CARRY statistics

Foreign Commerce Weekly International Trade Statistics Series Foreign Commerce Yearbook. Annual volumes reporting on trade of American Republics with the world. Latest ed. 1949. Volume carrying statistics through 1950 is in press... 

The collection of retention data for all test solutes is time-consuming, and it would be very useful to select only those test solutes that carried statistically valid information, to apply these species to IGC experiments, and then to use the retention data in calculations of X23 vvith the Zhao-Choi procedure. Today, PCA has... 

Carry out a statistical analysis of this data set including a fitting equation and all uncertainties. 

Design of experiments. When conclusions are to be drawn or decisions made on the basis of experimental evidence, statistical techniques are most useful when experimental data are subject to errors. The design of experiments may then often be carried out in such a fashion as to avoid some of the sources of experimental error and make the necessary allowances for that portion which is unavoidable. Second, the results can be presented in terms of probability statements which express the reliabihty of the results. Third, a statistical approach frequently forces a more thorough evaluation of the experimental aims and leads to a more definitive experiment than would otherwise have been performed. 

Estimations based on statistics can be made for total accuracy, precision, and reproducibility of results related to the sampling procedure being applied. Statistical error is expressed in terms of variance. Total samphng error is the sum of error variance from each step of the process. However, discussions herein will take into consideration only step (I)—mechanical extraction of samples. Mechanical-extracdion accuracy is dependent on design reflecding mechanical and statistical factors in carrying out efficient and practical collection of representative samples S from a bulk quantity B,... 

Sample reduction in successive stages—primaiy to secondaiy, secondary to tertiary etc.—can be fulfilled using automatic sampling equipment while observing design principles of statistical sampling. Alternatively, sample quantity reduction may be carried out in a lab-oratoiy. 

Statistical errors of dynamic properties could be expressed by breaking a simulation up into multiple blocks, taking the average from each block, and using those values for statistical analysis. In principle, a block analysis of dynamic properties could be carried out in much the same way as that applied to a static average. However, the block lengths would have to be substantial to make a reasonably accurate estimate of the errors. This approach is based on the assumption that each block is an independent sample. 

It is possible to go beyond the SASA/PB approximation and develop better approximations to current implicit solvent representations with sophisticated statistical mechanical models based on distribution functions or integral equations (see Section V.A). An alternative intermediate approach consists in including a small number of explicit solvent molecules near the solute while the influence of the remain bulk solvent molecules is taken into account implicitly (see Section V.B). On the other hand, in some cases it is necessary to use a treatment that is markedly simpler than SASA/PB to carry out extensive conformational searches. In such situations, it possible to use empirical models that describe the entire solvation free energy on the basis of the SASA (see Section V.C). An even simpler class of approximations consists in using infonnation-based potentials constructed to mimic and reproduce the statistical trends observed in macromolecular structures (see Section V.D). Although the microscopic basis of these approximations is not yet formally linked to a statistical mechanical formulation of implicit solvent, full SASA models and empirical information-based potentials may be very effective for particular problems. 

A capability study is a statistical tool which measures the variations within a manufacturing process. Samples of the product are taken, measured and the variation is compared with a tolerance. This comparison is used to establish how capable the process is in producing the product. Process capability is attributable to a combination of the variability in all of the inputs. Machine capability is calculated when the rest of the inputs are fixed. This means that the process capability is not the same as machine capability. A capability study can be carried out on any of the inputs by fixing all the others. All processes can be described by Figure 1, where the distribution curve for a process shows the variability due to its particular elements. 

When reaction is carried out homogeneously in solution this state of affairs more or less exists and it is possible to achieve a statistically random degree of substitution. (It is to be noted that the primary hydroxyl groups will be more reactive than the secondary hydroxyl groups.)... 

For smaller values of Vj, the behavior of the composite material might not follow Equation (3.84) because there might not be enough fibers to control the matrix elongation. That is, the matrix dominates the composite material and carries the fibers along for the ride. Thus, the fibers would be subjected to high strains with only small loads and would fracture. If all fibers break at the same strain (an occurrence that is quite unlikely from a statistical standpoint), then the composite material will fracture unless the matrix (which occupies only of the representative volume element) can take the entire load imposed on the composite material, that is. 

Equipment failure rate data points carry varying degrees of uncertainty expressed by two measures, confidence and tolerance. Confidence, the statistical measurement of uncertainty, expresses how well the experimentally measured parameter represents the actual parameter. Confidence in the data increases as the sample size is increased. 

---