Variance heterogenous

Wolfinger, R.D. Heterogeneous variance-covariance structures for repeated measures. Journal of Agricultural, Biological, and Environmental Statistics 1996 1 205-230. Wolfinger, R.D. An example of using mixed models and PROC MIXED for longitudinal data. Journal of Biophar-maceutical Statistics 1997 7 481-500. 

Wolfmger, R.D. Heterogeneous variance-covariance structures for repeated measures. Journal of Agricultural, Biological, and Environmental Statistics 1996 1 205-230. 

The broader the working range ABx, the earlier the deviation from ordinary linear regression can be detected. The F-test is used to discriminate between homogeneous and heterogeneous variances. 

Sampling of slurries and solids, differs fundamentally from sampling a completely mixed liquid or gas, A hulk quantity of sohds incorporates characteristic heterogenity—that is, a sample Sj differs inherently from a sample S2 when both are taken from a thoroughly mixed load of solids as a result of property variances embodied in solids. In contrast, all individual samples from a completely mixed liquid or gas container are statistically identical. 

The mean field treatment of such a model has been presented by Forgacs et al. [172]. They have considered the particular problem of the effects of surface heterogeneity on the order of wetting transition. Using the replica trick and assuming a Gaussian distribution of 8 Vq with the variance A (A/kT < 1), they found that the prewetting transition critical point is a function of A and... 

This is an equation which fixes the relation existing between the number of phases (/ ), the number of components ( i), and the variance, or number of degrees of f reedom (F), of a heterogeneous system in equilibrium, subject to certain conditions which are usually satisfied in practice. The rule states that... 

By the variance, or number of degrees of freedom of the system, we mean the number of independent variables which must be arbitrarily fixed before the state of equilibrium is completely determined. According to the number of these, we have avariant, univariant, bivariant, trivariant,. . . systems. Thus, a completely heterogeneous system is univariant, because its equilibrium is completely specified by fixing a single variable— the temperature. But a salt solution requires two variables— temperature and composition—to be fixed before the equilibrium is determined, since the vapour-pressure depends on both. 

In this case the column-norms dp are called column-standard deviations. The square of these numbers are the column-variances, whose sum represents the global variance in the data. Note that the column-variances are heterogeneous which means that they are very different from each other. 

The observed elemental variances of each measurement experiment and the components of the analytical variances discussed above are used to calculate variances due to heterogeneity for each element which are converted to relative uncertainties Rj. These relative uncertainties then provide the input in the two relevant Equations (4.3 and 4.4) that are commonly used to express elemental homogeneity of a sample as a function of sample mass (w). 

Protocols should require documentation of actual application practices and times. Samples of applied pesticides should be collected to document application rates to study sites. The test substance must be applied with typical equipment used for the crop, and the application must be made in accordance with the labeled use. Another variable that impacts such studies is the fact that most landowners have their own application equipment, which increases the variance in actual application rates among fields and may cause differential intra-field heterogeneity in application rates. 

Hartley HO (1950) The maximum F-ratio as a short cut test for heterogeneity of variance. 

The Cochran test should be used to compare two groups of continuous data when the variances (as indicated by the F test) are heterogeneous and the numbers of data within the groups are not equal (N N2). This is the situation, for example, when the data, though expected to be randomly distributed, were found not to be (Cochran and Cox, 1975, pp. 100-102). 

Considerable heterogeneity has been demonstrated with respect to average plasma Lp(a) levels in different ethnic groups. These differences cannot be entirely explained by differences in allele frequencies that exist between these groups [i.e., are not entirely due to allele-specific effects on Lp(a) concentrations] (M13, S3, S4). Interestingly, in the Sudanese population, Lp(a) levels are primarily (81%) determined by factors other than the size of the apo(a) allele, while in the Malay population, only 23% of the variation in Lp(a) levels could not be accounted for by size differences in the gene (S3). In Caucasians, it has previously been reported that 40-70% of the variance in Lp(a) levels can be... 

The essential feature is that CHp is defined as the variance of all heterogeneity contributions from all fragments which together make up the whole lot (Figure 3.1). 

The distributional lot heterogeneity, DHl, can then be defined as the variance of the heterogeneity between all increments (groups), x (/t ) there are Nq groups making up the lot. 

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