Mean corrected value

The mean corrected values of the observed electromotive force in... 

Correction for the mean Subtraction of the grand mean from each measurement result in ANOYA. This quantity is also known as the mean corrected value. (Section 4.4)... 

Total sum of squares, SST (also corrected sum of squares) In ANOYA the number arising from the sum of the squares of the mean corrected values. (Section 4.4)... 

Square each mean-corrected value and then sum them all to give the total sum of squares also known as the corrected sum of squares ... 

For each column (i.e., instance of the factor) average the mean-corrected values... 

On the other hand, the correction factor by which W r) is altered through this refined treatment, namely, exp[ —(9n/20)(r/r, ) ] from Eq. (16), depends both on n and on r/Vm If the distance of separation of the ends of the chain lies in the vicinity of its root-mean-square value, i.e., if r / then... 

These compounds have been the subject of several theoretical [7,11,13,20)] and experimental[21] studies. Ward and Elliott [20] measured the dynamic y hyperpolarizability of butadiene and hexatriene in the vapour phase by means of the dc-SHG technique. Waite and Papadopoulos[7,ll] computed static y values, using a Mac Weeny type Coupled Hartree-Fock Perturbation Theory (CHFPT) in the CNDO approximation, and an extended basis set. Kurtz [15] evaluated by means of a finite perturbation technique at the MNDO level [17] and using the AMI [22] and PM3[23] parametrizations, the mean y values of a series of polyenes containing from 2 to 11 unit cells. At the ab initio level, Hurst et al. [13] and Chopra et al. [20] studied basis sets effects on and y. It appeared that diffuse orbitals must be included in the basis set in order to describe correctly the external part of the molecules which is the most sensitive to the electrical perturbation and to ensure the obtention of accurate values of the calculated properties. 

Let the cation M4+ in a compound MX4 also have coordination number 6 its electrostatic bond strength is s = 4/6 = . For an anion X- having coordination number a = 2 we obtain = + = for an anion with a = 1 the sum is = . For other values of a the resulting p deviate even more from the expected value z = -1. The most favorable structure will have anions with a = 2 and with a = 1, and these in a ratio of 1 1, so that the correct value for z results in the mean. 

Fig. 6.10. Comparison of overlap sampling and FEP calculation results for the free energy change along the mutation of an adenosine in aqueous solution (between A = 0.05 and 0.45) in a molecular dynamics simulation. The results represent the average behavior of 14 independent runs. (MD time step.) The sampling interval is 0.75 ps. The upper half of the plot presents the standard deviation of the mean (with gives statistical error) for AA as a function of sample size N the lower half of the plot gives the estimate of A A - for comparison of the accuracy, the correct value of AA is indicated by the bold horizontal line...

When we say that some program we have just written is "correct", what do we really mean We do not mean "correct" in some absolute sense - correctness is not in this case an ethical judgment. We simply mean that it does what we want it to do. In other words, it fits some pre-arranged condition or relationship between input and output values. If we later decide that we really wanted some other output, then the program may no longer be "correct" for our purposes. 

Continuing from our previous discussion in Chapter 18 from reference [1], analogous to making what we have called (and is the standard statistical terminology) the a error when the data is above the critical value but is really from P0, this new error is called the [3 error, and the corresponding probability is called the (3 probability. As a caveat, we must note that the correct value of [3 can be obtained only subject to the usual considerations of all statistical calculations errors are random and independent, and so on. In addition, since we do not really know the characteristics of the alternate population, we must make additional assumptions. One of these assumptions is that the standard deviation of the alternate population (Pa) is the same as that of the hypothesized population (P0), regardless of the value of its mean. 

Post-processing, n - performing a mathematical operation on an intermediate analysis result to produce the final result, including correcting for temperature effects, adding a mean property value of the calibration model, or converting the instrument results into appropriate units for reporting purposes. 

Table 4 shows the projected anomalies of annual and seasonal precipitation and air temperature for the Ebro River, whereas Figs. 7-12 show the spatial variation of these anomalies, computed using ordinary kriging. Anomalies are computed as the difference between projected bias-corrected values for the climate scenarios (January 2071 to December 2100) and the corresponding values observed during the control period (January 1961 to December 1990), and they can be viewed as expected values about which uncertainties of different origin exist. Table 4 shows that both RCMs predict a reduction in the mean annual precipitation, accompanied by an increase in the mean annual temperature with respect to the control period. In particular, the RCAO E model projects a reduction of 21.8% for the mean annual precipitation and an increase of +6.3°C for the mean annual temperature. 

