Mean values and standard

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...

Mean value and standard error from the FEP calculations (ref. 46). 

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). 

Table 3 Mean values and standard error (italic) of the parameters of the symmetric logistic function adjusted to the total volatile matter production from anhydrous wood samples (HO) carbonization.

Table I Mean values and standard error of the mass yield and fixed carbon content of charcoal, as a function of the carbonization temperature and the residence time at this... 

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... 

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