U statistic

Table 7.1 Pb and U statistical parameters of 2389 stream sediment samples from campania region...

Many statistical packages can be used to construct ROC plots and shareware is available in the public domain. In this example (taken from ref. 7), the AUC is estimated for an ELISA for T3 using a test reference (Tl), given the mean values of 1.04 and 0.11 the SDs 0.47 and 0.13 and the sample sizes 25 (positive subpopulation) and 75 (negative subpopulation). The rank sum and the U statistic are as follows ... 

A multi-group criterion is the called Wilks X or McCabe U statistics (McCabe, 1975). This is a general statistic used as a measure for testing the difference among group centroids. All classes are assumed to be homogeneous variance-covarianoe matrices and the statistic is defined as... 

Area of Opportunity Use a C Chart if c Statistic Use a U Chart if u Statistic... 

Simha, R., and Yahsi, U., Statistical thermodynamic of hydrocarbon fluids scaling parameters and their group contributions, J. Chem. Soc. Faraday Trans., 91, 707-715 (1995). 

Bertocci, U., Statistics of Localized Breakdown Noise, Proceedings of the 2nd International Conference on Localized Corrosion, NACE-9, H. Isaacs, U. Bertocci, J. Kruger, and S. Smialowska, Eds., NACE International, Houston, TX, 1990, pp. 127-136. 

Wicke, E., and Onken, H. U. Statistical fluctuations of conversion and temperature in an adiabatic fixed-bed reactor for carbon monoxide oxidation. Chem. Eng. Sci. 41(6), 1681-1687, 1986. 

Morris, K., Szynal, D., Some U-statistics in goodness-of-fit tests derived from characterizations via record values. International Journal of Pure and Applied... 

Even if we accept (hat the recording process in a particular population could be reliable, we are still left with the fact that the variability of incident rates is quite high for small groups or for short periods of observation. As we discussed in Chapter 2, the appropriate statistic for computing the standard deviation of an accident rate is the U statistic, based on the Poisson distribution. The standard deviation. 

Incident rates should be plotted on a control chart in order to see if the process is changing over time. The first step is to establish a process mean, which would be the mean recordable rate over the past 12 months or so. The next step is to calculate control limits. The upper control limit is equal to the mean plus 3 standard deviation units as calculated by the U statistic. The lower control limit is the mean minus 3 standard deviation units. Of course it cannot go below zero. The mean and control limits are laid out on a chart, and each month the recordable rate is plotted. The following events indicate that the process has changed (Nelson 1986) ... 

These measures, with their inherent variation, especially with small populations, are likely to generate tampering, namely, management intervention based on the assumption that the process has shifted when it has not. To avoid this, incident rates should be plotted on a control chart, using the U statistic. 

Another statistical mechanical approach makes use of the radial distribution function g(r), which gives the probability of finding a molecule at a distance r from a given one. This function may be obtained experimentally from x-ray or neutron scattering on a liquid or from computer simulation or statistical mechanical theories for model potential energies [56]. Kirkwood and Buff [38] showed that for a given potential function, U(r)... 

The resolution of this issue is based on the application of the Pauli exclusion principle and Femii-Dirac statistics. From the free electron model, the total electronic energy, U, can be written as... 

If one denotes the averages over a canonical distribution by (.. . ), then the relation A = U-T S and U = (W) leads to the statistical mechanical coimection to the themiodynamic free energy A ... 

Reiss H 1977 Scaled particle theory of hard sphere fluids Statistical Mechanics and Statistical Methods in Theory and Application ed U Landman (New York Plenum) pp 99-140... 

Yule G U 1944 Statistical Study of Literary Vocabulary (Cambridge Cambridge University Press)... 

For a given potential energy function U r ), the corresponding generalized statistical probability distribution which is generated by the Monte Carlo algorithm is proportional to... 

K (66.46 e.u.) with the spectroscopic value calculated from experimental data (66.41 0.009 e.u.) (295, 289) indicates that the crystal is an ordered form at 0°K. Thermodynamic functions of thiazole were also determined by statistical thermodynamics from vibrational spectra (297, 298). 

In 1994 in the U.S., recycled PET, HDPE, LDPE, and PS had a 16—46% cost advantage (4). This cost advantage largely disappeared by 1996. Bureau of Labor Statistics data indicate U.S. plastics prices in mid-1997 are seven percent below those of mid-1995 after being more than ten percent less in 1996... 

The U.S. Bureau of Labor Statistics (20) has Hsted 416,000 persons employed as welders, cutters, and welding machine operators, with 90% employed in the fields of manufacturing, services, constmction, and wholesale trades. The same report projects a decline in employment for welders job prospects remain good, however, as the number of qualified workers entering the market is expected to balance workers leaving the field. 

W. G. Heid, U.S. Wheat Industy, Agricultural Economics Report No. 432, U.S. Department of Agricultural Economics, Statistics and Cooperative Service, Washington, D.C., 1979. 

Abrasives have evolved iato an essential component of modem iadustry. Sandstone, emery, and comndum were the abrasives of choice until the late 1800s when artificial materials were developed. Today synthetic abrasives offer such improved performance that the natural ones have been largely replaced except for jobs where cost is paramount. In 1987 U.S. statistics (4) showed natural abrasive production to be about 7 million while that of cmde manufactured abrasives was over 182 million. Total value of abrasives and abrasive products worldwide is estimated to be over 6 biUion dollars. 

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. 

EST)A Agricultural Statistics, U.S. Government Printing Office, Washington, D.C., 1990. 

Economic Aspects. Pertinent statistics on the U.S. production and consumption of fluorspar are given in Table 4. For many years the United States has rehed on imports for more than 80% of fluorspar needs. The principal sources are Mexico, China, and the Repubflc of South Africa. Imports from Mexico have declined in part because Mexican export regulations favor domestic conversion of fluorspar to hydrogen fluoride for export to the United States. 

E. H. Dole and R. A. Barnhart, iiighwaj Statistics, Summary to 1985, U.S. Dept, of Transportation, Eederal Highway Administration, Washington, D.C., 1986, Table VM-201A, pp. 229-232. 

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