Deviation ratio, standard

Number of experiments Number of accumulations Signal-to-noise ratio Standard deviation... 

M = male mo = month(s) NOAEL = no-observed-adverse-effect-level NS = not specified (occup) = occupational Resp = respiratory SD = standard deviation SMR = standard mortality ratio TR = tremolite yr = year(s)... 

The standard error is identical to the relative (%) standard deviation, since ap.B relative = a/N = Sp-B. The standard deviation and standard error of the k-ratio are calculated by summing the uncertainties in both calibration of the standard (std) and analysis of the unknown (unk), i.e.,... 

Eigen (A) values represent variances CIs are ratios of the variances, and V, the standard deviation ratios. The larger the ratio, the greater the problem of multicollinearity, but how large is large We consider this in a moment. 

Plate speed (mm) Arm speed (rpm) Rotation ratio Standard deviation of part wall thickness (mm)... 

For external method evaluation results from interlaboratory studies may be presented in tables and figures including mean, standard deviation, ratio/recoveiy, relative mean square error, a histogram of all results, and plots of the method evaluation function, Youden, and Z score. Furthermore, limits for acceptance of the performance characteristics parameters after which the methods have to be evaluated, e.g., tolerance limits as well as confidence and/or prediction intervals are essential. 

The phenomena that cause slight deviations under standard conditions exert more influence as the temperature deaeases and pressure increases. Figure 5.21 shows a plot of PV/RT versus external pressure (P xt) for 1 iriol of several real gases and an ideal gas. The values on the horizontal axis are the external pressures at which the PV/RT ratios were calculated. The PV/RT values range from normal (at P xt = 1 atm, PV/RT = 1) to very high (at P xt 10(X) atm, PV/RT == 1.6 to 2.3). For the ideal gas, PV/RT is 1 at any P xf... 

Healthy euthyroid and nongoitrous subjects have been investigated for iodine intake directly and indirectly, by various methodologies including the determination of stable iodine concentration on 24 hr excretion collections (either directly measured on 24 hr urine collections or calculated by the use of the iodine/creatinine or l/Cr ratio), the determination of iodine concentration in the urines, iodine kinetic studies (particularly of the inorganic iodine compartment) and iodine balance studies as well. Most of the values are given as mean standard deviation the standard error of the mean (sem) is specified when used. 

Breindl et. al. published a model based on semi-empirical quantum mechanical descriptors and back-propagation neural networks [14]. The training data set consisted of 1085 compounds, and 36 descriptors were derived from AMI and PM3 calculations describing electronic and spatial effects. The best results with a standard deviation of 0.41 were obtained with the AMl-based descriptors and a net architecture 16-25-1, corresponding to 451 adjustable parameters and a ratio of 2.17 to the number of input data. For a test data set a standard deviation of 0.53 was reported, which is quite close to the training model. 

Example 12 Suppose Analyst A made five observations and obtained a standard deviation of 0.06, where Analyst B with six observations obtained 5-3 = 0.03. The experimental variance ratio is ... 

Usually, 10 to 20 measurements are made of the isotope ratio for one substance. Sometimes, one or more of these measurements appears to be sufficiently different from the mean value that the question arises as to whether or not it should be included in the set at all. Several statistical criteria are available for reaching an objective assessment of the reliability of the apparently rogue result (Figure 48.10). Such odd results are often called outliers, and ignoring them gives a more precise mean value (lower standard deviation). It is not advisable to remove such data more than once in any one set of measurements. 

In connection with Eq. (1.4), we noted that the standard deviation measures the spread of a distribution now we see that the ratio M /M also measures this polydispersity. The relationship between these two different measures of polydispersity is easily shown. Equation (1.14) may be written as... 

This result shows that the square root of the amount by which the ratio M /M exceeds unity equals the standard deviation of the distribution relative to the number average molecular weight. Thus if a distribution is characterized by M = 10,000 and a = 3000, then M /M = 1.09. Alternatively, if M / n then the standard deviation is 71% of the value of M. This shows that reporting the mean and standard deviation of a distribution or the values of and Mw/Mn gives equivalent information about the distribution. We shall see in a moment that the second alternative is more easily accomplished for samples of polymers. First, however, consider the following example in which we apply some of the equations of this section to some numerical data. 

