Graph error bars

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. 

Figure 4 Effect on the serum stability of the incorporation of 5% cholesterol poly(ethy-lene glycol) (PEG) into cationic lipoplexes [hpopolyamine RPR209120/DOPE1/1, ratio (mol) lipid/DNA = 10 in 150 mM NaCl]. Lipoplexes were incubated in DMEM + 10% SVF, at 37°C, aliquots were regularly sampled and monitored by dynamic diffusion. Results represent a mean between three measurements. Error bars are not presented to simplify the graph, but differences among PEG, PEG-1, and PEG-2 are significant. Abbreviations PEG, poly(ethylene glycol) DOPE, dioleylphosphatidylethanolamine DMEM, Dulbecco s Modified Eagle Medium.

Fig. 9. Graph shows the logarithm of relative tumor volume as a function of days after treatment. Growth of tumors treated with adenovirus vector (dark square) or with radiation therapy (dark triangle) is diminished relative to that in the control group (light circle). Tumors receiving combined treatment (dark diamond) decreased in size over time. Error bars = SD.

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. 

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. 

Fig. 11.6. Bar graphs of the mean Raman depolarization ratio calculated from the parallel- and cross-polarized intensities of the 959 cm 1 PO43- peak. Data were obtained from 47 (sound) and 27 (caries) PRS measurements on 23 extracted teeth. Student s t-test analysis reveal p <0.001. Error bars show standard deviation...

Figure 2.3 Chamber gas phase and dust concentrations of DEHP in floor dust soiled on PVC flooring in CLIMPAQs for three different scenarios. The bar graphs show the dust concentrations (error bars are analytical 95% confidence intervals). The curves show...

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... 

By minimizing the error between b ) and the b simultaneously, which are respectively the intercept and the slope of the graph, one can find the best fit for the calculated data points. In (18.3), w, is the weight of the point on the line determined from the error bars in each isothermal-isobaric simulation. For the propagation of error, and in particular, by using the uncertainty in sums and differences and the uncertainty in products and quotients rules, the intersection of the lines, x, can be shown to be ... 

Figure 5.6 Odyssey Scanner results showing CCA enhancement of IRDye 800CW (Top two rows) and Alexa Fluor 680 (Bottom two rows) labelled streptavidin on glass slides. Scanner image (top) shows four CCA preparations (A-D) used to enhance the two near-IR fluorophores, as well as the fluorophores spotted on plain glass without CCA nanostructures added (Dye Alone). Bar graph (bottom) shows the relative fold enhancement over the Dye Alone samples for each of the CCA preparations. Error bars are shown that reflect the deviation between two samples for each preparation.

Figure 5.7 Linearity of CCA fluorescence enhancement. Two-fold serial dilutions of IRDye 800CW-labelled streptavidin are plotted. Each plotted point represents the average of 4 measurements, with one standard deviation shown by error bars. Note that only the error bars for the sample at 0.5pg is large enough to be visible on the graph.

Fifjure 6. Angular and kinetic energy distribution of the outgoing hydrogen atoms. Graphs a) and c) corresponds to the H + I exit channel, while b) and d) ndth the H + I channel. In the case a) and b) the dopant is placed in the second shell, while in the case c) and d) the dopant is on the surface, c) Simulation of the phorodissociation of the dopant on the surface (histogram) compared with a pick-up photodissociation experiment (line with error bars), f) Simulation of the photodissociation of the dopant in the sub-surface shell (histogram) compared with a pick-up photodissociation experiment (lino with error bars). 

As Figure 4 shows, the intensify response is linear across two orders of magnitude from 5 ppm (pmol/mol) up to 500 ppm. The intensities shown are after 10,000 averages with a gate dirration of 4 ps. The error bars represent 95% confidence hmits on the data points. This graph shows that qirantitative determination of gas-phase concentrations is possible using the CP-FTMW technique down to a level of 5 ppm imder the current spectrometer configuration. At concentrations above 500 ppm the response becomes non-linear. We attribute this to cluster formation in the supersonic expansion. 

