Research Catalog

Title

Statistical theory in research [by] R.L. Anderson [and] T.A. Bancroft.

Author

Anderson, R. L. (Richard Loree), 1915-

Publication

New York, McGraw-Hill, 1952.

Items in the Library & Off-site

Details

Additional Authors

Bancroft, T. A. (Theodore Alfonso), 1907-

Description

399 pages illustrations; 24 cm

Subject

• Statistics
• Research
• Statistics as Topic
• Research
• research (function)
• statistics
• Statistics
• Statistiek
• Probabilidade (Estatistica)
• Mathematical statistics

Genre/Form

• Statistics
• Statistics.
• Statistiques.

Bibliography (note)

• Includes bibliographies.

Contents

• PROBABILITY: Number of ways an event can occur: permutations and combinations -- Stirling's approximation -- Probability and arrangements -- Fundamental laws of probability -- A posteriori probability -- UNIVARIATEPARENT POPULATION DISTRIBUTIONS: Specification -- Discrete distributions -- The binomial distribution -- The poisson distribution -- Continuous distributions -- The normal distribution -- Probability distributions as specialized mathematical functions -- Some mathematical functions useful as probability distributions -- The gamma and beta functions -- PROPERTIES OF UNIVARIATE DISTRIBUTION FUNCTIONS: Mathematical expectation -- Operations with expected values -- Moments -- Moment generating functions -- Cumulants -- An inverse problem -- BIVARIATE AND MULTIVARIATE DISTRIBUTIONS AND THEIR PROPERTIES: Discrete bivariate distributions -- Continuous bivariate distribution -- Distribution of functions of discrete variates -- Distributions of functions of continuous variates -- Expected values for bivariate distributions -- Moments -- Moment and cumulant generating functions -- Extension to k variates -- DERIVED SAMPLING DISTRIBUTIONS AND ORTHOGONAL LINEAR FUNCTIONS: Derived sampling distribution problems -- Random and systematic samples -- Linear functions -- Properties of linear functions -- Orthogonal linear forms -- Linear forms with normally distributed variates --
• DERIVED SAMPLING DISTRIBUTIONS: NORMAL PARENT POPULATION: Distribution of the sample mean X -- Law of large numbers -- The central-limit theorem -- Chi-square distribution -- Properties of the chi-square distribution -- Distribution of a sum of squares of deviations -- Reproductive property of the chi-square distribution -- Simultaneous distribution of the sample mean X and variance estimate 3[squared] -- Distribution of t -- Test of the difference between two means -- Distribution of F -- INTRODUCTION TO POINT ESTIMATION AND CRITERIA OF "GOODNESS": The problem of point estimation -- Unbiasedness -- Consistency -- Efficiency -- Sufficiency -- Amount of information and a measure of efficiency for small samples -- Other forms of I -- PRINCIPLES OF POINT ESTIMATION: MAXIMUM LIKELIHOOD: Basic theory -- Maximum-likelihood and efficient estimators in small samples -- Maximum-likelihood estimators for two or more parameters -- Examples using the principle of maximum likelihood -- INTERVAL ESTIMATION: Intervals for sufficient estimators -- Shortest confidence interval -- More than one unknown parameter -- TESTS OF HYPOTHESES: The general problem -- Types of hypotheses -- Simple hypothesis for a one-parameter distribution -- Composite hypotheses -- Use of power-function tables in planning experiments -- The likelihood-ratio criterion --
• SPECIAL USES OF CHI-SQUARE: Goodness of fit -- Contingency tables -- Homogeneity of a binomial series -- Homogeneity of a poisson series -- Combination of probabilities -- Bartlett's test of homogeneity of variances -- Test of a second-order interaction in a 2X2X2 contingency table -- REGRESSION ANALYSIS: Regression of Y on a single fixed variate -- GENERAL REGRESSION MODEL WITH r FIXED VARIATES: Matrix algebra -- Theory of tests of significance -- The regression problem when certain assumptions are relaxed -- COMPUTATIONAL METHODS AND METHOBS OF ANALYSIS FOR A GENERAL REGRESSION MODEL: The doolittle method of inverting a matrix -- The abbreviated doolittle method -- Analysis of the results -- CURVILINEAR REGRESSION: ORTHOGONAL POLYNOMIALS: Determination of the polynomial -- Estimating the parameters, [alpha]i and o-2 -- LEAST SQUARES FOR EXPERIMENTAL DESIGN MODELS: Assumptions made in the experimental model -- Principles of setting up an experiment -- Methods of increasing the accuracy of the experiment -- THE ANALYSIS OF DESIGNS IN COPIETBLOCKS: Steps in the analysis -- Completely randomized design -- Randomized complete blocks -- Latin-square designs -- THE ANALYSIS OF INCOMPLETE-BLOCKS DESIGNS: General least-squares equations -- Balanced incomplete-blocks designs -- The simple lattice designs -- Other lattice designs -- Methods of constructing incomplete-blocks designs --
• FACTORIAL EXPERIMENTS: The analysis of a p X q factorial experiment -- An alternative analysis for a 2 X 2 factorial experiment -- The alternative analysis of a p X q factorial -- The analysis of a p X q factorial experiment with unequal numbers in the subclasses -- The use of incomplete-blocks designs for factorial experiments -- Construction of experimental designs -- THE ANALYSIS OF COVARIANCE: The use of simple covariance for a randomized complete-blocks experiment -- The use of simple covariance for other experimental designs -- The use of multiple covariance -- VARIANCE COMPONENTS: ALL RANDOM COMPONENTS, EXCEPT THE MEAN: A randomized-blocks model -- Repeated subsampling with equal numbers in the subclasses -- Repeated subsampling with unequal numbers in the subclasses -- ANALYSIS OF DATA WITH BOTH RANDOM AND FIXED EFFECTS (MIXED MODEL): Randomized complete blocks -- Split-plot designs -- THE RECOVERY OF INTERBLOCK INFORMATION IN INCOMPLETE-BLOCKS DESIGNS: Balanced incomplete-blocks designs -- Simple lattice designs -- Other lattice designs -- OTHER TOPICS CONCERNING COMPONENTS OF VARIANCE: SUMMARY OF NEEDED RESEARCH: Covariance -- The use of components of variance in regression problems -- Other topics in relation to variance components.

LCCN

52005984

OCLC

• ocm00180256
• 180256
• SCSB-235562

Owning Institutions

Princeton University Library