Statistical Subject

Visual inspection of plot Works Cannot be automated Cannot be tested statistically Subjective... 

OECD (2005). Statistics Subjects (various), http //www.oecd.org/statsportal. 

Gillings D and Koch G (1991) The application of the principle of intention-to-treat analysis of clinical trials Drug Information Journal, 25, 411-424 Greenwood M (1926) The errors of sampling of the survivorship tables Reports on Public Health and Statistical Subjects, No. 33, Appendix 1. London HMSO Grieve AP (2003) The number needed to treat a useful clinical measure or a case of the Emperor s new clothes Pharmaceutical Statistics, 2, 87-102 Haybittle JL (1971) Repeated assessment of results in clinical trials of cancer treatment British Journal of Radiology, 44, 793-797... 

Optimization studies then, both because of their inherent difficulty and the fact that they are recurrent, will involve repeated use of the mathematical model. It is for this reason that its adaptation to a computer is important. In spite of the great reduction in calculating cost due to the automatic computer, however, the total cost of a study will usually not be so small that efficient design of the investigation is not important. The problem is quite similar to that encountered in the statistical subject of design of experiments, and it seems apparent that the two fields should have several common aspects. 

Table 5.11 Values of the Statistics Subject to Various Instability Conditions... 

The most important statistical subjects relevant to reverse engineering are statistical average and statistical reliability. Most statistical averages of material properties such as tensile strength or hardness can be calculated based on their respective normal distributions. However, the Weibull analysis is the most suitable statistical theory for reliability analyses such as fatigue lifing calculation and part life prediction. This chapter will introduce the basic concepts of statistics based on normal distribution, such as probability, confidence level, and interval. It will also discuss the Weibull analysis and reliability prediction. 

There are two types of measurement errors, systematic and random. The former are due to an inherent bias in the measurement procedure, resulting in a consistent deviation of the experimental measurement from its true value. An experimenter s skill and experience provide the only means of consistently detecting and avoiding systematic errors. By contrast, random or statistical errors are assumed to result from a large number of small disturbances. Such errors tend to have simple distributions subject to statistical characterization. 

In the first step, a screening process will be applied to separate the major potential hazards these will be addressed in more detail. QRA techniques are used to evaluate the extent of the risk arising from hazards with the potential to cause major accidents, based on the prediction of the likelihood and magnitude of the event. This assessment will be based on engineering judgement and statistics of previous performance. Where necessary, risk reduction measures will be applied until the level of risk is acceptable. This of course is an emotive subject, since it implies placing a value on human life. 

It is customary in statistical mechanics to obtain the average properties of members of an ensemble, an essentially infinite set of systems subject to the same constraints. Of course each of the systems contains the... 

A reactive species in liquid solution is subject to pemianent random collisions with solvent molecules that lead to statistical fluctuations of position, momentum and internal energy of the solute. The situation can be described by a reaction coordinate X coupled to a huge number of solvent bath modes. If there is a reaction... 

Kramers solution of the barrier crossing problem [45] is discussed at length in chapter A3.8 dealing with condensed-phase reaction dynamics. As the starting point to derive its simplest version one may use the Langevin equation, a stochastic differential equation for the time evolution of a slow variable, the reaction coordinate r, subject to a rapidly statistically fluctuating force F caused by microscopic solute-solvent interactions under the influence of an external force field generated by the PES F for the reaction... 

Simulation runs are typically short (t 10 - 10 MD or MC steps, correspondmg to perhaps a few nanoseconds of real time) compared with the time allowed in laboratory experiments. This means that we need to test whether or not a simulation has reached equilibrium before we can trust the averages calculated in it. Moreover, there is a clear need to subject the simulation averages to a statistical analysis, to make a realistic estimate of the errors. 

Finally, let us consider molecules with identical nuclei that are subject to C (n > 2) rotations. For C2v molecules in which the C2 rotation exchanges two nuclei of half-integer spin, the nuclear statistical weights of the symmetric and antisymmetric rotational levels will be one and three, respectively. For molecules where C2 exchanges two spinless nuclei, one-half of the rotational levels (odd or even J values, depending on the vibrational and electronic states)... 

The Boltzmann distribution is fundamental to statistical mechanics. The Boltzmann distribution is derived by maximising the entropy of the system (in accordance with the second law of thermodynamics) subject to the constraints on the system. Let us consider a system containing N particles (atoms or molecules) such that the energy levels of the... 

The raw data collected during the experiment are then analyzed. Frequently the data must be reduced or transformed to a more readily analyzable form. A statistical treatment of the data is used to evaluate the accuracy and precision of the analysis and to validate the procedure. These results are compared with the criteria established during the design of the experiment, and then the design is reconsidered, additional experimental trials are run, or a solution to the problem is proposed. When a solution is proposed, the results are subject to an external evaluation that may result in a new problem and the beginning of a new analytical cycle. 

Statistical control of an analysis or instmment is best demonstrated by SQC of a standard sample analysis. The preferred approach to demonstrate statistical control is to use a reference sample of the subject material that has been carefully analyzed or, alternatively, to use a purchased reference standard. Either material must be stored so that it remains unchanged, eg, sealed in ampuls or septum capped bottles. Periodically a sample can then be reanalyzed by the technique used for routine analysis. These results are plotted in a control chart. Any change in the stabihty of the test in question results in a lack of... 

Flow cytometer cell counts are much more precise and more accurate than hemocytometer counts. Hemocytometer cell counts are subject both to distributional (13) and sampling (14—16) errors. The distribution of cells across the surface of a hemocytometer is sensitive to the technique used to charge the hemocytometer, and nonuniform cell distribution causes counting errors. In contrast, flow cytometer counts are free of distributional errors. Statistically, count precision improves as the square root of the number of cells counted increases. Flow cytometer counts usually involve 100 times as many cells per sample as hemocytometer counts. Therefore, flow cytometry sampling imprecision is one-tenth that of hemocytometry. 

Subject Categories. The deterrninant for user selection of a database is usually subject matter. That is, when chemical information is desired, a chemical database is selected. The form or media of the database is of secondary importance. The type of search may dictate the need for a full-text or statistical database. If none exists, however, a bibhographic database in the topic area may be used to locate full-text or numeric compilations in hard-copy form. 

C. Lipson and N. J. Sheth, Statistica/Design andAna/ysis of Engineering Experiments, McGraw-HiU, New York, 1972. "This book is written in a relatively simple style so that a reader with a moderate knowledge of mathematics may foUow the subject matter. No prior knowledge of statistics is necessary." Appreciably more discussion is devoted to statistical analysis than to the planning of experiments. Some relatively nonstandard subjects (for an introductory text), such as accelerated experiments, fatigue experiments, and renewal analysis are also included. 

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. 

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