A study was conducted to measure the concentration of D-fenfluramine HCl (desired product) and L-fenfluramine HCl (enantiomeric impurity) in the final pharmaceutical product, in the possible presence of its isomeric variants (57). Sensitivity, stabiUty, and specificity were enhanced by derivatizing the analyte with 3,5-dinitrophenylisocyanate using a Pirkle chiral recognition approach. Analysis of the caUbration curve data and quaUty assurance samples showed an overall assay precision of 1.78 and 2.52%, for D-fenfluramine HCl and L-fenfluramine, with an overall intra-assay precision of 4.75 and 3.67%, respectively. The minimum quantitation limit was 50 ng/mL, having a minimum signal-to-noise ratio of 10, with relative standard deviations of 2.39 and 3.62% for D-fenfluramine and L-fenfluramine. 

F Distribution In reference to the tensile-strength table, the successive pairs of daily standard deviations could be ratioed and squared. These ratios of variance would represent a sample from a distribution called the F distribution or F ratio. In general, the F ratio is defined by the identity... 

Select (X =. 05, and since with the change in draw ratio the uniformity might change, the sample standard deviation would be used, and therefore t would be the appropriate test statistic. 

Process Capability (Cp) The ratio of the specification range to six standard deviations of the process. 

The standard deviation multiplier, z, is the ratio of the toleranee and standard deviation, for one half of the distribution in this ease ... 

The curves show that the peak capacity increases with the column efficiency, which is much as one would expect, however the major factor that influences peak capacity is clearly the capacity ratio of the last eluted peak. It follows that any aspect of the chromatographic system that might limit the value of (k ) for the last peak will also limit the peak capacity. Davis and Giddings [15] have pointed out that the theoretical peak capacity is an exaggerated value of the true peak capacity. They claim that the individual (k ) values for each solute in a realistic multi-component mixture will have a statistically irregular distribution. As they very adroitly point out, the solutes in a real sample do not array themselves conveniently along the chromatogram four standard deviations apart to provide the maximum peak capacity. 

The average experimental value of the coefficient 0 is 1.7 with a standard deviation (og) of 0.05. Equation (7.160) allows one to calculate the momentum ratio (/rj2/foi) required to extend the length of zone I to the value equal to Xj, given that the distance between the directing nozzles is equal to The graph presented in Fig. 7.56 is plotted according to Eq. (7.160) for and X,2 equal to 6.2. The maximum value of reverse flow velocity (n,, .) was found to be in the cross-section at X equal to Xy... 

The ratio f/f° is called activity, a. Note This is not the activity coefficient. The activity is an indication of how active a substance is relative to its standard state (not necessarily zero pressure), f°. The standard state is the reference condition, which may be anything however, most references are to constant temperature, with composition and pressure varying as required. Fugacity becomes a corrected pressure, representing a specific component s deviation from ideal. The fugacity coefficient is ... 

O = Standard deviation (statistics), or interfacial tension x = Torque on shaft, consistent units, FL or ML2/t2 = Np = P0 = Power number, dimensionless 3> = Power number, POJ or ratio of power number to Fioude number, Njrr, to exponential power, n... 

The top and the bottom x-ray detector each contain a multiplier phototube coated with phosphor. This tube compares the intensity of the x-ray beam entering the detector with that of the light from the reference standard, a discharge lamp. The reference beam is part of a circuit that maintains the x-ray source at constant intensity. The deviation wedge comes to rest when the intensities of the transmitted x-ray beams stand in a predetermined ratio. At this point, the unbalance in the servo system has been compensated, and the position of the deviation wedge consequently indicates the thickness of the strip. In 1955, this application was made fully automatic that is, the unbalance (or error signal) just mentioned was used to readjust tandem cold reduction mills of the United States Steel Corporation. Automatic control proved significantly more effective than manual control. 

No calibration was required and the percentage of only one element needed to be established, for the alloy was binary. The atomic numbers of copper and zinc being adjacent, the intensity ratio of their K lines could, after an appropriate adjustment of experimental conditions, be assumed equal to the ratio of the number of atoms present of each metal. Under these simple conditions, compositions could be calculated satisfactorily from intensity ratios, as is shown by the following results for a series of 16 x-ray determinations on such an alloy found by chemical methods (details not given) to contain 73.00% copper average copper content, 73.16% standard deviation for a single determination, 0.27%... 

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