We have made references in the foregoing discussion to the precision of data, or how precise the data are. We have also made reference to the accuracy of data. Precision refers to the repeatability of a measurement. If you repeat a given measurement over and over and these measurements deviate only slightly from one another, within the limits of the number of significant figures obtainable, then we say that the data are precise, or that the results exhibit a high degree of precision. The mean of such data may or may not represent the real value of that parameter. In other words, it may not be accurate. Accuracy refers to the correctness of a measurement, or how close it comes to the correct value of a parameter. 

The state function property of the enthalpy should be kept in mind for the next move of our discussion. In figure 2.1 we have decomposed reaction 2.1 in a series of steps whose net effect must correspond to the overall reaction. This means that the correct value for Asin//(2) is the solution enthalpy of 1 mol of oxygen in the (ethanol + water) mixture described—and not the solution enthalpy of the gas in pure water. Unfortunately, solution enthalpy data in organic liquid mixtures are not abundant in the chemical literature. So, either we are lucky to find them, we have the equipment to measure them in the laboratory, or we assume that the values will be identical to the ones in the pure solvent. The validity of this assumption depends on the system under discussion and on the accuracy needed for the final result, but in the present case it seems fair. Leaving further discussion to section 2.5, we shall take Asin//(2) = -12 4 kJ mol-1 [17],... 

We keep moving in the eorreet direction at this fixed step size until there is a change in e sign of the term (P - p ). This means we have erossed over the correct value of T. Then we back up halfway, i.e., we halve the increment AT. With each successive iteration we again halve AT, always moving either up or down in temperature. 

We should first correct the wavevector inside the crystal for the mean refractive index, by multiplying the wavevectors by the mean refractive index (1 + IT). This expression is derived from classical dispersion theory. Equation (4. 18) shows us that is negative, so the wavevector inside the crystal is shorter than that in vacuum (by a few parts in 10 ), in contrast to the behaviom of electrons or optical light. The locus of wavevectors that have this corrected value of k lie on spheres centred on the origin of the reciprocal lattice and at the end of the vector h, as shown in Figure 4.11 (only the circular sections of the spheres are seen in two dimensions). The spheres are in effect the kinematic dispersion surface, and indeed are perfectly correct when the wavevectors are far from the Bragg condition, since if D 0 then the deviation parameter y, 0 from... 

In a situation such as that described in Fig. 4, there is no difficulty in establishing the value for AT. However, when fluid is flowing through a pipe surrounded by a medium at another temperature, the fluid s temperature changes as it travels down the pipe and, consequently, the temperature difference varies with position along the pipe. In such cases, it can be shown that the correct value of AT to use in eqn. (74) is the logarithmic mean temperature difference, ATy which is given by... 

Details of dating There is a strange and confusing convention in dating. Although it is accepted that the most accurate half-life is 5730 years (mean life of 8267 years and decay constant of 0.00012097 yr ), an older value of the half-life of 5568 years (and hence a mean life of 8033 years and a decay constant of 0.00012449 yr, 2.9% different from the correct value) is conventionally used in calculating the age. This convention is adopted to avoid confusion between age reported in old literature and that reported in new literature. 

Although in this case the indirect estimate of the intramolecular bonding leads to the correct value, this simple condition does not gener ally prevail (idem, ibid.). It is probable that proton magnetic resonance spectra will provide the best means of assessing intramolecular bond energies—and their practical and theoretical interest is considerable. 

Another problem is the equilibrium concentration cL. Use of the correct value of cL is essential for calculating a correct A , a. The value for cL is derived from the gas phase ozone concentration by applying Henry s Law. It is evident that the value calculated for the effluent gas will be lower than that calculated for the influent gas. In small laboratory scale ozonation reactors, such as STRs, a mean value can be calculated ... 

Figure 12-2 shows the results of Equation 12-18. The meanings of the dashed curves are similar to the meanings of the dashed curves in Figure 12-1. The solid curve represents the solution to Example 12-4 in which a correct value of 0.547 moles is obtained for nL.

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