Statistics variance

Data belonging to distribution profiles may be compared either vertically along the release/response ordinate or horizontally along the time abscissa. The semi-invariants (moments) provide a complete set of metrics, representing both aspects in logical sequence AUC accounts (vertically) for the difference of the extent, the mean compares (horizontally) the rates, and higher-order moments and higher-order statistics (variance, etc.) characterize the shape aspect from coarse to finer. 

The required degree of understanding of the physical properties of metal thin films used for interconnects on chips is illustrated by the following example. It was found that the performance of conductors on chips, A1 or Cu, depends on the structure of the conductor metal. For example, Vaidya and Sinha (10) reported that the measured median time to failure (MTF) of Al-0.5% Cu thin films is a function of three microstructural variables (attributes) median grain size, statistical variance (cr ) of the grain size distribution, and degree of [111] fiber texture in the film. 

A generic problem in all studies of the effects of chemical exposures on health is the need to differentiate real" effects from random background noise." Statistical variance in an experiment can result in a safe substance s being declared hazardous. And vice versa. 

These policy problems will not be resolved through more scientific investigation. "Better" science can only reduce statistical variance. Once that is accomplished, disagreements about value choices still remain. The next two chapters discuss how those disagreements might be resolved, first for private exposures and then for public ones. 

In 1980, the NAS (38) reported that a review of 10 epidemiological studies failed to support or refute the results of the positive animal bioassays. This report suggested that chloroform may cause cancer in humans. The NAS stated that any association between THMs and bladder cancer was small and had a large margin of error both because of statistical variance and the nature of the studies that had been conducted. The NAS reached the following conclusion (38) ... 

The quantifiable components of sampling error are the natural variability within a sample itself and the variability between sample populations that may be randomly selected from the same sampled area. Both of these errors can be evaluated quantitatively in the form of statistical variance and controlled to some extent through the application of appropriate sampling designs. 

That paper suggests why an absorption spectrum is frequently reported near 576 nm. The experimentation used a 17 Hz. flicker rate. The paper presents data with a statistical variance on the order of 1-2 nm that is consistent with the theoretical values of this work. Based on the theory of this work, obtaining a higher degree of accuracy will require measuring, and reporting, the core temperature of subjects to an accuracy of close to 0.1 Celsius. 

The approximate relationship between the constitution heterogeneity (CH) and the statistical variance, discussed in the next section, can be used to determine the optimal sample mass when sampling to determine the relative amount of trace constituents in the lot. Two series of samples of large and small sample masses are collected and analyzed. The statistical coefficients of variation are calculated. These, together with the values of the sample mass, can be used to determine the minimum sample mass needed to obtain the desired sampling precision of the estimated critical content of the trace constituent. For details, see Chapter 20 of Pitard (1993). 

The statistical variance of the critical content was higher in the second case, similar to the situation with CH. However, the statistical relative variance of the mean was lower, similar to the situation with the Var(FE). 

Notice that (Ceq) is identical to Ceq given by the solution to the deterministic model [Eq. (7)] this is a general result for linear equations. The interesting and important observation is that the statistical variance expected at equilibrium binding is proportional to the total number of cell... 

Effect of A-site Disorder and Cation Radius on D(T i) and Tco- The effect of changing the contents of the A-site on the various transition temperatures of interest, Tc (Curie temperature for ferromagnetism), which is generally the same as Tmi (the metal/insulator transition temperature) and Tco (the charge ordering transition temperature), can be quite large as in Figure 26 Attfield was able to show that Tc(Tmi) correlated very well with the statistical variance, a, of the A-site ions, that is, a = Ily,r — (rA). Here the r, are the standard Shannon radii for 9-fold t coordination, y,... 

STOCSY-scaling (STOCSY(S)) H/ H NMR Scaling of statistical variance of compound signals [133]... 

Four of these are introduced as estimated values of the statistical variance ... 

Variance (v) The sample variance (v) of a set of replicates is simply s, which, like the standard deviation, gauges the spread, expected error, or variance within that data set. Forensic chemists favor standard deviation as their primary measure of reproducibility, but variance is used in analysis-of-variance (ANOVA) procedures as well as in multivariate statistics. Variances are additive and are the basis of error propagation, as seen in equation (2.1), where the variance was represented by e. ... 

The quantity F A, A) = 2(A) is a localization index, equal to the number of self-pairs formed in the basin The difference between the average population of basin N A) = Jj drp(r) and the localization index is the statistical variance cr of the basin population (i.e. its fluctuation). When 2(A) = iV(A), all electrons are confined in that basin and the statistical variance is equal to zero. Thus the value of localization index reflects the number of electrons confined in the basin. 

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