Average variance extracted

Convei nt validity describes the extent to which extent the items convei e on their theoretical construct (Campbell and Fiske 1959). In PLS, convergent validity is measured via the average variance extracted, which should be higher than 0,5 to fulfill the criterion (Hair et aL 2011b). Average variance extracted measures the extent to which the average variance of the indicators is explained by its theoretic construct (Fomell and Larcker 1981). As indicated in Table 12 and Table 14, all the reflective constructs used are substantially above the cutoff value of 0,5, and convergent validity is established. 

In addition, according to the standard of convergent validity assessed by FomeU and Larcker (1981), all standardized factor loadings should be greater than 0.5 and should be above 0.6 in terms of composite reliability, as shown in Table 1 that all constructs indicator-factor loadings are above 0.5, all composite reliabilities (CR) are above 0.7, average variance extracted (AVE) is above 0.5. Measurement scales see Appendix A. 

The typical approach to reliability assessment is the Cronbach s a coefficient. However, Cronbach s a is based on the restricted assumption of equal importance of all indicators. Following Hair et al. (1995), the composite reliability (pc) and the average variance extracted (AVE) of multiple indicators of a constmct can be used to assess reliability of a constmct. The formulas for calculating them are shown below. When AVE is greater than 0.50 and is greater than 0.70, it implies that the variance by the trait is more than that by error components (Hair et al. 1995). 

Normed Chi-square/degrees of freedom (<3.0) AVE Average variance extracted (>0.50)... 

Another possibility is to include a number of factors such that variance extraction reaches a predefined level, say 90%. If factor analysis starts from the correlation matrix a simple decision is to include all factors associated with eigenvalues larger than the average value of 1. 

Analysis of variance was used to assess the effects on polyaromatic hydrocarbons extraction at the 99% confidence level for the four factors varied. The percentage of 14C in the extract and soil residue does not total 100% because of degradation and volatilization during incubation and due to losses during analysis. The data are presented in Table 2.3 and represent the average of the three replicates for the extract or soil residue. 

Measurements of wind velocity components, such as depicted in Figure 16.1, are important in characterizing atmospheric turbulence. Certain statistical properties of the tur-bulence can be extracted from such records. The intensity of turbulence is related to u[ or (Ty (no summation), the variance of the velocity distribution of the /th component about its mean value. The values bear a direct relation to the diffusing power of the atmosphere. Two other useful properties are the standard deviations of the fluctuations in the horizontal direction of the wind, 00, and the vertical direction of the wind a. It is important to realize that Ou, (7(51, and depend on the sampling and averaging times inherent to a velocity record such as that shown in Figure 16.1. 

This is a population value, and refers to the statistical distribution of the averages of all random samples with n elements that might be extracted from the population. The variance of this distribution is smaller than the variance of the distribution of individual observations, a, by a factor inversely proportional to sample size. The distribution of the averages is therefore narrower than the distribution of the individual values, and the more so the larger the sample taken to calculate the average. 

In line with these authors approaches, we recommend not to average spectra over the whole sample but to take advantage of the spatial display of spectra in order to reinforce the spectral analysis. Attributes, as simple as the variance spectrum of the sample, or more complex ones similar to those extracted from a mapping process or from textural analysis such as the GLCM, should be systematically tested as additional variables to decide whether it is preferable to use HSI instead of NIR spectrometry. 

This variance is a measure of how much the concentration differs from the mean value. The procedure to determine whether or not the mixture is grossly uniform is obvious from the above discussion samples are extracted from the mixture, their average concentration is calculated, and finally the concentration distribution is checked against the binomial distribution. If there is a match between these two distributions, the mixture is considered to be grossly uniform or a random mixture. In the limit of zero variance the mixture attains the uniform state. 

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