Mean values and standard deviations

Further discussion of the significance of mean values and standard deviations can be found in Chapters 14 and 28 and in any textbook on statistics. 

Table 1.3. 5 C%is and 5 N%o mean values and standard deviations (s.d.) for human bone collagen by age group.

Fig. 5 Mean annual TDS (a) expressed in mg L 1 and TDS Flux (b) expressed in t year 1, together with mean value and standard deviation at each monitoring station. All the data are reported versus the distance from the source of the Ebro River...

Gamma densities are often a suitable a priori choice to describe random demands, see, e.g., Tempelmeier [11], The reason for this is that they are not defined for negative numbers (demands are always positive) and that they are uniquely determined by their (positive) mean values and standard deviations. A further important property is that gamma densities are infinitely divisible, which means, for example, that there is a straightforward calculation of the daily demand from the weekly random demand. 

Mean values and standard deviations (like letters within each row indicate no significant differences at P < 0.05 by Tukey mean separation n = 3)... 

To check traeness using a reference material, a series of replicate tests is carried out and the mean value and standard deviation are compared with the characterized value for the reference material. Certified matrix reference materials may be purchased and used directly for validation. If this is not possible reference materials for validation may be prepared by spiking... 

Endothelial defects of ex vivo corneas at different time points after exposure to various concentrations of are shown in Fig. 5.15. The ordinate shows the score of epithelial defects. The bars over the abscissa give the mean values and standard deviations, from left to right with exposure to 1.5, 3, 6, and 12% H O, respectively, for each concentration of H O. The time points zero mark the state inunediately after application of H Oj, then the healing progress or failure on day 2 and 7 is presented. Each bar represents the mean value of n = 3 individual ex vivo corneas no dose responses, but increasing damage with time. 

I. 77. Because fcalcu ated (= 20.2) > 1.77, we conclude that the null hypothesis is false. Cell F10 states that the probability of observing these two mean values and standard deviations by random chance if method 1 does not give a higher result than method 2 is 1.66 X 10 u. 

In order to determine the effectiveness of the matrix correction procedure for elements fighter than manganese, a sample of known concentration was measured. The mean values and standard deviations of five separate measurements of NBS orchard leaves (SRM 1571) are shown in Table 7.14. 

FIGURE 2 Dissolved organic matter (a) concentration (mgL-1) and (b) flux (kgha 1yr 1) in wet precipitation over continental landmasses. Source of data Mean values and standard deviations from data in Table I. 

Mean values and standard deviations were calculated from at least n = 3. 

A normally distributed parent population X is characterized by its expected mean value /< and standard deviation a. If the samples taken from this population are representative, the sample average x is an unbiased estimate of /c... 

Table 6. Results of dynamic mechanical measurements. Mean values and standard deviations from four measurements of each sample are reported...

Table 2 represents the mean values and standard deviations in percent of the mean value of the four separate hand swabs, right back, (RB), right palm, (RP), left back (LB), left palm (LP), collected from 30 persons. The hands of crime lab technicians and police officers were swabbed "as is" without any pretreatment. 

Table II. Mean Values and Standard Deviations for Cloud Runs...

Cetin et al. [29] proposed a simple, precise, fast, and low-cost differential pulse (DP) polarographic method for fhe deferminafion of lornoxicam in pharmaceutical formulations. Results have been compared with those of high-performance liquid chromatographic (HPLC) method. Mean values and standard deviations calculated by 10 determinations were 8.10 0.12 mg for DP polarography and six determinations were 8.02 0.08 mg for HPLC mefhod. The sfafisfical evaluations indicated that there was no significant difference between the mean values and precessions of fhe fwo mefhods af 95% confidence level (f = 2.64, F = 2.25). 

In the above example it was assumed that the mean value and standard deviation of the sodium concentration in the parent sample were known. In practice this is rarely possible as all the mineral water from the source would not have been analysed and the best that can be achieved is to obtain recorded estimates of p, and a from repetitive sampling. Both the recorded mean value and the standard deviation will undoubtedly vary and there will be a degree of uncertainty in the precise shape of the parent normal distribution curve. This uncertainty, arising from the use of sampled data, can be compensated for by using a probability distribution with a wider spread than the normal curve. The most common such distribution used in practice is Student s t-distribution. The i-distribution curve is of a similar form to the normal function. As the number of samples selected and analysed increases the two functions become increasingly more similar. Using the t-distribution the well known /-test can be performed to establish the likelihood that a given sample is a member of a... 

FIGURE 12.12 Distribution of organic matter in different regions of the Baltic Sea. For 13 selected stations (cf. Fig. 1.2) mean values of DOC, DON, POC, PON, and the C/N ratios in the dissolved and particulate fraction are shown. The calculation based on the data measured from 1995 to 2005 on five regular cruises per year. Mean values and standard deviations are separately calculated for the whole water column (columns), for the surface layer (circles) and, the bottom layer (triangles). (Adopted from Nausch et al., 2006.)... 

Fig. 10.6 Gastric and duodenal pH variations during test meals in humans. Mean values and standard deviations were estimated from...

Barrow [772] derived a kinetic model for sorption of ions on soils. This model considers two steps adsorption on heterogeneous surface and diffusive penetration. Eight parameters were used to model sorption kinetics at constant temperature and another parameter (activation energy of diffusion) was necessary to model kinetics at variable T. Normal distribution of initial surface potential was used with its mean value and standard deviation as adjustable parameters. This surface potential was assumed to decrease linearly with the amount adsorbed and amount transferred to the interior (diffusion), and the proportionality factors were two other adjustable parameters. The other model parameters were sorption capacity, binding constant and one rate constant of reaction representing the adsorption, and diffusion coefficient of the adsorbate in tire solid. The results used to test the model cover a broad range of T (3-80°C) and reaction times (1-75 days with uptake steadily increasing). The pH was not recorded or controlled. 

Figure 7.6. (a) Dissolved organic carbon (DOC) and (fc) Cu activity expressed as a percentage of total H2O-soluble Cu in the bulk soil, the outer rhizosphere, and the inner rhizosphere along a soil contamination gradient at Sudbury. Mean values and standard deviations are for three field replicates (Modified from Legrand et al.. 2005.)... 

T able 6.2. Mean values and standard deviations of crystal size in the zirconia aerogels according to the thermal annealing temperature... 

This expression can be used as a starting point for analysis of the scattered light intensity by polydisperse samples. If the shape of the particles is known (that is, r (M) is a known function see Equation 5.412), we can determine two parameters characterizing the distribution fiM) (e-8-> its mean value and standard deviation) from the experimentally measured intercept and slope of the line, [cA // (9)] vs. q. For small particles, P(9 9,M) 1 and... 

Table 1. Composition of lenses and host rocks as determined by point counting thin sections (outcrop Findel, Fig. 1). Mean values and standard deviations are shown. The compaction is estimated by assuming a primary porosity of 40%...

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