Measurement units, "relative" versus

A statistical method for plotting the relative frequency (dN/N) of a probable error in a single measured value X versus the deviation (z) from fi, the mean of the data, in units of standard deviation (o-), such that z = (x -fji)/a. The standard error curve (shown below) does not depend on either the magnitude of the mean or the standard deviation of the data set. The maximum of the normal error curve is poised at zero, indicating that the mean is the most frequently observed value. 

Measurement Units. Perhaps the most obvious yet confusing aspect of many detection limit comparisons is the use of "relative" versus "absolute" units. Relative units reflect a mass per unit volume, such as micrograms per milliliter, while absolute units reflect a mass only, such as micrograms. Obviously, "relative and "absolute" units should not be directly compared. However, absolute units can be converted into relative units and vice versa, employing the volume of solution utilized by a particular technique. Nonetheless, how that conversion is done or how it is doctjmented can significantly bias the observer. Table I illustrates several examples, taken from the scientific literature, of the use of detection limit values in a table for comparison purposes. In each case the author provides adequate information for the informed reader to make an accurate comparison. Nevertheless, the conclusions drawn by the careless or uninformed reader who does not read or understand the footnotes or the text which describes the table, can be biased by several orders of magnitude. 

From such measurements, surface areas (normalized cumulative and relative), pore radii (choice of three measuring units), pore volumes (raw, normalized, cumulative and relative) and pore-size distribution functions of samples can calculated. Figure 8 presents the graphs of mercury-penetrated volume versus pressure in pores of Na- and La-montmorillonite samples. Figure 9 shows pore-size distribution functions from porosimetry data. 

Where all cations are expressed as atoms per six oxygen formula unit and T is in K. This expression reproduces to within 0.011 A. The predicted versus observed are plotted in Figure 12. Given that the experimental values are rarely measured to better than 30% relative, the fit is considered acceptable. Significantly, using the derived... 

In addition to the TDI experiment, the partition ratio measures the TDI efficiency. Specifically, the partition ratio is the number of inactivation kinetic events (k nact) versus the number of substrate turnover events per unit enzyme (kcat) [161], Thus, the most potent partition ratio is zero. The most common experimental setup for determining the partition ratio is the titration method that increases the inhibitor concentration relative to a known amount of enzyme. After the incubations, a secondary incubation containing a probe substrate similar to the TDI experiment is used to define the remaining activity. For accurate determination of the partition ratio from the titration method, it is assumed that the inhibitor is 100% metabolized ... 

Chlorides RMe2CCH2Cl [(a) R = Me, R = Ph and (b) R = CH2Ph] reacted with diphenylphosphide ions in liquid ammonia, via a proposed 5rn 1 mechanism and their reactivities were measured. The higher reactivity of (a) has been attributed to efficient intramolecular electron transfer from the phenyl ring to the C—Cl a bond (intra-ET catalysis). The lower reactivity of (b) is ascribed to a decrease in the rate of the intra-ET by elongation of the bridge by one methylene unit. The relative reactivity of (a) versus (b) is proposed to indicate the ratio of the intra-ET rates of the radical anions of both compounds. ... 

Plot of the cumulative frequency of craters versus crater diameter, for three geologic units on the Moon. Crater density measurements provide a means of ordering units in relative time. Modified from Neukum etal. (2001). 

Fig. 2.40 Properties of single-crystal BaTi03 (a) unit-cell distortions of the polymorphs (b) lattice dimensions versus temperature (after R. Clarke J. Appl. Cryst. 9, 335, 1976) (c) spontaneous polarization versus temperature (d) relative permittivities measured in the a and c directions versus temperature (after W.J. Merz Phys. Rev. 76, 1221, 1949).

The density of PS can be expressed as absolute density in units of grams per cubic centimeter or relative density (versus single-crystalline silicon) in units of percent. It can also be expressed as porosity which measures the amount of the open space with PS. Thus, the relative density plus porosity equals 1. In many studies the density of PS is determined by a simple gravimetric method of measuring the weight difference before and after anodization and the actual volume of ps 32,36,48,50 determined... 

The ideal absorbance range for most measurements is in the region of 0.5 to 1.5 absorbance units for most modern instruments, as the concentration-versus-absorbance curve is relatively linear between these absorbance values. 

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