Data error bars

Fig. 4.3. (A) Composite multispecies benthic foraminiferal Mg/Ca records from three deep-sea sites DSDP Site 573, ODP Site 926, and ODP Site 689. (B) Species-adjusted Mg/Ca data. Error bars represent standard deviations of the means where more than one species was present in a sample. The smoothed curve through the data represents a 15% weighted average. (C) Mg temperature record obtained by applying a Mg calibration to the record in (B). Broken line indicates temperatures calculated from the record assuming an ice-free world. Blue areas indicate periods of substantial ice-sheet growth determined from the S 0 record in conjunction with the Mg temperature. (D) Cenozoic composite benthic foraminiferal S 0 record based on Atlantic cores and normalized to Cibicidoides spp. Vertical dashed line indicates probable existence of ice sheets as estimated by (2). 3w, seawater S 0. (E) Estimated variation in 8 0 composition of seawater, a measure of global ice volume, calculated by substituting Mg temperatures and benthic 8 0 data into the 8 0 paleotemperature equation (Lear et al., 2000).

Figure 9. The observed variation of the coincidence count rates as functions of the phase of entangled photons 0 at zero delay for the photon-number entangled photons. Solid triangles represent the two-fold coincidences with Da Da and show the phase of input photons. Solid diamonds represent the four-fold coincidences with Di D2 Da Da which show the phase of the output photons demonstrating a successful NS operation. Error bars are based on the usual Poisson fluctuation in the number of counts on the uncorrected data (error bars of two-fold coincidences are too small to display). The phase of four-fold coincidence is shifted (1.05 0.06) tv against two-fold coincidence in agreement with the expected tv phase shift.

Figure 2 Experimental and predicted methane hydrate dissociation (si) conditions in the presence MEG (Model predictions are independent from experimental data) (Error bars 1 °C, only for visual purpose)...

While previous statistical attempts at using SEM analysis to relate a 2D projection of the 3D pore structure proved unsuccessful, correlations do exist between the pore diameter and screen properties for all meshes examined in the current work. Figures 10.2 and 10.3 plot the effective pore diameter against the shute wire diameter and the square root of the number of pores per square inch of screen ( nwarp shute). respectively for the 26 screens that have room temperature bubble point data. Error bars are also plotted in both figures, but are barely distinguishable. 

Figure 10.6a and h plot the model generated curves against data for normally saturated liquid states in LH2 and LN2, respectively. LH2 saturated state data is taken from Chapter 5, while the saturated LN2 data is taken from LN2 data collected edongside other cryogenic bubble point data. Error bars are plotted but are barely distinguishable. Excellent agreement is seen between LH2 data and new temperature dependent bubble point model. The model also matches LN2 data reasonably well, despite some scatter in the GN2/LN2 bubble point data taken in warmer liquid states. 

Data Reduction and Analysis For inhibition profiles, the means of triplicate data points (at individual inhibitor concentrations) were plotted. IC50 values were determined using either a log-logit or four parameter fit. (Correlation coefficients were determined from the best fit of these data.) Error bars representing standard deviations (SD) are only presented in selected inhibition profiles. Paraoxon equivalence (%), PE, was determined using the following relationship ... 

Figure B2.5.19. The collisional deactivation rate constant /c, (O3) (equation B2.5.42 ) as a fimction of the vibrational level v". Adapted from [ ]. Experimental data are represented by full circles with error bars. The broken curve is to serve as a guide to the eye.

Fig. 3. Release rate of pilocarpine from Ocusert Pilo-20. Data points shown with standard deviation error bars (94).

Fig. 7 gives an example of such a comparison between a number of different polymer simulations and an experiment. The data contain a variety of Monte Carlo simulations employing different models, molecular dynamics simulations, as well as experimental results for polyethylene. Within the error bars this universal analysis of the diffusion constant is independent of the chemical species, be they simple computer models or real chemical materials. Thus, on this level, the simplified models are the most suitable models for investigating polymer materials. (For polymers with side branches or more complicated monomers, the situation is not that clear cut.) It also shows that the so-called entanglement length or entanglement molecular mass Mg is the universal scaling variable which allows one to compare different polymeric melts in order to interpret their viscoelastic behavior. 

