Total Variation

To determine what confidence should be placed in a test result it is useful to evaluate the variability of test values. The factors influencing a test value are preanalytical, analytical, and within an individual. As the sources of variation (squares of the standard deviations) are additive, the total variation (SDt) for any one laboratory result is 

SDp — Standard deviation of preanalytical variation SDa = Standard deviation of analytical variation SDj = Standard deviation of within individual biological variation 

It is possible to substitute the coefficient of variation for the standard deviation in the above equation. If the conditions of patient preparation, sample collection, and sample handling are standardized, preanalytical variation is minimized and the total variation is then determined by the combined influence of the analytical and intraindividual variations, thus  

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Thus, the principal components are constructed in order of declining importance the first principal component comprise.s as much of the total variation of all variables as possible, the second principal component as much of the remaining variation, and so on. 

The data used to construct a two-sample chart can also be used to separate the total variation of the data, Otot> into contributions from random error. Grand) and systematic errors due to the analysts, Osys. Since an analyst s systematic errors should be present at the same level in the analysis of samples X and Y, the difference, D, between the results for the two samples... 

Speed variation is the total variation in speed from the set point and includes both dead band and oscillation. 

Stability is the total variation in the measurements obtained with a measurement system on the same part when measuring a single characteristic over a period of time. 

Diameter of Wire and Tolerance Limits. In separating the wire rope for gaging of wire, care must be taken to separate the various sizes of wire composing the different layers of bright (uncoated), drawn-galvanized, or galvanized wires in the strand. In like-positioned wires total variations of wire diameters shall not exceed the values of Table 4-24. 

Fully implicit total-variation-diminishing (TVD) high-order algorithm for compositional simulation and chemical flooding simulator [1116]... 

In general, one maximizes between-cluster Euclidean distance or minimizes within-cluster Euclidean distance or variance. This really amounts to the same. As described by Bratchell [6], one can partition total variation, represented by T, into between-group (B) and within-group components (W). 

Some of the results are collected in Table 35.7. Table 35.7a shows that some sensory attributes can be fitted rather well by the RRR model, especially yellow and green (/ == 0.75), whereas for instance brown and syrup do much worse R 0.40). These fits are based on the first two PCs of the least-squares fit (Y. The PCA on the OLS predictions showed the 2-dimensional approximation to be very good, accounting for 99.2% of the total variation of Y. The table shows the PC weights of the (fitted) sensory variables. Particularly the attributes brown , and to a lesser extent syrup , stand out as being different and being the main contributors to the second dimension. 

Figure 2.5 illustrates the state of affairs, and shows that heterogeneous material may be characterized by an inhomogeneous (C) or homogeneous (D) concentration function dependent on the relation between the total variation of concentration and the uncertainty of measurement on the one hand and the sample amount (or microprobe diameter in case of distribution-analytical investigations) on the other. 

In general, the total variation of a measured result y is composed of several variation components y, yi,..., ym- In the course of the analytical process, all the steps of the analytical procedure (e.g., sampling, sample preparation, separation, and measurement) and of single operations (e.g.,... 

The seven ways (r, through r7) for calculating correlation as the square root of the ratio of the explained variation over the total variation between X (concentration of analyte data) and Y (measured data) are described using many notational forms. For example, many software packages provide built-in functions capable of calculating the coefficient of correlation directly from a pair of X and Y vectors as given by rx (Equation 59-7). 

In both the linear and the nonlinear cases the total variation of the residuals is the sum of the random error, plus the departure from linearity. When the data is linear, the variance due to the departure from nonlinearity is effectively zero. For a nonlinear set of data, since the X-difference between adjacent data points is small, the nonlinearity of the function makes minimal contribution to the total difference between adjacent residuals and most of that difference contributing to the successive differences in the numerator of the DW calculation is due to the random noise of the data. The denominator term, on the other hand, is dependent almost entirely on the systematic variation due to the curvature, and for nonlinear data this is much larger than the random noise contribution. Therefore the denominator variance of the residuals is much larger than the numerator variance when nonlinearity is present, and the Durbin-Watson statistic reflects this by assuming a value less than 2. 

Figure 65-1 shows a schematic representation of the F-test for linearity. Note that there are some similarities to the Durbin-Watson test. The key difference between this test and the Durbin-Watson test is that in order to use the F-test as a test for (non) linearity, you must have measured many repeat samples at each value of the analyte. The variabilities of the readings for each sample are pooled, providing an estimate of the within-sample variance. This is indicated by the label Operative difference for denominator . By Analysis of Variance, we know that the total variation of residuals around the calibration line is the sum of the within-sample variance (52within) plus the variance of the means around the calibration line. Now, if the residuals are truly random, unbiased, and in particular the model is linear, then we know that the means for each sample will cluster... 

Solve the convection equation of high order (3rd order) essentially non-oscillatory (ENO) upwind scheme (Sussman et al., 1994) is used to calculate the convective term V V

velocity field P". The time advancement is accomplished using the second-order total variation diminishing (TVD) Runge-Kutta method (Chen and Fan, 2004). 

We conclude that L2a-Qb donor-donor interactions are generally ineffective at lowering the total variational energy,28 whereas L2a-f2b donor-acceptor interactions are universally stabilizing. Comparison of Fig. 3.2 (or Fig. 1.3) with Fig. 3.13 shows clearly how this fundamental difference arises from the Pauli restriction on orbital occupancies. 

If the valve is included, then the total variation or range of overhead product flowrate = 0.15 AC, which is equal to the range of the reflux flowrate, or ... 

Mean value of peak contrast (MP) can be expressed as total variation/ number of peaks, where total variation is the sum of gray level difference between the peaks and the valleys in a line profile. The difference of the MP between the membranes of the Golgi cistemae and of the ER is expressed by the ratio V G/VER, where VG is the MP of the Golgi apparatus, and VER the MP of the ER. As shown in Table 1, the ratio VG/VER was about 1.2 times higher than the control, confirming that the differ-... 

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