Elementary statistics

E is elementary, no background in statistics needed and I is intermediate, assumes one or two elementary statistics courses. 

C. Daniel, App/ications of Statistics to lndustria/Experimentation, ]oE Wiley Sons, Inc., New York, 1976. This book is based on the personal experiences and insights of the author, an eminent practitioner of industrial appHcations of experimental design. It provides extensive discussions and concepts, especially in the areas of factorial and fractional factorial designs. "The book should be of use to experimenters who have some knowledge of elementary statistics and to statisticians who want simple explanations, detailed examples, and a documentation of the variety of outcomes that may be encountered." Some of the unusual features are chapters on "Sequences of fractional repHcates" and "Trend-robust plans," and sections entided, "What is the answer (what is the question )," and "Conclusions and apologies."... 

N. O. Smith, Elementary Statistical Thermodynamics—-A Problems Approach, Plenum Press, New York, 1982. 

To understand the properties of this new phase, it is instructive to contrast them with what we know about conventional ferromagnetic and anti-ferromagnetic phases. For example, we recall from elementary statistical physics, that ferromagnetic systems - that is, systems whose couplings Jij = J > 0, for all i, j - have two... 

SAS System for Elementary Statistical Analysis, Second Edition by Sandra D. Schlotzhauer and Ramon C. Littell... 

By going to a table or graph of the normal distribution, the probability that2 will not be exceeded can be determined. This is the probability that the project can be completed on time. The table can be found in nearly any elementary statistics book3 and in many handbooks. 

Mandel J (1961) Non-additivity in two-way analysis of variance. J Am Statist Assoc 56 878 Neave HR (1981) Elementary statistical tables. Allen Unwin, London... 

While a discussion of /3 properly belongs in the realm of elementary statistics, at this point it is worthwhile to go back to some of those discussions, to examine how this impacts our current interests. We will proceed along with this digression in our next chapter. 

Statistics establish quality limits for the answers derived from a given method. A given laboratory result, or a sample giving rise to a given result, is considered good if it is within these limits. In order to understand how these limits are established, and therefore how it is known if a given result is unacceptable, some basic knowledge of statistics is needed. We now present a limited treatment of elementary statistics. 

The procedure used to determine whether a given result is unacceptable involves running a series of identical tests on the same sample, using the same instrument or other piece of equipment, over and over. In such a scenario, the indeterminate errors manifest themselves in values that deviate, positively and negatively, from the mean (average) of all the values obtained. Given this brief background, let us proceed to define some terms related to elementary statistics. 

Using a spreadsheet function or analysis tool, perform a Smdent s f-test to compare the mean values of each of the first four wear rates with that of gold (the last value in the column) at an agreed-upon confidence level—for example, 95% confidence level. If you have not yet learned how to do Student s f-test, check out any book on elementary statistics, and learn how to do a f-test, or use the Help menus in your spreadsheet package. The goal is to determine if the mean wear rates of the four ceramic materials are statistically different from the wear rate for gold. If done correctly, you will have performed four separate f-tests in this step. 

From elementary statistical thermodynamics we know that the Gibbs free energy of the system is... 

Chapter 5 gives a microscopic-world explanation of the second law, and uses Boltzmann s definition of entropy to derive some elementary statistical mechanics relationships. These are used to develop the kinetic theory of gases and derive formulas for thermodynamic functions based on microscopic partition functions. These formulas are apphed to ideal gases, simple polymer mechanics, and the classical approximation to rotations and vibrations of molecules. 

Ch. Kittel, Elementary Statistical Physics, John Wiley Sons, New York, 1958. 

Smith, N. O. (1982). Elementary Statistical Thermodynamics. Plenum, New York. 

R. Johnson, Elementary Statistics, 4th ed., Dux bury Press, Boston, 1984. 

The classical approximation for the rotational density of states of a molecule is familiar from elementary statistical mechanics, where it is common to assume that the rotational states form a continuum in calculating the rotational partition function. For the external rotations of most molecules this approximation is very good. For example the classical approximation for the rotational partition function of an asymmetric top is... 

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