Principles of StatisticsThere are many textbooks which describe current methods of statistical analysis, while neglecting related theory. There are equally many advanced textbooks which delve into the far reaches of statistical theory, while bypassing practical applications. But between these two approaches is an unfilled gap, in which theory and practice merge at an intermediate level. Professor M. G. Bulmer's Principles of Statistics, originally published in 1965, was created to fill that need. The new, corrected Dover edition of Principles of Statistics makes this invaluable mid-level text available once again for the classroom or for self-study. Principles of Statistics was created primarily for the student of natural sciences, the social scientist, the undergraduate mathematics student, or anyone familiar with the basics of mathematical language. It assumes no previous knowledge of statistics or probability; nor is extensive mathematical knowledge necessary beyond a familiarity with the fundamentals of differential and integral calculus. (The calculus is used primarily for ease of notation; skill in the techniques of integration is not necessary in order to understand the text.) Professor Bulmer devotes the first chapters to a concise, admirably clear description of basic terminology and fundamental statistical theory: abstract concepts of probability and their applications in dice games, Mendelian heredity, etc.; definitions and examples of discrete and continuous random variables; multivariate distributions and the descriptive tools used to delineate them; expected values; etc. The book then moves quickly to more advanced levels, as Professor Bulmer describes important distributions (binomial, Poisson, exponential, normal, etc.), tests of significance, statistical inference, point estimation, regression, and correlation. Dozens of exercises and problems appear at the end of various chapters, with answers provided at the back of the book. Also included are a number of statistical tables and selected references. |
Contents
RANDOM VARIABLES AND PROBABILITY | |
DESCRIPTIVE PROPERTIES OF DISTRIBUTIONS | |
EXPECTED VALUES | |
THE BINOMIAL POISSON AND EXPONENTIAL | |
THE NORMAL DISTRIBUTION | |
THE χ2 t AND F DISTRIBUTIONS | |
STATISTICAL INFERENCE | |
POINT ESTIMATION | |
REGRESSION AND CORRELATION | |
REFERENCES | |
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Common terms and phrases
95 per cent approximately normally distributed average binomial distribution calculated cells cent confidence interval central limit theorem CHAPTER comb-growth confidence interval consider correlation coefficient covariance cumulative probability function data in Table degrees of freedom denoted dice discrete distributed with mean equal equation error example Expected numbers Expected value experiment exponential distribution fiducial Fisher follows formula frequency distribution head breadth head length histogram independent random variables inductive probability interquartile range kurtosis large number less male birth mathematical mean and variance mean deviation mean µ measure median Mendel method normally distributed null hypothesis number of observations number of successes occur parameter Poisson distribution Poisson variate posterior probability probability distribution probability of obtaining problem proportion quantity regression relative frequency result sampling distribution significance test skewness standard deviation statistical inference statistical probability stillbirth sum of squares Suppose tails theory throw unbiased estimator underlying distribution variate with mean zero