This same data is plotted in the chart on the following page. The mean absolute deviation and standard deviation are plotted as points with error bars, and the shaded blocks plot the largest positive and negative-magnitude errors. 

Figure 6-14. Average domain size vs. inverse deposition temperature Tor different film thicknesses. Error bars represent the mean absolute error and straight lines the best lit for each film thickness. Doited line is the locus of the transition from grains to lamellae. Data for 50-nm films are estimated from the correlation length of the topography fluctuations. Adapted from Ref. [501.

Fig. 3.13. Density-dependence of the Qo, branch line width y of methane (the dashed line is for pure vibrational dephasing, supposed to be Unear in density), (o) experimental data (with error bars) [162] Top part rotational contribution yR and its theoretical estimation in motional narrowing limit [162] (solid line) the points were obtained by subtraction of dephasing contribution y

Figure 2.9. The confidence interval for an individual result CI( 3 ) and that of the regression line s CLj A are compared (schematic, left). The information can be combined as per Eq. (2.25), which yields curves B (and S, not shown). In the right panel curves A and B are depicted relative to the linear regression line. If e > 0 or d > 0, the probability of the point belonging to the population of the calibration measurements is smaller than alpha cf. Section 1.5.5. The distance e is the difference between a measurement y (error bars indicate 95% CL) and the appropriate tolerance limit B this is easy to calculate because the error is calculated using the calibration data set. The distance d is used for the same purpose, but the calculation is more difficult because both a CL(regression line) A and an estimate for the CL( y) have to be provided.

Fig. 11. Capillary data showing an increase in the release of intracellular calcium content (340/380 ratio) as s increases. Data refer to experiments in which the cell suspension was circulated through a fine bore capillary for 15 min. Error bars represent the 8.0% standard deviation [87]...

Fig. 14. Calcium response of Sf-9 insect cells subjected to different values of e in a stirred bioreactor equipped with a 5.1 cm diameter 6-bladed Rushton impeller (closed circles) or in the capillary flow system (open squares). Error bars for stirred bioreactor are standard deviation for each experiment but for the capillary, data are hard to discern [99]...

Fig. 2. Whole cell biocatalytic reactions for four types of recombinant whole cell systems. Bioconversion reactions were performed in resting cell condition. All data were based on unit cell concentration (1 mg-dry cell weight ml ). Each value and error bar represents the mean of two independent experiments and its standard deviation.

Figure 15. Circular dichroism of the C=0 C li peak (BE = 292.7 eV) in fenchone at three different photon energies, indicated, (a) Photoelectron spectrum of the carbonyl peak of the (1S,4R) enantiomer, recorded with right (solid line) and left (broken line) circularly polarized radiation at the magic angle, 54.7° to the beam direction, (b) The circular dichroism signal for fenchone for (1R,4A)-fenchone (x) and the (lS,41 )-fenchone (+) plotted as the raw difference / p — /rep of the 54.7° spectra, for example, as in the row above, (c) The asymmetry factor, F, obtained by normalizing the raw difference. In the lower rows, error bars are included, but are often comparable to size of plotting symbol (l/ ,4S)-fenchone (x), (lS,4R)-fenchone (+). Data are taken from Ref. [38],...

FIG. 6 Dependence of the square root of the SHG intensity ( I(2a>)) for membrane 2 without KTpCIPB (a) with KTpCIPB (b) on K+ ion concentrations in the adjacent aqueous solution containing KCl (O) and KSCN ( ), respectively. Inset The corresponding observed EMF to KCl and KSCN. The concentrations of ionophore 2 and KTpCIPB were 3.0 X 10 M and 1.0 x 10 M, respectively for both SHG and EMF measurements. The data points present averages for three sets of measurements. Error bars show standard deviations. (From Ref. 15.)... 

Figure 4. Fits of lattice strain model to experimental mineral-melt partition coefficients for (a) plagioclase (run 90-6 of Blundy and Wood 1994) and (b) elinopyroxene (ran DC23 of Blundy and Dalton 2000). Different valence cations, entering the large cation site of each mineral, are denoted by different symbols. The curves are non-linear least squares fits of Equation (1) to the data for each valence. Errors bars, when larger than symbol, are 1 s.d. Ionic radii in Vlll-fold coordination are taken from Shannon (1976).