Fig. 9. Graph of temperature rise vs. time as a function of microwave heating (and subsequent cooling periods), in a tumour induced in a rat. The temperature was measured using a Co chemical shift method. The error bars correspond to one standard deviation. (Fig. from ref. 113, Copyright 1996 by Academic Press, reproduced by permission of the publisher.)...

The shorthand instruction for using Trendline in Excel 95 might read Insert O Trendline, but if you look in the pull-down menu under Insert you may not find Trendline. The problem is that the Trendline option appears only after you have activated the graph (by double-clicking on an embedded chart, or by clicking on the tab of a separate chart). Even then, it shows but cannot be used for the latter, you must first select the particular data set in the graph to which you want it to apply. Only then can you select Trendline (or, for that matter, Error Bars). 

Plot the average absorbance values and 3SD error bars on a graph (see Fig. 3.) or enter the data in a table (see Table 1.). 

Fig. 57 Dependence of the signal intensity on the laser energy (266 nm). The irradiated area is about 1.25X10-3 cm2. A typical error bar is shown in the graph. The bandwidth of the IR probe is 8 creT1. REPRINTED WITH PERMISSION OF [Ref. 251], COPYRIGHT (1997) Elsevier Science...

Fig. 1.1 Morphological and biochemical studies (a) One biochemical approach to study enzymes is to analyze the activity levels with results plotted on a graph and to include error bars from multiple assays. The morphological approach gives information about where the enzyme is located. Three different types of liver cells are shown here as circular, elongated, and rectangular, (b) The enzyme (dark cells) can be located in all the different types of liver cells, (c) More likely the enzyme is found in only one cell type, the rectangular cells, (d) As a result of disease, the enzyme may be expressed in only a small number of cells in a single cell type, (e) Following an injury, the enzyme may be expressed in multiple cell types located near the injury sites...

Figure 1. Bar graphs showing changes in electronic particle count in PMN suspensions with and without drugs (1 x 10-6M RA-233 and 3 x 10 6M PGE, ). All incubations and shearing were done at 37°C. The unincubated samples were maintained at room temperature for the time specified. The 200 dyn/cm2 columns show no error bars as they represent the results of a single day s runs. Key , without drug (control) and , with drug.

Figure 1. C versus T (upper graph) computed using the histogram method. The solid line in the lower graph is the C versus T for the same annealing run computed using <( — < 2>T 2. The dotted line is <( — < 2>7"2 averaged over five runs. In both graphs, the error bars represent the 2a point, where a is variance observed over five runs.

Figure 27. Plot of ln(KEg) -F PAVg/RT vs. reciprocal temperature ror the reaction YAG + OH-apatite + 25/4 quartz = 5/4 grossular + 5/4 anorthite + 3 YPO4 monazite + 1/2 H2O. Solid squares = xenotime-bearing assemblages, open squares = xenotime-absent assemblages. Least squares regression line is fit to all data points. Horizontal error bars represent temperature uncertainty of 30°C. Vertical error bars ate la (In Kgq + PAV/RT), derived from propagation of uncertainties in P ( 1000 bars), T ( 30°C), AVrxn (1%), compositional parameters (0.001 mole fraction YAG, 0.01 mole fraction all others), and /(H2O) ( 7.5 1000 trial Monte Carlo simulation). Labels on graph indicate sample numbers. From Pyle et al. (2001).

Figure 8.1-6. The vertical bar graph illustrates the mean relative mechanical threshold of afferent fibers at various time points after a 10- xL injection of phosphate-buffered saline control (black bars, n = 10) or 25- xg/mL human NGF (gray bars, n = l) into the masseter muscle. The error bars represent the standard error of the mean. p < 0.05 ANOVA and post hoc Holm-Sidak method compared with the baseline relative mechanical threshold.

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