Mean, observational

Strictly, the mean observed values, (y), which appear in Equation (12.39) should corresponc to the mean of the values for each cross-vahdation group as appropriate rather than the overall mean value of the dependent variables, though often the mean of the entire date set will be used instead. 

The recommended density at a particular temperature is the weighted mean observed density for that temperature. The corresponding uncertainty is the standard deviation from the mean for each value. 

Soil is a mixture of solid materials, air and, usually, water and organic matter. The radium content of soil often reflects that of the rocks from which the solid materials are derived by physical and chemical activity. The observed ranges are from 0 to 20 Bq kg for ultrabasic rocks (dunite) to 1 to 1835 Bq kg for igneous metamorphic rocks (gneiss) (Wollenberg, 1984). While these ranges are broader than those for measured for soils, the mean values for rocks, excluding alkali rocks, is consistent with the means observed for soils. 

Figure 10 Mean observed concentration-time profiles for the three extended-release formulations, fast ( ), medium (o), and slow ( ), whose in vitro dissolution data are shown in Figure 3 (panel a) and the derived mean absorption-time profiles (panel b).

Figure 13 Comparison of the mean observed and predicted concentration-time profiles for the three ER formulations, fast ( ), medium (o), and slow ( ), whose dissolution behavior is shown in Figure 3. Pharmacokinetic parameters F= 1, ka = 1000 hr-1, io = 0.17hr 1, V = 114L, fcoi =, coi = 9hr, abs = 96hr. Dosing parameters dose = 10 mg, r = 24hr. IVIVC equation xViVO=Jcvitro (1 1 IVIVC panel a) or 4th order polynomial shown in Figure 11 (panel b). Double Weibull (drug release) parameters for each of the three formulations are listed in Table 2.

Station ALOHA (see Figure 23.4 for location information). Three-point running mean observations of N/P molar ratios in (a) total dissolved inorganic plus organic pool, (b) total suspended particulate matter in the upper 0-100 m, (c) in exported particulate matter at 150 m depth, and (d) cycling in nutrient limitation (described in text). Source From Karl, D. M. (2002). Trends in Microbiology 10(9), 410-418. 

The predicted distribution corresponds to an unskewed Gaussian curve. Distributions for the other programs and MM3 with the vacuum dielectric constant were similar, but their maxima were located at about 4.55 A. We judged that distance to be too long, in part because the mean observed value is about 0.14 A (7.4 standard deviations) smaller. Also, those predicted distributions based on vacuum dielectric constants called for a large fraction of... 

Fig. 12.1. Typical scatter of results from nine replicate analyses, a = absolute error of the determination, d = systematic error, n = total number of results (=9 in Fig. 12.1 see under Replicates in the text), t= true value, x = mean observed concentration value, x = observed value (see under Replicates in text).

In a second stage GastroPlus was used to simulate oral absorption, and oral profiles were produced by feeding this predicted input into a compartmental disposition model fitted to the mean observed intravenous data. 

The value of K calculated from the mean values of Kh K, and K% (Table VIII) was 2.1 X 103 liter mole-1, i.e., in almost exact agreement with the mean observed value of 2.0 X 103 liter mole-1 (Table VII). 

The mean observed active energies obtained by regression of the experimental data for various crystal seeds with different mean diameters and in different crystallizers are listed in Table 12.4, where, similarly, the subscripts IS and FB denote the parameters in the impinging stream crystallizer and the fluidized bed crystallizer, respectively. ... 

At an intake equal to the mean observed requirement, 50% of the population have heen included, and there is thus a 50% prohahility that this level of intake will he adequate for an individual. 

Fig. 15.2 Mean observed (a) and calculated (b) concentrations for sulphates in 2000, and absolute (c) and relative (d) differences. Unit pg S...

For all practical purposes the Gibbs monolayers, discussed so far could be treated as fully relaxed. (Figure 4.20, giving measurements taken at extremely short times, illustrates the sole exception.) Complete equilibration, meaning observation at De... 

The mass balance equation and Y,/ and Yp, values erf corresponding carbon-limited cultures are then used to determine the carbon substrate and oxygen requirements for cell production. The yield of exopolysaccharide (corrected for cell production) is then compared to the thecsetical yield. The latter being calculated from the mean observed P/O quotient of carbon-limited cultures. 

The conclusion just reached forms the bams of the generalized, or reduced, compresmbility curves (Fig. 4). From actual experiments on a numbw of gases, the mean observed compressibility factors at various temperatures and pressures have been derived, and the values of k are plotted against the corresponding reduced pressures, with the reduced temperature as parameter. From these curves it is posmble to derive, with a fair degree of accuracy, the value of either the pressure, volume or temperature of any gas, if the other two variables are given. The determination of the volume can be achieved directly from Fig. 4, but the evaluation of either pressure or temperature is not quite as simple.f... 

As a simple example, let us consider a problem arising out of the testing of a hydrogenation catalyst in a differential reactor. Conditions are held constant in two series of runs save that the catalyst is much more finely divided for one series. The same mass of catalyst occupies the same volume in the two cases so that the external voidage of the bed is not significantly changed. There are no great differences in the shape of the particles in the two sizes, so that the normalized Thiele moduli, //I and Zrl, will be proportional to and 2, characteristic dimensions of the particles. The mean observed reaction rates in Ib-mol/hr lb catalyst are r, and a in the two series of runs and the data are as follows ... 

Thus, "green" rather than "grue," for example, where "grue" means "observed before 2000 and green, or blue" (Goodman). 

QCs are prepared at a central laboratory and sent to various clinical chemistry laboratories that participate in the program. The mean observed values among the laboratories, not the theoretical values of the QCs, are used for laboratory proficiency evaluation. Criteria are set differently for different tests by CLIA 88 regulations. Also, bioanalytical laboratories involved in a drug-development program may exchange QCs and test samples to ensure lab-to-lab reproducibility in the analyses. 

Note that the standard error of prediction is not a constant for all values of xo. but reflects where xo is collected in relation to the mean. Observations removed from the mean of x will have larger standard errors of prediction than values close to the mean. Equation (2.34) is developed as the confidence interval for a single observation measured at x0. If more than one observation is made at xo, the term 1/n in Eqs. (2.33) and (2.34) is substituted with the term m/n, where m is the number of observations at x0. Note that m is contained within n. If the confidence interval is made for all points on the regression line, the result would be a confidence band. 

The OSPAR solution was the introduction of Background Assessment Criteria. BACs are statistical tools that enable precautionary testing of whether mean observed concentrations can be considered to be near background concentrations. A more detailed... 

Thus, green ratherthan gruefor example, where grue means observed before 2005 and green, or blue (Goodman 1955). 

Whereas the observed decay profile no longer is characterized by a single decay rate, the steady-state fluorescence intensity becomes dependent on both 7obs and fc>bs. The typical Stern-Volmer plot is no longer represented by equation 7a, but rather by equation 7b, where fcobs is defined by equation 6b, fc q is the bimolecular quenching rate constant, fco is the probe s mean excited-state unimolecular decay rate constant, fcobs is the mean observed decay rate constant, 70 is the distribution parameter of the Gaussian for the unimolecular decay, and 7obs is the distribution parameter for the observed unimolecular decay rate. 

Fig. 1-5. Vertical temperature structure of the atmosphere. The solid curve represents the U.S. Standard Atmosphere, and the horizontal bars indicate the range of monthly means observed between equator and north pole. [Adapted from U.S. Standard Atmosphere (1976).]...

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