Figure 19. Variation in dimension of the X-fold cation site in alkali-feldspar for 2+ cations (), obtained by fitting the experimental data of Icenhower and London (1996) for Dca, >sr and Dsa at 0.2 GPa and 650-750°C. In performing the fits was set at 91 GPa for all runs. Error bars are 1 s.d. The positive slope is consistent with measured changes in metal-oxygen bond length from albite to orthoclase (cf Fig. 6). The solid line shows the best-fit linear regression given in Equation (35).

Overall, the accuracy reached by the hybrid functionals tested is quite pleasing, in particular if we keep in mind the favorable scaling of computational demands and the obviously much lower basis set requirements. The binding energy of the water molecule computed with the B3LYP and the mPWIPW functional miss the lower experimental error bar by only 0.1 kcal/mol and approach quite closely the best available conventional wave function based data. 

Figure 5.24(B) shows a line profile extracted from the map of Figure 5.24(A) by averaging over 30 pixels parallel to the boundary direction corresponding to an actual distance of about 20 nm. The analytical resolution was 4 nm, and the error bars (95% confidence) were calculated from the total Cu X-ray peak intensities (after background subtraction) associated with each data point in the profile (the error associated with A1 counting statistics was assumed to be negligible). It is clear that these mapping parameters are not suitable for measurement of large numbers of boundaries, since typically only one boundary can be included in the field of view.

Figure 5.25. (A) Quantitative Cu map of an Al-4wt% Cu film at 230 kX, 128 x 128 pixels, probe size 2.7nm, probe current 1.9 nA, dwell time 120 msec per pixel, frame time 0.75 hr. Composition range is shown on the intensity scale (Reproduced with permission by Carpenter et al. 1999). (B) Line profile extracted from the edge-on boundary marked in Figure 5.25a, averaged over 20 pixels ( 55 nm) parallel to the boundary, showing an analytical resolution of 8nm FWTM. Error bars represent 95% confidence, and solid curve is a Gaussian distribution fitted to the data (Reproduced with permission by Carpenter...

Fig. 3 Semilogarithmic plot of concentration versus time for the hydrolysis of ethyl acetate. (Data shown in Table 2. One standard deviation is indicated by error bars.)...

In crystals, the scattering densities are periodic and the Bragg amplitudes are the Fourier components of these periodic distributions. In principle, the scattering density p(r) is given by the inverse Fourier series of the experimental structure factors. Such a series implies an infinite sum on the Miller indices h, k, l. Actually, what is performed is a truncated sum, where the indices are limited to those reflections really measured, and where all the structure factors are noisy, as a result of the uncertainty of the measurement. Given these error bars and the limited set of measured reflections, there exist a very large number of maps compatible with the data. Among those, the truncated Fourier inversion procedure selects one of them the map whose Fourier coefficients are equal to zero for the unmeasured reflections and equal to the exact observed values otherwise. This is certainly an arbitrary choice. 

After a simple Fourier inversion of a set of magnetic structure factors MbU, one can retrieve the magnetisation density. A much better result, e.g. the most probable density map, can be obtained using the Maximum Entropy (MaxEnt) method. It takes into account the lack and the uncertainty of the information not all the Bragg reflections are accessible on the instrument, and all the values contained in the error bars are satisfactory and have to be considered. However, as this method extracts all the information contained in the data, it is important to keep in mind that it may show spurious small details associated to a low accuracy and/or a specific lack of information located in (/-space. 

Fig. 25. Comparison between the experimental abstraction reaction H + H2O(00)(0) cross-section (solid point with error bars), and the 5D QM calculations (solid line). The 6D QM cross-sections with the CS approximation (dotted line), and the QCT data using normal (o) and Gaussian (A) binning procedures are shown.

Figure 9 Influence of hexamethylene amiloride, an Na+/H+ exchange inhibitor, on the corneal and conjunctival permeability of (A) mannitol and (B) atenolol. Error bars denote mean SEM for n = 4. (Kompella, Kim, and Lee, unpublished data.)...

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