Y error bars

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.

IP Set up a spreadsheet to reproduce Figure 4-13. Add error bars Double click on a data point on the graph and select Y Error Bars. Check Custom and enter the value of sy in each box for the + and — error. Better yet, enter the cell containing sy in both boxes. 

Perhaps the most common situation involving graphing scientific data is to generate a linear regression plot with y error bars. In most situations, the error in the x data is regarded as being so much smaller than that of the y data that it can... 

Figure 11.6 Summary of single particle fluorescence vs. SPR peak position measurements by Chen et al. with three different fluorescent dyes. The SPR peak positions are binned in 20 nm intervals along the x-axis. The average fluorescence intensity observed from particles within each bin is then plotted as a fimction of the SPR position for silver nanoprisms functionalized with (A) Alexa Fluor 488, (B) Alexa Fluor 532, and (C) Rhodamine Red dyes. The excitation spectra (dotted lines) and emission spectra (dashed lines) are plotted for reference for each dye. The solid line is a guide to the eye. Y-error bars represent the standard deviation of the mean fluorescence intensity observed from particles with SPR peaks within each 20 nm bin. D) Schematic illustrating use of DNA oligonucleotides to conjugate fluorophores a finite distance from the nanoprism surface. Reprinted with permission from reference [25] (2007)...

To add error bars, click on one of the points to highlight all points on the graph. In Chart Tools, Layout, select Error Bars and choose More Error Bars Options. For Error Amount, choose Custom and Specify Value. For both Positive Error Value and Negative Error Value, enter D4 D9. You just told the spreadsheet to use 95% confidence intervals for error bars. When you click OK, the graph has both jc and y error bars. Click on any jc error bar and press Delete to remove all jc error bars. 

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

Error bars defined by the confidence limits CL(y,) will shrink or expand, most likely in an asymmetric manner. Since we here presuppose near absence of error from the abscissa values, this point applies only to y-transformations. A numerical example is 17 1 ( 5.9%, symmetric CL), upon logarithmic transformation becomes 1.23045 -0.02633. .. 1.23045 + 0.02482. 

Fig. n.i. Human duodenal expression variability of peptide and amino acid transporters (our unpublished data). Shaded box indicates 25-75% of expression range, the line within the box marks the median, and error bars indicate 10-90% of expression range. PEPT1, di-, tri-peptide transporter HPT1 (Ll-cadherin) peptide transporter SLC3A1, cystine, dibasic and neutral amino acid transporter y+LATl, cationic amino acid transporter ATBq, neutral... 

Fig. 2.2 Stability of IgCi monoclonal antibody added to sterile plant and animal cell culture media. ( ) Murashige and Skoog (MS) medium (A) Dulbecco s minimal essential medium (DMEM) with 10% serum and (A) serum-free Ex-cell 302 medium. The error bars indicate standard errors from triplicate flasks. (Reproduced with permission, from B. M. -Y. Tsoi and P. M. Doran, Biotechnol. Appi. Bio-chem. 2002, 35, 171-180. Portland Press on behalf of the IUBMB.)...

Ref. 31 Xs=0 87 x 10- esu for CHCI3 and Xs=l 06 x 10 esu for hexane. There are no two-photon resonances in the solvents in the frequency range of interest here (31). The resulting values of Y t and y"t> with 90% confidence limits expressed as error bars, are shown in Fig. 9. Each data pair is determined from the... 

Figure 22. The dependence of the A exciton shifts on the number of layers in the IF structure (90). The x error bar represents the distribution of the number of layers determined with TEM for each sample. The y-axis error bar is 10 meV.

When any experimental measurements are plotted on a graph, the errors should also be plotted, using a pair of error bars. These extend on either side of the point in both x and the y direction and give a visual impression of the size of the errors for that particular measurement. If the errors for all the points on the graph are roughly the same, it is acceptable to mark this as a single set of error bars somewhere away from the actual points. 

Fig. 22 Plot of C-OX bond length versus Hammett a for the aromatic substituent Y for triphenylmethyl ethers and esters [108]. The error bars represent two standard deviations in the bond-length measurements. Reprinted with permission from Edwards et al. (1986a). Copyright 1986 American Chemical Society.

Figure 2. The composite standard calibration for the quantification of salvinorin A by HPLC (the error bars indicate 1 standard deviation the linear regression equation for the calibration curve is y= 759,334x 44,127).

Here is a least-squares problem that you can do by hand with a calculator. Find the slope and intercept and their standard deviations for the straight line drawn through the points (x.y) = (0,1), (2,2), and (3,3). Make a graph showing the three points and the line. Place error bars ( sv) on the points. 

In the upper portion, the observed data are shown by the dots with error bars the calculated pattern is shown as the solid line pattern. In the central portion, the vertical markers show positions calculated for Bragg reflections. The lower portion is a plot of the y, difference, observed minus calculated. Gaussian profiles were used, 28 parameters were varied, and Rp = 12%, R p = 14%. 

