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Statistics in physical science : estimation, hypothesis testing, and least squares

Author
Hamilton, Walter Clark
Published
New York : Ronald Press Co., [1964]
Physical Description
xi,230 pages : illustrations ; 24 cm

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Contents
BASIC CONCEPTS AND MATHEMATICAL PRELIMINARIES: Sample spaces and probability -- Conditional probability -- Continuous probability distributions -- Functions of a random variable --- Expected values and moments -- Estimation of parameters, confifence intervals, and hypothesis-testing -- Linear equations and Matrix theory -- ESTIMATE WHEN A SINGLE VARIABLE IS INVOLVED: Point estimation -- Normal distribution -- Central limit theorem -- Distribution of a single obsercation from a normal population -- Distribution of the sample mean -- Hypothesis tests when the variance is unknown -- Distribution of the estimate of the variance in a normal population -- Distribution of the ration of two estimates of the same variance; the F distribution -- Condifence limits for the poisson distribution -- Use of x2 as a goodness-of-fit test -- Fisher-Behrens problem -- ANALYSIS OF VARIANCE: Analysis of variance in a r-Way classification -- Analysis of variance in a one-way classification: equal cariances and sample sizes -- Analysis of cariance in a one-war classification: equal cariances and unequal variances and unequal sample sizes; Models I and II -- Analysis of variance in a one-way classification: unequal cariances and sample sizes -- Analysis of cariance for very large sample -- Test for the homogeneity of variances -- Multiple comparisons -- and METHOD OF LEAST SQUARES AND THEORY OF LINEAR HYPOTHESES: Method of least squares -- Geometrical interpretation of the error matrix -- Multivariate normal distribution and distribution properties of quatratuc forms -- Distribution of quadratic forms arising from the least-squares problem -- Linear least squares with constraints -- Multivariate linear hypotheses -- Power of the variance-ratio test for a multidimensional linear hypothesis -- Alternative derication of the least-squares normal equations -- MISCELLANEOUS TOPICS: Choice of weights for least-squares treatments -- Propagation of error -- Nonlinear least squares -- Signifance tests on the value of R -- Problem in experimental design -- Empirical fitting of polynomials to experimental data -- Effects of non-normality of hypothesis tests -- Least square plane through a set of points -- Some further results on correlaiton coefficients -- MISCELLANEOUS APPLICATIONS: Analysis of radioactive decay curves -- Refinement of force constants from infrared spectra -- Application of the least-squares methods to crystallography.
Subject(s)
Bibliography Note
Bibliography: pages 223-225.
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