Application Statistics

Introduction Many types of statistical applications are characterized by enumeration data in the form of counts. Examples are the number of lost-time accidents in a plant, the number of defective items in a sample, and the number of items in a sample that fall within several specified categories. 

Nature Some types of statistical applications deal with counts and proportions rather than measurements. Examples are (1) the... 

Description on statistical applications and clinical interpretation of test results by providing interpretive algorithm for appropriate test follow-up (e.g., an upward trend in test levels in successive time periods or a test value exceeding a specific cutoff level). 

Characterization of Chance Occurrences To deal with a broad area of statistical applications, it is necessary to characterize the way in which random variables will vary by chance alone. The basic foundation for this characteristic is laid through a density called the gaussian, or normal, distribution. 

Nature Some types of statistical applications deal with counts and proportions rather than measurements. Examples are (1) the proportion of workers in a plant who are out sick, (2) lost-time worker accidents per month, (3) defective items in a shipment lot, and (4) preference in consumer surveys. 

H. Mark and J. Workman, Jr., Statistics in Spectroscopy, 2nd ed. (Amsterdam Elsevier, 2003) J. E. DeMuth, Basic Statistics and Pharmaceutical Statistical Applications (New York Marcel Dekker, 1999) and R. N. Forthofer and E. S. Lee, Introduction to Biostatistics (San Diego Academic Press, 1995). 

Two methods appear to be very powerful for the study of critical phenomena field theory as a description of many-body systems, and cell methods grouping together sets of neighboring sites and describing them by an effective Hamiltonian. Both methods are based on the old idea that the relevant scale of critical phenomena is much larger than the interatomic distance and this leads to the notion of scale invariance and to the statistical applications of the renormalization group technique.93... 

In summary, the overall error in microanalysis using GELS is a combination of the statistical error in the measurement of Ia (P, A) which for Poisson statistics (applicable in the case of EELS) is given by VIa, the errors in background fitting and extrapolation (-5%) above VlA, and the accuracy of the ionization cross-sections (theory -5-15%, experiments -2-5%). 

G. Taguchi Reports of statistical application research. JUSE 6, 1-52 (1960)... 

One possible model choice for p(k) that is of widespread use in statistical applications, because of its simplicity and flexibility, is the two-parameter gamma distribution 13... 

BC-MWLAP Government of British Columbia, Ministry of Water, Land and Air Protection (2001). Composite samples A guide for regulators and project managers on the use of composite samples. Contaminated sites statistical applications guidance document No. 12—10. ... 

The magnitude of the operation is perhaps best depicted in terms of the statistics applicable to our recently completed tenth year of operation (see Box 4.1). 

Messina, W. S., Montgomery, D. C. and Keats, J. B., 1996, Strategies for Statistical Monitoring of Integral Control for the Continuous Process Industries, Statistical Applications in Process Control, New York, Marcel Dekker, 47, 193-214. 

I7e. Heat Capacities at High Temperatures.—Although the theoretical treatment of heat capacities requires the limiting high temperature value to be 3/2, i.e., 5.96 cal. deg. g. atom , experimental determinations have shown that with increasing temperature Cv increases still further. The increase is, however, gradual for example, tfie heat capacity of silver is 5.85 cal. deg. g. atom at 300° K and about 6.5 cal. deg. g. atom at 1300° K. This increase is attributed mainly to the relatively free electrons of the metal behaving as an electron gas. By the use of the special form of quantum statistics, viz., Fermi-Dirac statistics, applicable to electrons, the relationship... 

The unknown quantities of interest described in the previous section are examples of parameters. A parameter is a numerical property of a population. One may be interested in measures of central tendency or dispersion in populations. Two parameters of interest for our purposes are the mean and standard deviation. The population mean and standard deviation are represented by p and cr, respectively. The population mean, p, could represent the average treatment effect in the population of individuals with a particular condition. The standard deviation, cr, could represent the typical variability of treatment responses about the population mean. The corresponding properties of a sample, the sample mean and the sample standard deviation, are typically represented by x and s, which were introduced in Chapter 5. Recall that the term "parameter" was encountered in Section 6.5 when describing the two quantities that define the normal distribution. In statistical applications, the values of the parameters of the normal distribution cannot be known, but are estimated by sample statistics. In this sense, the use of the word "parameter" is consistent between the earlier context and the present one. We have adhered to convention by using the term "parameter" in these two slightly different contexts. 

Smyth, G.K. 2004. Linear models and empirical Bayes methods for assessing differential expression in microarray experiments. Statistical Applications in Genetics and Molecular Biology 3 Article 3. 

In the statistical discussion of any gas containing identical molecules, cognizance must be taken of the type of statistics applicable. Often, however, we are not primarily interested in the translational motion of the molecules but only in their distribution among various rotational, vibrational, and electronic states. This distribution can usually be calculated by the use of the Boltzmann distribution law, the effect of the symmetry character being ordinarily negligible (except in so far as the sym-... 

This function is proportional to the probability that a value of x will occur in a number of statistical applications and is discussed in Chapter 11. 

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