One standard deviation

In contr ast to the linear case, there are three degrees of freedom, but there is still only one standard deviation of the regression, s. The reader has the opportunity to try out these ideas in Computer Project 3-4. 

Precision Variation about the mean of repeated measurements of the same pollutant concentration expressed as one standard deviation about the mean. 

Emissions of gases or particles less than 20 microns (larger particles settle more quickly due to gravitational effects) disperse with an origin and plume centerline at the effective stack height. Pollutant concentrations are greatest within one standard deviation of the plume centerline. Thus, the determination of the value of these standard deviations is an important factor in calculating ambient concentrations. 

The gaussian distribution is a good example of a case where the mean and standard derivation are good measures of the center of the distribution and its spread about the center . This is indicated by an inspection of Fig. 3-3, which shows that the mean gives the location of the central peak of the density, and the standard deviation is the distance from the mean where the density has fallen to e 112 = 0.607 its peak value. Another indication that the standard deviation is a good measure of spread in this case is that 68% of the probability under the density function is located within one standard deviation of the mean. A similar discussion can be given for the Poisson distribution. The details are left as an exercise. 

Field Tests. Recently we conducted a field test at a site contaminated with fuel oil. Our measurements were 0.0625 0.0212 mA for the well water and 0.0189 0.0119 mA for distilled water (showing errors of one standard deviation). From calibration curves, these numbers can be reported as equivalent to 50 ppb phenol or 34 ppb xylenes. Nine-month-old laboratory results (EPA method 624 and GC/FID) for this site indicated concentrations of 25 ppb for benzene, toluene, and xylenes combined and 100 ppb for fuel oil. The important result is the significant difference between the distilled-water and well-water measurements. We are very encouraged by these results and are planning future field tests. 

Figure 2.3. Carbon and nitrogen isotope values of human bone collagen at Maya sites in Belize. The value for the modem sample has been corrected for collagen-hair spacing and the Industrial Effect. Boxes represent isotopic means one standard deviation.

For Klasies, although most values for both enamel and bone apatite fall within one standard deviation of the mean of (corrected) modem browser values (Fig. 5.5), some bone specimens fall outside this range. These enriched specimens suggest that a limited degree of equilibration with matrix carbonates has taken place, although inclusion of a limited amount of Q grass in the diet is a plausible alternative explanation for UCT 1025, Raphicerus sp. which as noted above could be the more opportunistic species, Raphicerus campestris. 

We see that the energy and time obey an uncertainty relation when At is defined as the period of time required for the expectation value of S to change by one standard deviation. This definition depends on the choice of the dynamical variable S so that At is relatively larger or smaller depending on that choice. If d(S)/dt is small so that S changes slowly with time, then the period At will be long and the uncertainty in the energy will be small. 

Conversely, if B ehanges rapidly with time, then the period A/ for 5 to ehange by one standard deviation will be short and the uneertainty in the energy of the system will be large. 

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.)...

Fig. 1. Comparisons of amino add compositions of ordered protein and disordered protein. (Top) Amino acid compositions of three disordered datasets. (Middle) Amino acid compositions of three ordered datasets. (Bottom) Compositions of disordered datasets relative to the Globular 3-D dataset (from Romero et al., Proteins Struct., Fund., Gen. 42, 38-48, copyright 2001. Reprinted by permission of Wiley-Liss, Inc., a subsidiary of John Wiley Sons, Inc.). The ordinates are (% amino acid in disordered dataset — % amino acid in Globular 3-D)/(% amino acid in Globular 3-D) = (D —0)/0. Negative values indicate that the disordered database has less than the ordered, positive indicates more than the ordered. Error bars are one standard deviation.

Results and discussion Some results of the indirect method obtained in the field work are shown in Table II., and they are compared with those of the direct method. Results of the two methods are barely in agreement within one standard deviation. The correction factor of Equation 3. used in the direct method was found not in a large error when the sampling time was less than about two half lives of Rn-220. 

Errors quoted are one standard deviation for several measurements. 

The historical background is presented for the asteroid-impact theory that is based on the iridium anomaly found in rocks frm the Cretaceous-Tertiary boundary. Recent measurements of Ir, Pt, and Au abundances from such rocks in Denmark have shown that the element abundance ratios are different from mantle-derived sources and agree with values for chondritic meteorites within one standard deviation of the measurement errors (7-10%). Rare-earth patterns for these rocks are... 

The relationship between the decrease in BMD and an increased fracture risk has been widely demonstrated, in all the measured skeletal regions and by different techniques (Melton et al. 1993 Marshall et al. 1996 Cummings et al. 1993). Marshall et al. (1996) demonstrated in a metaanalysis that one standard deviation decrease in BMD in lumbar spine, hip, or proximal radius increased the risk of fracture in these locations by 50 to 60% (Fig. 8.2). A different picture is seen, however, when the effects on BMD of the different antiresorptives and their relationship with the fracture risk reduction are analyzed. 

FIGURE 6.21 Results of evaluation of autosampler accuracy. Peak area values for methyl paraben are plotted against corresponding volume of injection. Values represent average peak areas obtained after triplicate injections. Error bars represent + one standard deviation. 

FIGURE 6.22 Standard calibration curve obtained for methyl paraben. Peak area values represent average value for four replicates. Error bars represent + one standard deviation (%RSD is very small error bars may not be visible at all concentration values). 

FIGURE 6.32 Solubility values at different pH values for phenazopyridine and piroxicam samples obtained with a Nanostream PLC system (error bars represent + one standard deviation). Values are compared with reported values. Literature values adapted from cited manuscripts. 

FIGURE 6.38 External standard calibration curve for acetaminophen (error bars represent + one standard deviation). 

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