Intermediate Statistical MethodsThis book began many years ago as course notes for students at the University of Bath, and later at the University of Kent. Students used draft versions of the chapters, which were consequently revised. Second and third year students, as well as those taking MSc courses have used selections of the chapters. In particular, Chapters I to 7 (only) have been the basis of a very successful second-year course, the more difficult sections being omitted. The aims of this particular course were:- (a) to cover some interesting and useful applications of statistics with an emphasis on applications, but with really adequate theory; (b) to lay the foundations for interesting third-year courses; (c) to tie up with certain areas of pure mathematics and numerical analysis. 2 Students will find Chapter I a useful means of revising the t, X and F procedures, which is material assumed in this text, see Section 1.1. Later sections of Chapter I cover robustness and can be omitted by second-year students or at a first reading. Chapter 2 introduces some simple statistical models, so that the discussion of later chapters is more meaningful. |
Contents
page | 14 |
Further reading | 23 |
Statistical models and statistical inference | 47 |
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analysis of variance analysis-of-variance table apply approximately assumptions asymptotic B₁ B₂ batch calculate cell cent confidence interval Chapter coefficients column components of variance confidence intervals connectors corrected sum correlation covariance matrix CS(x CS(y degrees of freedom Deviations discussed Due to regression effect Equation estimate of o² Example 2.1 Exercise experiment explanatory variables exponential distribution F-test follows hypothesis independent interaction least-squares estimates likelihood function linear regression log-likelihood maximum maximum-likelihood estimate method minimized sum multiple regression normally distributed observations obtain orthogonal outliers plot polynomial problem procedure quadratic random variables replicated residuals response variable sample Section shown in Table shows significance tests Smin Source CSS d.f. squares due standard error statistical statistically independent sum of squares Theorem 4.2 Total transformation treatment two-way unbiased estimator unknown parameters variance-covariance matrix x²-distribution Y₁ Y₂ zero σ² ㅁㅁㅁ