Deviation Plot

Fig. 4.13. Evidence for the presence of 5 2 per cent 6Li in the warm halo subdwarf HD 84937 with [Fe/H] = -2.4, 7 = 6090 K. The left panel shows synthesized profiles for 0, 5 and 10 per cent 6Li with the observational points on an absolute wavelength scale in the rest frame of the stellar photosphere. The right panel shows the central wavelengths of the doublets of each isotope and a deviation plot for the three hypotheses on 6Li/7Li. Adapted from Smith, Lambert and Nissen (1993).

Figure 2. Interference fringe deviation plots for Gouy diffusion of reacting hemocyanin at a — 0.92. Points are experimental (------), simulation...

Figure 6. Bond length deviation plotted against quadrupole splittihg of Fe3+ ions in a variety of distorted coordination sites in minerals.

Figure 4 Bootstrap standard deviation plot exhibiting the possibility for qualitative identification of polymer film coating endpoint. Dashed line indicates the three-standard deviation limit for spectral similarity. Near-IR spectra from 10 samples obtained at the 16% theoretical applied solids level were used as a training group.

In column G calculate the averages of 30 consecutive data points, and in column H the corresponding standard deviations. Plot the resulting thirty-point averages, with their individual error bars. Figure 2.2-5 shows an example. 

Misfits can be made more apparent by plotting the deviation of the experimental value from the parity line on the y-axis against the experimental value itself on the x-axis. Such plots should be generated routinely for the overall experimental data-set or for appropriate subsets of data. In general, two types of phenomena are observed in such deviation plots. 

The scatter is uniform about the x-axis. In this case there is no trend in the scatter and the sum of the deviations tends to zero. A linear regression of this data gives zero intercept and zero slope for the deviation plot. This behaviour identifies random noise as the cause of the scatter. Trends in the scatter become apparent and may well differ between distinguishable sets of data from the overall parity plot. The trends seen can be monotonic or linear or even weave around an overall trend. This behaviour identifies distortion as the cause of the misfit. 

The parity plot of a fit obtained using the SSR as a criterion offit is shown in the first part of this figure. The corresponding deviation plot shows that errors are not evenly distributed about zero and distortion seems to be present in the several of the reactant compositions tested... 

Which fit is better Figure 10.2 clearly shows less distortion on the deviation plot even though the SSR for this fit is higher. Often improvements in fit can be obtained by fitting with restricted sets of the variables, after the global fit using all the variables has settled into a minimum. This and other procedures are given at the end of the chapter. 

The clearest sign that distortion is present is seen when the noise about the distorted trend is small relative to the distortion. Distortion then clearly indicates that a correlation exists in the data but it is not the correlation being attempted. This reading of the deviation plot offers an opportunity to use the information thus supplied to improve the fitting criterion in searching for the best parameters. The conventional numerical SSR criterion ignores the form of the deviation revealed on the deviation plot and cannot satisfactorily deal with distortion. 

Figure 10.4 shows an example of distortion in fitting the same data as that in Figures 10.1 and 10.2. Convergence on the line of parity is excellent but the deviation plot clearly shows that deviations exist and differ for the several reaction condition sets used. The statistical fit as measured by the SSR and SUD is not bad when compared with the results reported above. 

A fit showing good convergence on the line of parity but significant distortion when viewed on the deviation plot. 

Figure 6. A deviation plot for the Group C histogram in Figure 5. Dev = 100[cal-...

The accuracy difference between Eqs. (3.50) and (3.51) is illustrated with the deviation plot shown in Figure 3.9. Coefficients for Eq. (3.51) for a large number of substances are given in [28]. 

Figure 3.9 Density deviation plot for R125 (pentafluo-roethane) for the PPDS and Rackett equation. (Data from Widiatmo et al. [46].)...

Figure 3.11 Deviation plots for the enthalpy of vaporization of propane using the extended Watson equation and the PPDS equation. Reference data from high-precision equation of state [10].

In Figure 3.19, the deviation plots of the PPDS and the extended Kirchhoff equation for viscosity data of R134a (1,1,1,2-tetrafluoroethane) are compared. The superior flexibility of the PPDS equation is clearly demonstrated especially the viscosities at low temperatures and in the vicinity of the critical point are much better reproduced. Coefficients for Eq. (3.110) can be found in [28]. 

Figure 3.19 Deviation plots of the PPDS and the extended Kirchhoff equation for liquid viscosities of R134a. (Data from Okubo et al. [65], Oliveira and Wakeham [66], Assael et al. [67], and Lavrenchenko et al. [68].)...

Figure E.2 shows the deviation plot for the vapor pressure curve of R134a which could be fitted reasonably well with the Wagner equation. The deviations are scattered around the zero line, and a systematic error cannot be detected.

Figure E.3 Deviation plot for the vapor pressure regression correlation is not flexible enough (Antoine equation).

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