Bimodal data

Figure 2.4 Individual changes in a global assessment score. Neither mean nor median indicates a typical value with bimodal data. Only modes achieve this...

Figure 3.1 Bimodal data. Isoniazid concentrations ((.ig/mL) 6 h after a standard oral dose...

Data for CAIs from CH chondrites are shown in Figure 26(b) (unpublished data courtesy of K. D. McKeegan and A. N. Krot). The bimodal data reflect two apparent populations of CAIs and not variations within individual CAIs. 

Figure A3.9.3. Time-of-flight spectra for Ar scattered from Pt(l 11) at a surface temperature of 100 K [10], Points in the upper plot are actual experimental data. Curve tinough points is a fit to a model in which the bimodal distribution is composed of a sharp, fast moving (lienee short flight time), direct-inelastic (DI) component and a broad, slower moving, trapping-desorption (TD) component. These components are shown...

The mode of distribution is simply the value of the most frequent size present. A distribution exhibiting a single maximum is referred to as a unimodal distribution. When two or more maxima are present, the distribution is caUed bimodal, trimodal, and so on. The mode representing a particle population may have different values depending on whether the measurement is carried out on the basis of particle length, surface area, mass, or volume, or whether the data are represented ia terms of the diameter or log (diameter). 

One further point might be made here. Although the example illustrates the difference between the two types of molecular weight average, the weight average molecular weight in this example cannot be said to be truly representative, an essential requirement of any measure of central tendency. In such circumstances where there is a bimodal, i.e. two-peaked, distribution additional data should be provided such as the modal values (100 and 100000 in this case) of the two peaks. 

Figure 1 and Table 1 show the data obtained using PIB s prepared with the f-BuCl/ Et2AlCl/MeCl system in the -30° to -65 °C range. PIB s prepared in the range from —30° to —45 °C have monomodal MWD while those prepared below -45 °C exhibit bimodal distributions. MWD s broaden with decreasing polymerization temperature. 

Miyashita (1995) proposed that the epithermal mineralizations in Hokusatsu district (Kyushu) are related to strata volcanoes in the volcanic depression and not to caldera formation, hy compiling the data on the ages of mineralization and volcanic activities, gravity and geology. He considered that the Hokusatsu volcanic depression zone is an extension of the Okinawa Trough. This volcanic depression started from 5-6 Ma (Kamata and Watanabe, 1985), where bimodal volcanism is found. 

L.S. Ramos, E. Sanchez and B.R. Kowalski, Generalized rank annihilation method. II Analysis of bimodal chromatographic data. J. Chromatog., 385 (1987) 165-180. 

One characteristic of shear banded flow is the presence of fluctuations in the flow field. Such fluctuations also occur in some glassy colloidal materials at colloid volume fractions close to the glass transition. One such system is the soft gel formed by crowded monodisperse multiarm (122) star 1,4-polybutadienes in decane. Using NMR velocimetry Holmes et al. [23] found evidence for fluctuations in the flow behavior across the gap of a wide gap concentric cylindrical Couette device, in association with a degree of apparent slip at the inner wall. The timescale of these fluctuations appeared to be rapid (with respect to the measurement time per shear rate in the flow curve), in the order of tens to hundreds of milliseconds. As a result, the velocity distributions, measured at different points across the cell, exhibited bimodal behavior, as apparent in Figure 2.8.13. These workers interpreted their data... 

Our initial studies (23) were performed in toluene, and Table I shows the results from the polymerization of a number of representative monomers. The data reported in Table I are for direct addition of the monomer to the sodium dispersion. Inverse addition often leads to higher molecular weights, although the overall polymer yields are usually lower (15,23). The results in Table I show that, under these reaction conditions, a bimodal molecular molecular weight distribution is normally obtained. Furthermore, it is obvious that the crude polymer yields drop precipitously as the steric hindrance in the monomer increases. 

The bimodal feature in the lower wavelength images is accounted for by the presence of the two processes for which evidence has been presented above. There is also a clear bimodality in the data from 266 nm dissociation. The energy distribution displays peaks at 2.7 and 3.6 eV. This distribution raises further questions since the process creating > 26) at lower... 

The raw data in the more comprehensive study (61) were conversions, determined in duplicate, when each of 104 coals selected from three geological provinces was heated with tetralin under standard conditions, together with the results of 14 commonly made analytical determinations for each coal. An early observation in this study was that when data for all 104 samples were plotted against volatile matter, a steady decrease of conversion with decreasing volatile matter was apparent. But there was a great deal of scatter (r=0.85). In any case, the formal requirements that make possible the employment of valid statistical analyses were not met by the data matrix, as evidenced by skewed and bimodal relationships between the variables the sample set was heterogeneous. ... 

In Fischer-Tropsch synthesis the readsorption and incorporation of 1-alkenes, alcohols, and aldehydes and their subsequent chain growth play an important role on product distribution. Therefore, it is very useful to study these reactions in the presence of co-fed 13C- or 14 C-labeled compounds in an effort to obtain data helpful to elucidate the reaction mechanism. It has been shown that co-feeding of CF12N2, which dissociates toward CF12 and N2 on the catalyst surface, has led to the sound interpretation that the bimodal carbon number distribution is caused by superposition of two incompatible mechanisms. The distribution characterized by the lower growth probability is assigned to the CH2 insertion mechanism. 

Later Rytter et al. reported possible polymer chain exchange with polypropylene produced with a combination of 8 and 11 with TMA [32], The number of stereoerrors increased in the binary system at higher TMA levels. As discussed in the case of Przybyla and Fink (vida supra), pentad analysis is less compelling evidence for reversible chain transfer. In addition, the gel permeation chromatography (GPC) data showed bimodal peaks, indicating very limited reversible transfer. 

The L-mode analysis of the simulated taxonic data produced a bimodal distribution, while analyses of the simulated nontaxonic data and the actual data revealed only one mode. What this means is unclear. It is possible that depression is actually taxonic, but the simulated taxonic data does not adequately reflect the structure of the actual data set. For example, higher nuisance correlations and lower indicator validities in the actual data may not have allowed a latent bimodality to emerge, even though this was detected in the simulated data. Another possibility, of course, is that the BDI items do not define a taxon. 

The basis of all performance criteria are prediction errors (residuals), yt - yh obtained from an independent test set, or by CV or bootstrap, or sometimes by less reliable methods. It is crucial to document from which data set and by which strategy the prediction errors have been obtained furthermore, a large number of prediction errors is desirable. Various measures can be derived from the residuals to characterize the prediction performance of a single model or a model type. If enough values are available, visualization of the error distribution gives a comprehensive picture. In many cases, the distribution is similar to a normal distribution and has a mean of approximately zero. Such distribution can well be described by a single parameter that measures the spread. Other distributions of the errors, for instance a bimodal distribution or a skewed distribution, may occur and can for instance be characterized by a tolerance interval. 

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