Statistics for

The statistics for the initial conditions, aj(0), are detennined by tlie equilibrium distribution obtained from the... 

It is beyond the scope of these introductory notes to treat individual problems in fine detail, but it is interesting to close the discussion by considering certain, geometric phase related, symmetry effects associated with systems of identical particles. The following account summarizes results from Mead and Truhlar [10] for three such particles. We know, for example, that the fermion statistics for H atoms require that the vibrational-rotational states on the ground electronic energy surface of NH3 must be antisymmetric with respect to binary exchange... 

Caulcutt, R., and R. Boddy, Statistics for Analytical Chemists, Chapman and Hall, London, 1983. Dixon, W. J., and F. J. Massey, Introduction to Statistical Analysis, McGraw-Hill, New York, 1969. 

Miller, J. C., and J. N. Miller, Statistics for Analytical Chemists, Halsted Press, John Wiley, New York, 1984. 

Next, an equation for a test statistic is written, and the test statistic s critical value is found from an appropriate table. This critical value defines the breakpoint between values of the test statistic for which the null hypothesis will be retained or rejected. The test statistic is calculated from the data, compared with the critical value, and the null hypothesis is either rejected or retained. Finally, the result of the significance test is used to answer the original question. 

The test statistic for evaluating the null hypothesis is called an f-test, and is given as either... 

Anderson, R. L. Practical Statistics for Analytical Chemists. Van Nostrand Reinhold New York, 1987. 

Winn, R. L. Statistics for Scientists and Engineers, Prentice-Hall Englewood Cliffs, NJ, 1964 pp. 165-174. 

Rearranging equation 5.f7 gives the test statistic for the slope... 

Once a significant difference has been demonstrated by an analysis of variance, a modified version of the f-test, known as Fisher s least significant difference, can be used to determine which analyst or analysts are responsible for the difference. The test statistic for comparing the mean values Xj and X2 is the f-test described in Chapter 4, except that Spool is replaced by the square root of the within-sample variance obtained from an analysis of variance. 

Miller, J. C. Miller, J. N. Statistics for Analytical Chemistry, 3rd ed. Ellis Horwood Limited Chichester, England, 1993. 

The probabilities of the various dyad, triad, and other sequences that we have examined have all been described by a single probability parameter p. When we used the same kind of statistics for copolymers, we called the situation one of terminal control. We are considering similar statistics here, but the idea that the stereochemistry is controlled by the terminal unit is inappropriate. The active center of the chain end governs the chemistry of the addition, but not the stereochemistry. Neither the terminal unit nor any other repeat unit considered alone has any stereochemistry. Equations (7.62) and (7.63) merely state that an addition must be of one kind or another, but that the rates are not necessarily identical. 

Supply and demand statistics for 1988 for all regions of the wodd as compiled by SRI International are given in Table 5. The wodd producers of acetal resins and their aimual capacities are Hsted in Table 6 (29). Hoechst Celanese and Ultraform Corporation (a joint venture of Degussa and BASF) have aimounced capacity expansions in the United States to 77,000 t and 16,000 t, respectively both were due in place in 1990. Part of general capacity expansion plans, aimounced by Du Pont for completion in 1991, are beHeved to apply to acetal resins. 

In 1988 diaphragm cells accounted for 76% of all U.S. chlorine production, mercury cells for 17%, membrane cells for 5%, and all other production methods for 2%. Corresponding statistics for Canadian production are diaphragm cells, 81% mercury cells, 15% and membrane cells, 4% (5). for a number of reasons, including concerns over mercury pollution, recent trends are away from mercury cell production toward the more environmentally acceptable membrane cells, which also produce higher quality product and have favorable economics. 

International Narcotics Control Board—Vienna, Narcotic Drugs, Estimated World Requirementsfor 1990, Statistics for 1988, United Nations Publ. E/F/S.89.XI.3, New York, 1989, pp. 33ff... 

