Variance homogeneity, application

When doing an experiment by application of a second-order CCRD, one need not replicate trials to estimate Sy2 in all trials of the design since the variance homogeneity of the trials makes several replications in one point possible as well as a determination of its error in that point, which is valid as an estimate for all other points of the design of experiments. 

Variance homogeneity of the y-values (responses) over the calibration range was proven using both the F-test and the Bartlett-test (although its application is not completely... 

Check the variance homogeneity Before using the variance obtained on the Reference Materials over the last two years, the variance homogeneity has to be checked the variance being used as a measure of the spread or dispersion of the data. This analysis is not applicable to all data obtained for each element because sometimes there is no replication of measurements under repeatability conditions or there are too few data. Under these circumstances the application of this statistical analysis would not be relevant. 

The results of the DFR assessment of different crop zones indicate that low-volume applications result in a more homogeneous distribution over the crop compared to high-volume applications. A recent study on the interception of high-volume applications in the cultivation of chrysanthemums revealed interception ratios from 0.2 to 1 related to the leaf area index (LAI) (Veerman et al., 1994). In our study, it was not easy to assess the LAI because of the structure of the carnation crop. Estimation of the LAI based on the results of estimation of the crop density (leaf volume index) was not reliable enough and resulted in a large variance of the calculated interception ratio (from 0.4 up to 5). 

Danzer K, Marx G (1979) Application of two-dimensional variance analysis for the investigation of homogeneity of solids. Anal Chim Acta 110 145... 

The results just obtained for < y) are, however, rarely used in applications because (v ) and T are generally not known. The Gaussian dispersion parameters aj and al are, in a sense, generalizations of (Cj) and particle displacement variances o-y and a-] are not calculated by Eq. (8.8). Rather, they are treated as empirical dispersion coefficients the functional forms of which are determined by matching the Gaussian solution to data. In that way, the empirically determined a-y and deviations from stationary, homogeneous conditions which are inherent in the assumed Gaussian distribution. 

There are a few requirements for the application of the standard addition method. The analytical results have to be corrected for blank. Otherwise we would add the blank value to our sample content. Since we are using linear regression we need a linear relationship between signal and concentration. As stated above the homogeneity of variances is also a prerequisite for linear regression. We want to divide our sample into several sub-samples and spike them with known amounts of analyte. This means that we need to divide the sample homogeneously and to precisely add the analyte. 

The linearity test based on the XPT 90-210 (French Standard, 1999) was checked by performing a homogeneity test of variances based on the analysis of 5 standard solutions (ranging from 25 to 122 pg/L) using five different electrodes for each metal Cu, Pb and Cd. The application of the linearity test which has taken into account the five calibration curves gave correct results and revealed no problem of linearity. 

For homogeneity testing in natural materials, the between-bottle variability (S[,b) was evaluated following the IRMM approach (Linsinger et al., 2001), after the application of one-way analysis of variance (ANOVA) to the duplicates obtained in ten different units. 

Normalization is a very important step, as it aims to reduce experimental variance. Normalization is most often performed by dividing each spectrum by a normalization factor (Figure 2G). The most popular normalization factor is calculated as the total ion count (TIC), which is the sum of all ion intensities in a spectrum. Several studies discovered that in MSI the assumptions for TIC applicability hold true only for very homogeneous tissues. In heterogeneous samples, more robust normalization factors based on the median or the TIC with exclusion of very localized mass signals have been proposed (35-37). 

An expression is developed for computing the mean size z, of randomly dispersed agglomerates, from the variance S2, obtained with a certain sample size, R. The author postulates a rate equation for solids mixing, which he feels may also be applicable to the homogenizing process in glass melting. 

Tests 1 and 2 determine the true model adequacy test 3 can only yield the best model. Applying the above statistics to models that are nonlinear in the parameters requires the model to be locally linear. For the particular application considered here, this means that the residual mean square distribution is approximated to a reasonable extent by the distribution. Furthermore, care has to be taken for outliers, since appears to be rather sensitive to departures of the data from normality. In Example 2.7.1.1.A, given below, this was taken care of by starting the elimination from scratch again after each experiment. Finally, the theory requires the variance estimates that are tested on homogeneity to be statistically independent. It is hard to say to what extent this restriction is fulfilled. From the examples given, which have a widely different character, it would seem that the procedure is efficient and reliable. 

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