all conditions clearly there is still much to be understood about the role of the catalyst in these reactions. 

Fig. 36.7. Percentage variance of X-content explained by the principal components from spectral data. Individual percentages (bars) are shown as well as cumulative percentages (circles).

Figure 38 shows the variance explained by the two principal component (PC) model as a percentage of each of the two indices batch number and time. The lower set of bars in Fig. 38a are the explained variances for the first PC, while the upper set of bars reflects the additional contribution of the second PC. The lower line in Fig. 38b is the explained variance over time for the first PC and the upper line is the combination of PC 1 and 2. Figure 38a indicates, for example, that batch numbers 13 and 30 have very small explained variances, while batch numbers 12 and 33 have variances that are captured very well by the reference model after two PCs. It is impossible to conclude from this plot alone, however, that batches 13 and 30 are poorly represented by the reference model. 

In 1968 the average selling costs were 10% of the sales dollar. There is, however, a large variance in this percentage. For basic bulk chemicals such as sulfuric acid, caustic, and soda ash the sales costs are less than 5% of the selling price, while for specialty chemicals having a low sales volume the sales costs may exceed 50% of the selling price. 

Fig. 3. Biplots of log-ratio factor loading for Aegean Sea sediments. Upper plot, complete dataset lower plot, offshore samples. Percentages indicate variance accounted for by factor.

Table 4.11. Eigenvalues of the correlation matrix of major-element concentrations in Coumiac limestones and percentage of variance explained by each component.

Table 4.13. Eigenvalues and percentage of explained variance for the oceanic island isotope...

Analysis of variance was used to assess the effects on polyaromatic hydrocarbons extraction at the 99% confidence level for the four factors varied. The percentage of 14C in the extract and soil residue does not total 100% because of degradation and volatilization during incubation and due to losses during analysis. The data are presented in Table 2.3 and represent the average of the three replicates for the extract or soil residue. 

Often simple strategies for the selection of a good set of PCA scores (for PCR) are applied (a) selection of the first PCA scores which cover a certain percentage of the total variance of X (for instance, 99%) (b) selection of the PCA scores with maximum correlation to y. Application of PCR within R is easy for a given number of components. For an example and a comparison of PCR and PLS, see Section 4.9.1. 

The x is best when the differences between theory and experiment are normally distributed and when the variance a is correctly estimated. The optimum has a value close to unity, y smaller than 1 indicates an overestimation of the variance. On the other hand, a is not needed for the evaluation of R-factor, which measures the residual difference in percentage. 

The variances of the parameter estimates can be used to set confidence intervals that would include the true value of the parameter a certain percentage of the time. In general, the confidence interval for a parameter p, based on is given by... 

For the styrene-butadiene example, the use of the PCR method to develop a calibration for di-butadiene is summarized in Table 12.6. It should be mentioned that the data were mean-centered before application of the PCR method. Figure 12.12 shows the percentage of explained variance in both x (the spectral data) andy (the c/i-butadiene concentration data) after each principal component. After four principal components, it does not appear that the use of any additional PCs results in a large increase in the explained variance of X or y. If a PCR regression model using four PCs is built and applied to the calibration data, a fit RMSEE of 1.26 is obtained. 

Figure 12.12 The percentage of explained variance in both the x data (solid line) and y data (dotted line), as a function of the number of PCs in the PCR regression model for c s-butadiene content in styrene-butadiene copolymers).

I. A measure, symbolized by square root of the variance. Hence, it is used to describe the distribution about a mean value. For a normal distribution curve centered on some mean value, fjt, multiples of the standard deviation provides information on what percentage of the values lie within na of that mean. Thus, 68.3% of the values lie within one standard deviation of the mean, 95.5% within 2 cr, and 99.7% within 3 cr. 2. The corresponding statistic, 5, used to estimate the true standard deviation cr = (2(Xi - x) )/(n - 1). See Statistics (A Primer)... 

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