Statistics for Kirk-Othmer Encyclopedia of Chemical T echnology... 

Annual Survey of Manufacturers, Statistics for Industry Group and Industries, M 89(AS-1), U.S. Department of Commerce, Washington, D.C., 1989. 

Table 10 summarizes sales statistics for the principal segments of the iadustry. The data were gathered by a survey conducted annually by the editors of Ceramic Indust iy magaziae. In 1991, the survey scope was changed from U.S. to a worldwide basis (119,124). Tables 11 and 12 present data gathered by U.S. Department of Commerce agencies. 

Container Glass. Statistics for food, beverage, dmg and cosmetic, and household and industrial containers are compiled and pubflshed by the... 

Production and consumption statistics for sucrose are shown ia Table 1. World production of sucrose dufing 1993—1994 was - 110 million metric tons, of which - 64% was derived from sugarcane. The largest producer is the European Union (EU), followed closely by India and Bra2il. In 1993—1994, the United States ranked fourth in production. World raw sugar prices from 1990—1995 ranged from 20.20—32. l0/kg (10). 

Table 1. Worldwide Production and Consumption Statistics for Beet and Cane Sugar ...

Statistics for the production of basic dyes include those products hsted as cationic dyes, eg, cyanines, for dyeing polyacrylonitrile fibers and the classical triaryhnethane dyes, eg, malachite green, for coloring paper and other office apphcations (2,53). Moreover, statistics for triaryhnethane dyes are also hidden in the production figures for acid, solvent, mordant, and food dyes, and also organic pigments. Between 1975 and 1984, the aimual production of basic dyes in the United States varied from 5000—7700 t. However, from 1985—1990, aimual production of basic dyes varied from 5000—5700 t, and the annual sales value increased from 56 to 73 million per year. 

Economic Aspects. U.S. production statistics for the period 1980 to 1988 are given ia Table 4 (220). Exports amount to ca 20% of annual United States production, and imports amount to almost 10% of domestic production. The main foreign producers are Japan, South Africa, and Canada. South Korea, Brazil, and The People s RepubHc of China are minor producers. Japan s Nippon Soda Co., Ltd. is the world s third largest producer. Two other Japanese producers are Toyo Soda Co., Ltd., and Nankai Chemical Industry, Ltd. 

The terms cocoa and cacao often are used interchangeably in the Hterature. Both terms describe various products from harvest through processing. In this article, the term cocoa will be used to describe products in general and the term cacao will be reserved for botanical contexts. Cocoa traders and brokers frequendy use the term raw cocoa to distinguish unroasted cocoa beans from finished products this term is used to report statistics for cocoa bean production and consumption. 

Production. Worldwide cocoa bean production has increased significantly over the past 10 years from approximately 1.6 million t in the 1979—1980 crop year to over 2.4 million t in 1990. The production share by country has also changed dramatically in the last 10 years. The big gainers are Malaysia, Indonesia, and the Ivory Coast. The large gains in Malaysia and Indonesia have helped to diversify production and partially shield the market from adverse weather-induced supply shocks. The biggest losers in production share have been Brazil and Ghana. Table 2 Hsts production statistics for these countries. 

Lapin, L. L. Statistics for Modern Business Decisions, 2d ed., Harcourt, New York (1982). 

Sincich, T, and Mendenhall, W. Statistics for Engineering and the Sciences. 4th ed., Prentice Hall, Englewood Cliffs, NJ (1995). 

Table 1 Mortality from cancer of the stomach and other causes between 1 January 1946 and 28 February 1981 among 1327 male workers in a factory making ammonium nitrate fertilizer. Deaths observed compared with deaths expected from statistics for workers in comparable jobs in the locality. Statistics for heavily and less heavily exposed workers combined ...

Annual Reports of Gumulative System and Gomponent Reliability for Period from July 1, 1974, through December 31, 1982,serves as a source of engineering and failure statistics for the nuclear industry. It contains data for most components used in nuclear power plants. 

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