Efficient comparison of two methods

Part 4 Performing a ranking test to determine if either analytical method or location affects the results as a systematic error (bias) and Part 5 Computing the efficient comparison of two methods as described by Youden and Steiner in reference [7],... 

Collaborative Laboratory Studies Part 5 - Efficient Comparison of Two Methods... 

COMPUTATIONS FOR EFFICIENT COMPARISON OF TWO METHODS (COMP METH WORKSHEET)... 

The section following shows a statistical test (text for the Comp Meth MathCad Worksheet) for the efficient comparison of two analytical methods. This test requires that replicate measurements be made on two different samples using two different analytical methods. The test will determine whether there is a significant difference in the precision and accuracy for the two methods. It will also determine whether there is significant systematic error between the methods, and calculate the magnitude of that error (as bias). 

This efficient statistical test requires the minimum data collection and analysis for the comparison of two methods. The experimental design for data collection has been shown graphically in Chapter 35 (Figure 35-2), with the numerical data for this test given in Table 38-1. Two methods are used to analyze two different samples, with approximately five replicate measurements per sample as shown graphically in the previously mentioned figure. 

Sections on matrix algebra, analytic geometry, experimental design, instrument and system calibration, noise, derivatives and their use in data analysis, linearity and nonlinearity are described. Collaborative laboratory studies, using ANOVA, testing for systematic error, ranking tests for collaborative studies, and efficient comparison of two analytical methods are included. Discussion on topics such as the limitations in analytical accuracy and brief introductions to the statistics of spectral searches and the chemometrics of imaging spectroscopy are included. 

Guillaume, Y. Guinchard, C. Study and optimization of column efficiency in HPLC Comparison of two methods for separating ten benzodiazepines. J.Liq.Chromatogr., 1994, 17, 1443-1459... 

Four cases were evaluated, since there was interest in the comparison of two alternate methods for HI separation. Required selling prices for hydrogen were calculated to be between about USD 3.00/kg and USD 3.50/kg, and efficiencies were from 39 to 44%. This result is shown in Table 1. 

Even though the spectral density approach requires computation of the inverse and determinant of a number of matrices, the size of these matrices is only No y. No. They are significantly smaller than the NgNp x NgNp matrix Eyj j (= E22) required in the time-domain approach. Comparison of the computational efficiency between the two methods depends on the number of the elements in the frequency index set and the number of data points in a fundamental period. The ratio of the computations required by the Bayesian spectral density approach and the Bayesian time-domain approach can be approximated by ... 

Secondly, there exists several techniques for integrating approximately over the k-points of the first Brillouin zone (BZ). For materials with ully occupied bands (e.g., semiconductors) the special points method is by far the most efficient (Chadi and Cohen, 1974 Monkhorst and Pack, 1976). The method appeals to the tight-binding picture of atomic interactions, integrating a definite number of interactions exactly with a suitably chosen set of k-points. For metallic systems it is necessary to exhaust the irreducible BZ with a fine mesh, and to choose a method of assigning occupation numbers to the electron states. Several methods prevail, and we refer to Fu and Ho (1983) for a detailed comparison of two schemes. 

If a higher accuracy is required, it is recommended to pass to the coupled clusters (CCs) theory. Basically, CC-SD is also an N procedure, but the test calculations showed that the timing ratio CC-SD/CI-SD ranged from 4 to 8, though as with any comparison of two different methods, the ratio depends strongly on the efficiency of the two programs. 

A successful application of GA to conformation sampling is, for example, as a part of flexible docking [12-14], It should be noted, however, that none of the three sampling methods discussed above, MD, MC, and GA, was shown to outperform the other two in any general way. In fact, a comparison of the three methods in the context of flexible docking showed similar efficiency for all three [12], although specific advantages are likely to exist for particular apphcations. 

Normally a calibration curve—molar mass against the total retention volume—exists for every GPC column or column combination. As a measure of the separation efficiency of a given column (set) the difference in the retention of two molar masses can be determined from this calibration curve. The same eluent and the same type of calibration standards have to be used for the comparison of different columns or sets. However, this volume difference is not in itself sufficient. In a first approximation the cross section area does not contribute to the separation. Dividing the retention difference by the cross section area normalizes the retention volume for different diameters of columns. The ISO standard method (3) contains such an equation... 

Gutfelt et al. (1997) have evaluated various ME formulations as reaction media for synthesis of decyl sulphonate from decylbromide and sodium sulphite. The reaction rate was fast both in water-in-oil and in bicontinuous ME based on non-ionic surfactants. A comparison was made with this reaction being conducted in a two-phase. system with quats as phase-transfer catalyst but was found to be much less efficient. However, when two other nucleophiles, NaCN and NaNOj, were used the PTC method was almost as efficient as the ME media. It seems that in the case of decyl sulphonate there is a strong ion pair formation between the product and the PTC. The rate in the ME media could be further increased by addition of a small amount of a cationic surfactant. 

Vibrational spectroscopy is of utmost importance in many areas of chemical research and the application of electronic structure methods for the calculation of harmonic frequencies has been of great value for the interpretation of complex experimental spectra. Numerous unusual molecules have been identified by comparison of computed and observed frequencies. Another standard use of harmonic frequencies in first principles computations is the derivation of thermochemical and kinetic data by statistical thermodynamics for which the frequencies are an important ingredient (see, e. g., Hehre et al. 1986). The theoretical evaluation of harmonic vibrational frequencies is efficiently done in modem programs by evaluation of analytic second derivatives of the total energy with respect to cartesian coordinates (see, e. g., Johnson and Frisch, 1994, for the corresponding DFT implementation and Stratman etal., 1997, for further developments). Alternatively, if the second derivatives are not available analytically, they are obtained by numerical differentiation of analytic first derivatives (i. e., by evaluating gradient differences obtained after finite displacements of atomic coordinates). In the past two decades, most of these calculations have been carried... 

The calculations for the efficient two-method comparison are shown in Table 38-2 and the subsequent equations following. The mathematical expressions are given in MathCad symbolic notation showing that the difference is taken for each replicate set of X and Y and the mean is computed. Then the sum for each replicate set of X and Y is calculated and the mean is computed. The difference in the sums is computed (as d) and the differences are summed and reported as an absolute value (as 2d ). The mean difference is calculated as mean(d). ... 

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