Figure 3. Relationship between leaf area (A), epidermal cell density (B), stomatal density (C) and stomatal index (D) versus altitude for Nothofagus solandri leaves growing on the slope of Mt. Ruapehu, New Zealand (collected in 1999). Black diamonds indicate the mean of ten counting fields on each leaf, white squares are the averages of five to eight leaves per elevation, with error bars of 1 S.E.M. Nested mixed-model ANOVA with a general linear model indicates significant differences for all factors (p = 0.000). Averages per elevation were used for regression analysis A. y = -0.0212 + 73.1 R2 = 0.276 p = 0.147. B. y = 1.70 + 3122 R2 = 0.505 p = 0.048. C. y = 0.164 + 360 R2 = 0.709 p = 0.009. D. linear (dashed) y = 0.004 + 9.33 R2 = 0.540 p = 0.038 non-linear (solid) y = 0.00001 2 - 0.0206 + 21.132 R2 = 0.770.

For a sample measured for 3He with an exposure time f of 100 1 kyr, L of 160 10 g cm-2, Pno of 103 4 atoms g 1 yr-1, z(0) of 1033.2 g cm-2, and expected 3He concentrations with 10% uncertainty, the lo uncertainties of v range from 200 m at low paleoelevations to 500 m at high paleoelevations (Fig. 3). The elevation dependence of the error bars stems from the uncertainty in Ln. The 10% uncertainty in N accounts for 1000 m of uncertainty in y. We caution that this simple error analysis represents only a minimum assessment of uncertainty since it does not include any uncertainty in the sample s depth history. 

Fig. 3 Mass and thermal diffusion coefficients D and Z>r as functions of reduced temperature . Literature PCS data for D taken from Meier [8] and Sato [92] (scattering angle 60° (open diamond) and 130° (open square)). See text for a discussion of the fit functions. Also shown Dj (upper curve, right y-axis) for the same temperature range together with fit function containing only thermal activation (dotted line). Open diamonds data with unclear error bars due to very long equilibration times. Note the different units of the two y-axes...

The three monomers yield similar small values of y with a deviation that is nevertheless larger than the experimental 10% error bar. The increase in the nonlinearity is concurrent with a shift in the absorption spectra to slightly longer wavelengths. The end groups can act as a very weak donor, with the donating effects smaller for TMS than TES and TIPS. 

FIGURE 16.14 MFFS data for the PS flame retarded formulations measured in the RPA. The error bars represent a standard uncertainty of +lo. The data points labeled with a single number are the pure APP/PER (3 1) in PS, where the number refers to the mass fraction (%) of APP/PER. All two number labels (X-Y) refer to the mass fraction (%) of APP/PER (X) and organoclay (Y) in the APP/PER-15A-PS blends. 

Figure 5.22 Reduced matrix elements dy, in atomic units, and relative phases (<5, — <5V), in radians, as functions of photon energy for 5p photoionization in xenon leading to the 5p5 2P3/2 final ionic state. The dashed vertical lines give the 2P3/2 and 2P,/2 ionization thresholds at 12.13 and 13.44 eV, respectively. The data in the continuous range above the 2P1/2 threshold are shown as full circles with error bars. The curves below the 2P3/2 and 2P,/2 ionization thresholds are expected to approach the values in the continuum continuously (for details see the discussion and references in the original publication). From [HSS86] the d, given here are larger by y/3 in order to adapt them to the cross section...

Fig. 5. Plasma concentration of intact 125I-cystatin C( ), 51Cr-EDTA ( ) and 131I-aprotinin(Y) relative to the initial plasma concentration after intravenous injection in 12 rats. Error bars show 1 SEM, when larger than the symbols. Aprotinin is a 6.5-kDa microprotein with a pi of 10.5.

Figure 5 Plot of the integrated Ols "shake-up" intensity (left y-axis) from fig. 2 and energy in eV (right y-axis) relative to the Ols carbonyl emission at various curing temperatures. Error bars are estimated.

Figure 3. Scaled energy transport curve. The data points and designations are the same as in Figures 1 and 2. Error bars were added to a few points to indicate experimental uncertainties. The dashed lines are least-squares fits to the experimental data, giving y = 2.1 0.2 and B = 0.13 0.05.

LEED-IV derived coordinates of oxygen atoms in water molecules (Mj) for MgO( 100)3x2-H2O. The error bars are estimated to be 0.15 A for the in-plane x,y distances (see Fig. 2 for definition of x and y axes) and 0.05 A for the surface-atom distances z. The positions obtained from semi-empirical calculations are in parentheses (from Ref 9). 

In Figure 3, aluminum is representative of refractory elements in general and the Al/Si ratios indicate the size of the refractory component relative to the major fraction of the meteorite. It is clear from this figure that the Al/Si ratio of Cl meteorites agrees best with the solar ratio, although the ratios in CM (Type 2 carbonaceous chondrites) and even OC (ordinary chondrites) are almost within the error bar of the solar ratio. The errors of the meteorite ratios are below 10%, in many cases below 5%. A very similar pattern as for aluminum would be obtained for other refractory elements (calcium, titanium, scandium, REEs, etc.), as ratios among refractory elements in meteorites are constant in all classes of chondritic meteorites, at least within —5-10%. The average Sun/CI meteorite ratio of 19 refractory lithophile elements (Al, Ca, Ti, V, Sr, Y, Zr, Nb, Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, Dy, Er, Lu, see Table 2) is... 

Error bars are often an important part of the graphical presentation of scientific data. You can add error bars to either the Y Axis, the X Axis or both axes of XY charts. The procedure for adding error bars in the Y Axis will be described, since this is what you ll almost always be doing. 

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