Quotients standard deviation

In Case a, only the standard deviation estimated from the experimental data for the test sample is needed, which is then used to normalize the difference Xmean f - The quotient difference/.5 c, the so-called Student s f, is compared with the critical tc for a chosen confidence level and f n - 1. (Use Eq. 1.13.)... 

The F test tells us whether two standard deviations are "significantly different from each other. F is the quotient of the squares of the standard deviations ... 

This quotient is the critical quantity for the practical application of an analytical method. In addition, the relative standard deviation of an analyte result sometimes must not exceed a specified maximum. These two requirements lead to the. .. pragmatic setting of so-called limits of quantitation. Since such limits depend on the particular value observed, they cannot be regarded as meaningful characteristics of the method [MULLER et al., 1994], In brief conclusion, the analyst is well advised not to report determinations below this limit, because they will probably be biased owing to unacceptably high random errors. 

The mean of these quotients Az2rei should be situated near zero and their standard deviation near unity, i.e. it should be a standardized normal distribution if the kriging estimation is distortion-free. 

In this situation, the standard deviations of two of the numbers in the calculation are larger than the result itself. Evidently, we need a different approach for multiplication and division. As shown in Table 6-4, the relative standard deviation of a product or quotient is determined by the relative standard deviations of the numbers forming the computed result. For example, in the case of... 

To find the absolute standard deviation in a product or a quotient, first find the relative standard deviation in the result and then multiply it by the result. 

Thus, for products and quotients, the relative standard deviation of the result is equal to the sum of the squares of the relative standard deviation of the number making up the product or quotient. 

Other figures of merit are the signal-to-noise ratio and the signal-to-background ratio. A measure for the signal-to-noise (S/N) ratio is the quotient of the signal means, y, and the standard deviation of the signal... 

This is the quotient of the residual standard deviation (Sy) and the sensitivity (aj[) of the analytical method (gradient of the calibration function) and is a measure of the quality of the analytical method in the working range under consideration. 

RELATIVE STANDARD DEVIATION. The standard deviation of a series of replicate analyses is divided by the mean and the resulting quotient is multiplied by 100. Also called coefficient of variation. 

Fig. 2. Knowing from the/test (variance quotient) that the assumption of the same standard deviation does not apply, we have to balance the disequilibrium by a factor-the weighting factor. Otherwise the calculation will be wrong. The 2-fold standard deviation...

Cost-effective, non-invasive, quantitative and simultaneous determination of low level Tlnuvin 770 (0.05 to 0.4 wt.%) and Irganox 225 (0.1 to 0.45 wt.%) contents in PP pellets by NIRS in diffuse reflection mode using MLWR and PLS spectroscopic models has been reported [287]. Seven samples were used for calibration and two for validation. Spectral bands attributable to Tinuvin 770 and Irganox 225 appear at 1560 nm and 1390 nm, respectively. For Tinuvin 770 a two factor PLS model from 1500 to 1600 nm was developed for Irganox 225 a four factor PLS model in the 1360 to 1460 nm region. A quotient-term multiple linear least-squares spectroscopic model was derived that characterises analyte concentration and corrects for spectroscopic differences within the matrix due to the extruder/pelletisers. Reported standard deviations of ca. 25 ppm for Tinuvin 770 and ca. 80 ppm for Irganox 225, or relative standard errors of 0.01 wt.% for Tinuvin 770 and 0.03 wt.% for Irganox 225, approach the accuracy of the reference analytical method. 

Figure 14.5. Normal distribution for Intelligence Quotient (IQ) which has a mean value of 100 and a standard deviation of 13. The distribution has a range extending from 60 to 140. The cross-hatched regions give the % of the population falling la above and below the mean (34%) from lato 2a and from -la to -2a(14%) and from 2ato 3a and -2ato -3a (2%). Approximately 0.1% will be above 140 and below 60 (see Table 14.3).

Table 17 Average enthalpy of combustion, modified enthalpy of combustion and oxycaloric quotient of biomass. The standard deviation for each group is indicated in parenthesis [38],...

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