Statistics defined

Design allowable Statistically defined material property allowable strengths, usually referring to stress and/or strain. 

In general, the attempt to retest every compound that passes a statistically defined threshold of activity for each assay and to implement a concomitant assay interference test has been rewarded by recovery of a full spectrum of biological activities and diverse chemotypes in the confirmed hit set. In many cases, the compounds that the medicinal chemists ultimately judge to be the best starting points for lead development exhibited only modest activity (e.g., IC50 values of 0.5-5 pM) in HTS. 

Dispersion parameter for the distribution of measured values, s2, or analytical results, s2, for a given sample or the population, o2 and o2. Statistically defined as the second moment about the mean. 

In recent years, we have extended the nature of our analysis to include certain statistically defined features of the surface electrostatic potential. Our purpose has been to expand the capabilities of V(r) for quantitatively describing macroscopic properties that reflect non-covalent molecular interactions. This has led to the development of the General Interaction Properties Function (GIPF), described by Eq. (3.7) ... 

After 77, we gradually introduced several more statistically-defined quantities, designed to aid more complete characterization of Vs(r) over the entire molecular surface [14-17, 84], These include the average positive and negative potentials, V[Pg.247]

Hydrogen bonding and cr-hole bonding can be treated in terms of the Vs,max and 4s,min on a molecular surface. To deal with noncovalent interactions in general, however, it is necessary to go beyond the qualitative pattern of Vs(r) and its Vs,max and Vs.min, and to fully access the whole range of information that Vs(r) contains. This is done by analyzing it in terms of several statistically defined features, adopted over a period of years as we saw specific needs to be addressed. These features are... 

Quantification of the limits of detection (LOD), or minimum detectable levels (MDL statistically defined in Section 13.4), is an important part of any analysis. They are used to describe the smallest concentration of each element which can be determined, and will vary from element to element, from matrix to matrix, and from day to day. Any element in a sample which has a value below, or similar to, the limits of detection should be excluded from subsequent interpretation. A generally accepted definition of detection limit is the concentration equal to a signal of twice (95% confidence level) or three times (99% confidence) the standard deviation of the signal produced by the background noise at the position of the peak. In practice, detection limits in ICP-MS are usually based on ten runs of a matrix matched blank and a standard. In this case ... 

The minimum detectable level, or detection limit, is defined as that concentration of a particular element which produces an analytical signal equal to twice the square root of the background above the background. It is a statistically defined term, and is a measure of the lower limit of detection for any element in the analytical process. (This definition corresponds to the 95% confidence interval, which is adequate for most purposes, but higher levels, such as 99% can be defined by using a multiplier of three rather than two.) It will vary from element to element, from machine to machine, and from day to day. It should be calculated explicitly for every element each time an analysis is performed. 

The extrema of Vs(r) are, however, only the beginning of the useful information that can be gleaned from it. The question is how to characterize the key features and overall pattern of Vs(r) sufficiently to permit quantitative correlations with physical properties. Over a period of several years, we have identified a group of statistically-defined quantities that are effective for this... 

State of a network-forming polymerization or crosslinking process in the pre-gel regime. Note In the pre-gel state, the sol fraction is equal to unity. All the molecules formed have finite (statistically definable) relative molecular masses. 

D Spearman s Z)-statistic, defined by Eq.(2) D the same with rank ties, defined by Eq.(8)... 

FM Friedman s statistic, defined by Eq.(14), without rank ties... 

Application-specific statistics defined by a model developer... 

The strategy consists of testing first the null hypothesis of equalities of slopes, which is given by Equation (14). To determine whether or not this hypothesis is rejected, the statistics defined by Equation (27) is computed ... 

This chapter describes the simpler cleanup approach of base extraction for XAD resin extracts. Quality assurance procedures statistically define the benefits of this analytical approach for broad spectrum capillary GC. The extraction procedure was optimized by studying UV absorbance of the base extractant. 

This is exactly J times the F statistic defined in (6-19) and (6-20). Finally, J times the F statistic in (6-20) equals the expression given above. 

The uneven distribution of mycotoxins in grain has so far been statistically defined only for aflatoxins in a few matrices (corn, cottonseed, peanuts) (15,16), and sampling plans have been developed worldwide almost entirely for these toxins. 

To find the degree of solvation and the corresponding statistically defined mol of the solvent in contact with the chain, the measurements of the heat of dilution of polystyrene in some solvents, as published by Schulz and Horbach 15), have to be considered. The heat of dilution Qd in such systems depends on both quantities, Hm and Hr, defined above the relation 15)... 

Statistically defined structures may also arise from the formation of crosslinks in a melt the resulting gels are described within a percolation framework which predicts the existence of definite meshes [7, 8]. Contact-lenses, jellies or even jellyfish are common examples of gels. Latex beads with specific functionalities attached, such as antigens, are used in biodiagnostics. 

While the patterns of positive and negative regions are themselves of interest, we wish to also characterize Vs(r) quantitatively. We do this by calculating certain statistically-defined properties.46-50 Those that will be relevant to the present discussion are the most positive and most negative values of Vs(r), VS max and Vs,min and its positive, negative and total variances, cr2, cr2 and cr2t ... 

A key result is the prediction 21) of a unique scaling of this statistically defined transit time with applied field and sample thickness that leads to an... 

As discussed in Section 1.2.1, for such systems near the percolation threshold Pc the nearest-neighbour occupied bonds (or sites) form a statistically defined super-lattice , made of tortuous link-bonds (of chemical length Lc) crossing at nodes separated by an average distance the percolation correlation length (see Fig. 1.3 of Chapter 1). The external stress... 

The low affinity of sulfur for alkali metal ions, however, renders template effects of less consequence in the synthesis of polythia macrocycles. Thus, the competition between cycli-zation and linear polymerization is more statistically defined, with cyclization kinetically favored only at high dilution 64,65,66). Consequently, most of the synthetic methods for the synthesis of polythia rings involve high-dilution techniques coupled with relatively long reaction times. Historically, the study of the coordination chemistry of macrocyclic thioethers has been hindered by difficulties in the synthesis of the free ligands. The synthesis of [BJaneSa, first reported by Ochrymowycz and co-workers in 1977 101), illustrates this well. 

Table 111-1 Selected thermodynamic data for selenium compounds and complexes. All ionic species listed in this table are aqueous species. Unless noted otherwise, all data refer to the reference temperature of 298.15 K and to the standard state, i.e., a pressure of 0.1 MPa and, for aqueous species, infinite dilution (/ = 0). The uncertainties listed below each value represent total uncertainties and correspond in principle to the statistically defined 95% confidence interval. Values obtained from internal calculation, cf. footnotes (a) and (b), are rounded at the third digit after the decimal point and may therefore not be exactly identical to those given in Part V. Systematically, all the values are presented with three digits after the decimal point, regardless of the significance of these digits. The data presented in this table are available on computer media from the OECD Nuclear Energy Agency.

The uncertainties listed below each reaction value in Table IV-2 are total uncertainties, and correspond mainly to the statistically defined 95% confidence interval. The uncertainties listed below each value in Table IV-1 have the following significance ... 

---