Statistics precision

Experience has shown that correlations of good precision are those for which SD/RMS. 1, where SD is the root mean square of the deviations and RMS is the root mean square of the data Pfs. SD is a measure equal to, or approaching in the limit, the standard deviation in parameter predetermined statistics, where a large number of data points determine a small number of parameters. In a few series, RMS is so small that even though SD appears acceptable, / values do exceed. 1. Such sets are of little significance pro or con. Evidence has been presented (2p) that this simple / measure of statistical precision is more trustworthy in measuring the precision of structure-reactivity correlations than is the more conventional correlation coefficient. 

There are some problems associated with this experiment in terms of low statistical precision, uncertainity in S02 concentrations, and the presence of butanol in the system. Statistical precision is low because of the small number of counts and low number of data points taken. Thus, the multiple peaks observed in Figure 3 may actually be only 2 distinct peaks where the broad peak has mobilities ranging from 0.4 cm2V 1s to 1.6 cnrV s and the narrow peak has mobilities centered around 2.0 qwlV s. These peaks thus correspond to those reported by Bricard et al. (1966). 

Why then, is such a complicated and expensive set up necessary AMS combines mass spectrometric features with efficient discrimination of isobaric and molecular interferences. Therefore, it can detect and quantify atomic species of very low abundance. In the case of 14C dating, before AMS was utilized, about 1 g of carbon was needed to date an archaeological item. One gram of fresh carbon contains about 6 x 1010 14C atoms, of which 14 decay per minute. To get 0.5% statistical precision using decay counting, a 48 h acquisition time is necessary. The same result can be obtained with AMS in about 10 min and with only 1 mg of carbon. 

Any time that you refer to statistics, precise numerical information, charts, tables, graphs, illustrations, or photographs to legitimize your points and analysis, you should always include a footnote or citation and credit your source. Numerical statistics are often subject to dispute. For instance, if you state ... 

Note that in the MC methodology, only die energy of the system is computed at any given point. In MD, by contrast, forces are the fundamental variables. Pangali, Rao, and Berne (1978) have described a sampling scheme where forces are used to choose the direction(s) for molecular perturbations. Such a force-biased MC procedure leads to higher acceptance rates and greater statistical precision, but at tlie cost of increased computational resources. 

These considerations will be primary determinants of the experimental design, which will determine the statistical precision and reliability of the models estimated. 

We have carried out the first measurement of the 2S /2 — 2P3/2 interval in 7V6+. Our result is in good agreement with the theory, but the precision of 0.07 cm-1, or. 17% of the Lamb Shift interval, is not sufficient to provide a useful test. However the count rates and signal-to-background ratio achieved, 100 kHz/particle-nA and 25 respectively, are consistent with obtaining a statistical precision of 0.001 cm-1. The beam current and detector solid angle can be increased in future experiments if necessary. 

The statistical precision of better than 10 can be achieved by 10 scattered photons in a given interval of scattering angle. Lets divide the scattering curve into 10 intervalls, then 10 ° scattered photons would be sufficient to solve the above problem. Assuming that the detector would count 10 useful photons per second and about the same amount of background scattering, then the 86 400 seconds of a 24 hour day at a 100% efficient synchrotron radiation source would just allow to do this experiment. Realistically one has to foresee at least two days of beam time for such an experiment. 

Fig. 51. Particle size histograms for the samples in Fig. 50 from electron micrographs of ultramicrotome slices. These particles are all inside the zeolite matrix, but most do not til in a supercage. Some rare particles larger than 3 nm (see Fig. 46) cannot be counted with any statistical precision.

In the application of electrode potential measurements to anaerobic digestion, the University of Michigan has pioneered (2, 6, 10). Physical chemists have stated that the system theoretically cannot generate sufii-cient electroactivity to make such measurements statistically precise further that thermodynamic reversibility, system equilibrium, and steady-state conditions in such biological systems are suflSciently inexact to permit potential results of meaningful nature lastly, that sludge contaminants are serious enough to distort materially all results (11). 

With fluids, we think of the pump as the source of pressure as well as the flow rate determining device. However, with supercritical fluids (in contrast to t3q)ical liquids), a pump needs a control point downstream to hmit the passage of molecules per unit time. This restriction then "holds-back" the previously unlimited flow of molecules to a definite, but not always pre-determined level. Ideally then, the restrictor serves to restrict the flow until the density of molecules distributed from the pump through the extraction region right up to the final restriction point in space is such that the operating density desired in the extraction zone is achieved. This is much easier to state in words than it is to achieve in actual experimental practice. This is especially true if you wish to achieve an experimental set of parameters and hold those values over a finite period of time (ranging from minutes to hours) and do it with the statistical precision and accuracy that are necessary to attain the final quantitative analytical results. 

Thus, the best statistical precision is obtained assuming = 4, supporting the correctness of the interpretion of the data in terms of the tetracarbonate complex. The log,g constant was extrapolated to zero ionic strength using the following interaction coefficients, taken from [97GRE/PLY2] (approximated values) or Table B-4, Appendix B in this review (s(Zr, NOT)) ... 

Quantities with small relaxation times can thus be determined with greater statistical precision, as it will be possible to include a greater number of data sets from a given simulation. Moreover, no quantity with a relaxation time greater than the length of the simulation can be determined accurately. 

To improve the statistical precision, replicate samples are processed for each set of conditions. Our error analysis methods have been described previously (28, 54). The cited measurement uncertainties represent single standard deviations at the 68% confidence level. In the case of yield branching ratios these uncertainties follow directly from statistical random error analysis. Speculative estimates of the contributions from possible systematic mechanistic errors have not been included. 

Precision (ICH) The closeness of agreement (degree of scatter) between a series of measurements obtained from multiple sampling of the same homogenous sample under defined conditions. Precision is considered at three levels repeatability, intermediate precision, and reproducibility. In statistics, precision is typically reported as % coefficient of variation (% CV), also referred to as relative standard deviation (RSD). 

The microscopy and projection microscope techniques are notoriously subject to error, suffering as they do from operator error, calling for considerable dexterity by the operator in cutting and manipulation, and at present 1 am not aware of any statistical precision data on the methods (although see ASTM D 578 ). It is unlikely that reproducibility R will ever approach a level enjoyed by some laboratories in repeatability r tests. 

Most industrial mixtures fail to conform to the statistically ideal pattern of equi-sized particles distinguishable only by colour. It is for this reason that equations (2.5) and (2.6) are so important in establishing the best attainable limits of mixture quality. The statistically precise work of Stange was applied to real powder mixtures by Poole, Taylor and Wall . This application involved assumptions and estimations which in view of the central value of the equation are worthy of investigation. 

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