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Error formulas

For the Euler-McLaurin discretization an error formula similar to (A. 4) holds, namely without the factor (1 - which corresponds to the expansion co-... [Pg.90]

For the difference between two proportions, for example if we are looking at the difference — t2 between the cure rate in the active group (group 1) and the cure rate in the placebo group (group 2), the standard error formula is /rl (1 — r jn - - r2 (1 — rj)ln2 where i and are the numbers of subjects in groups 1 and 2 respectively. [Pg.38]

With a ratio it is not possible to obtain a standard error formula directly however it is possible to obtain standard errors for log ratios. (Taking logs converts a ratio into a difference with log A/B = log A — log B.) So we first of all calculate confidence intervals on the log scale. It does, in fact, not make any difference what base we use for the logs but by convention we usually use natural logarithms, denoted fn . [Pg.70]

It is straightforward to obtain the estimated probability of surviving for various key time points from the Kaplan-Meier estimates. In the Packer et al. (2001) example, the estimated survival probability at 12 months in the carvedilol group was 0.886 compared to 0.815 in the placebo group, an absolute difference of 7.1 per cent in the survival rates. A standard error formula provided by Greenwood (1926) enables us to obtain confidence intervals for these individual survival rates and for their differences. [Pg.196]

Insisting that the propagation of error formula be used wherever appropriate in laboratory reports, we find it easier to introduce the total differential once the topic comes up during the thermodynamics portion of the course. The similarity between the propagation of error formula and the total differential provides a more intuitive model for our students. Because our order of topics delays thermodynamics to later in the semester, we have time to emphasize the more concrete example used to determine the uncertainty in a measurement. [Pg.287]

Crystal chemistry of erionites should be computed based upon the guidelines of the IMA Zeolite Report of 1997. The reliabilities of the crystal chemistries of these erionites should be evaluated using the balance error formula of = ((A1- -Fe ) —(Na-I-K)-I-2(Ca -F Mg -F Sr -F Ba))/(Na -P K) -P 2(Ca -P Mg -P Sr -P Ba) X 100. The results of chemical analyses of erionite are only considered to be reliable if the balance error (E%) is equal to or less than 10%. [Pg.1048]

It has been possible to use the statistics from the least squares fit of the microwave spectrum through propagation of errors formulas (including the correlation of errors between the determined rotational and distortion constants) to calculate standard deviations for the force constants calculated from the distortion constants. These standard deviations, which represent measurement errors, can be compared with the lack of internal consistency between force constants calculated from different distortion constants. This comparison gives the relative magnitude of measurement vs. model errors. [Pg.315]

There have been several empirical observations or conclusions based on the investigation of small model reaction systems that showed that the rates of consuming reactions of QSSA species are unusually high, that the concentrations, and the net rates of reaction of QSSA species are unusually low, that the induction period is usually short, and that most QSSA species are radicals, These observations are simple consequences of the physical pictures presented above and the error formulas derived from them. [Pg.124]

We express the derivatives w 1 = 2,3,4,which are terms of the local truncation error formulae, in terms of the equation (23). The expressions are presented as polynomials of G... [Pg.148]

Finally, we substitute the expressions of the derivatives, produced in the previous step, into the local truncation error formulae... [Pg.148]

Of course, the infinite sums have to be cut off at some radius. The cutoff radii can be determined using error formulas, for example the maximal error, denoted by r, of cp. It is calculated by summing the far formula up to a pq cutoff of R, hence... [Pg.81]

For a discussion of the maximal pairwise error estimate, see the section on MMM2D. As for MMM2D, a similar expression can be found for the maximal pairwise energy error (for details, see Arnold et al [25]). Using a zero cutoff corresponds to the Yeh and Berkowitz method, for which the ELC error formulas are vahd as well. From these we found that the error for these methods decays exponentially in kz. However, the errors are not uniformly distributed over the slab they are worst at the siuTaces of the slabs, hence the maximal pairwise error should be used instead of the usual rms errors of Eq. 26 (see Fig. 9). [Pg.92]

To summarize, the main profits of the ELC term are that it scales as the number N of particles and has a rigorous error bound. Moreover, this error bound can be used to estimate the size of the image layer contribution and therefore gives a bound on the error introduced by slabwise methods, as proposed by Yeh and Berkowitz [61]. In the second paper on ELC [26] we considered in detail the implementation of the layer correction for the standard Ewald and the P M methods. There we also derived anisotropic Ewald error formulas, gave some fundamental guidelines for optimization, demonstrated the accuracy, and gave error formulas and computation times for typical systems. [Pg.92]

As shown earlier, O Eq. (9.56) gives a different error formula for a different type of product. In the case of products therefore it is worthwhile to think it over whether or not a random sum is hiding behind the problem. This can only happen, of course, when one of the variables is an integer having no dimension. [Pg.413]

The second method is applied when more than two instruments are to be compared. In this case we use the standard error of pooled or average differences (ASD) among instruments. Some confusion occurs in that the formulas differ by the SQRT of 2.0 when applied to two instruments. The pooled error formula gives a smaller value. [Pg.379]


See other pages where Error formulas is mentioned: [Pg.90]    [Pg.38]    [Pg.307]    [Pg.287]    [Pg.294]    [Pg.244]    [Pg.21]    [Pg.264]    [Pg.389]    [Pg.16]    [Pg.301]    [Pg.27]    [Pg.195]    [Pg.59]    [Pg.60]    [Pg.81]    [Pg.86]    [Pg.100]    [Pg.106]    [Pg.59]    [Pg.60]    [Pg.81]    [Pg.86]    [Pg.100]    [Pg.106]    [Pg.90]    [Pg.227]   
See also in sourсe #XX -- [ Pg.100 ]




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Percent error formula

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