Suchergebnisse

1 Introduction -- 1.1 Examples of random variation -- 1.2 One-dimensional frequency distributions -- 1.3 Summarizing quantities -- 1.4 Frequency distributions in two or more dimensions -- 1.5 Some illustrative examples -- 1.6 Populations, samples and probability -- 2 Probability and Probability Distributions -- 2.1 Probability -- 2.2 Addition law of probability -- 2.3 Conditional probability and statistical independence -- 2.4 Examples -- 2.5 Discrete random variables -- 2.6 Continuous random variables -- 2.7 Several random variables -- 3 Expectation and its Applications -- 3.1 Expectation -- 3.2 Variance -- 3.3 Higher moments -- 3.4 Dependence and covariance -- 3.5 Normal models -- 4 Sampling Distributions and Statistical Inference -- 4.1 Statistical inference -- 4.2 Pseudo random deviates -- 4.3 A sampling experiment -- 4.4 Estimation -- 4.5 Significance tests -- 5 Single Sample Problems -- 5.1 Introduction -- 5.2 Point estimates of µ and ?2 -- 5.3 Interval estimates for µ (?2 unknown) -- 5.4 Interval estimates for ?2 -- 5.5 Significance test for a mean -- 5.6 Significance test for a variance -- 5.7 Departures from assumptions -- 6 Two Sample Problems -- 6.1 Introduction -- 6.2 The comparison of two independent sample means -- 6.3 The comparison of two independent sample variances -- 6.4 Analysis of paired samples -- 6.5 An example -- 6.6 Departures from assumptions -- 7 Non-parametric Tests -- 7.1 Introduction -- 7.2 Normal approximation to the binomial distribution -- 7.3 The sign test -- 7.4 The signed rank (Wilcoxon one sample) test -- 7.5 Two sample rank (Wilcoxon) test -- 7.6 Discussion -- 8 The Analysis of Discrete Data -- 8.1 Introduction -- 8.2 Distributions and approximations -- 8.3 Inference about a single Poisson mean -- 8.4 Inference about a single binomial probability -- 8.5 The comparison of two Poisson variates -- 8.6 The comparison of two binomial variates -- 8.7 Comparison of proportions in matched pairs -- 8.8 Examination of Poisson frequency table -- 8.9 Examination of binomial frequency tables -- 8.10 Comparison of observed and expected frequencies -- 8.11 Contingency tables -- 8.12 A tasting experiment -- 9 Statistical Models and Least Squares -- 9.1 General points -- 9.2 An example -- 9.3 Least squares -- 10 Linear Regression -- 10.1 Introduction -- 10.2 Least squares estimates -- 10.3 Properties of ? and ? -- 10.4 Predictions from regressions -- 10.5 Comparison of two regression lines -- 10.6 Equally spaced x-values -- 10.7 Use of residuals -- 10.8 Discussion of models -- 11 Multiple Regression -- 11.1 Introduction -- 11.2 Theory for two explanatory variables only -- 11.3 Analysis of Example 11.2 -- 11.4 Discussion -- 12 Analysis of Variance -- 12.1 The problem -- 12.2 Theory of one-way analysis of variance -- 12.3 Procedure for analysis -- 12.4 Two-way analysis of variance -- 12.5 Linear contrasts -- 12.6 Randomized blocks -- 12.7 Components of variance -- 12.8 Departures from assumptions -- Miscellaneous Exercises -- Appendix One Notes on calculation and computing 307 -- Appendix Two Statistical tables -- Appendix Three Hints to the solution of selected exercises -- References -- Author Index.

1 Some properties of basic statistical procedures -- 1.1 Problems of statistics -- 1.2 The t, X2 and F procedures -- 1.3 Standard assumptions and their plausibility -- 1.4 Tests of normality -- 1.5 Moments of $$\bar{x}$$ and s2 -- 1.6 The effect of skewness and kurtosis on the t-test -- 1.7 The effect of skewness and kurtosis on inferences about variances -- 1.8 The effect of serial correlation -- 1.9 The effect of unequal variances on the two-sample t-test -- 1.10 Discussion -- Further reading -- 2 Regression and the linear model -- 2.1 Linear models -- 2.2 The method of least squares -- 2.3 Properties of the estimators and sums of squares -- 2.4 Further analysis of Example 2.1 -- 2.5 The regressions of y on x and of x on y -- 2.6 Two regressor variables -- 2.7 Discussion -- 3 Statistical models and statistical inference -- 3.1 Parametric inference -- 3.2 Point estimates -- 3.3 The likelihood function -- 3.4 The method of maximum likelihood -- 3.5 The Cramér — Rao inequality -- 3.6 Sufficiency -- 3.7 The multivariate normal distribution -- 3.8 Proof of the Cramér — Rao inequality -- Further reading -- 4 Properties of the method of maximum likelihood -- 4.1 Introduction -- 4.2 Formal statements of main properties -- 4.3 Practical aspects — one-parameter case -- 4.4 Practical aspects — multiparameter case -- 4.5 Other methods of estimation -- 5 The method of least squares -- 5.1 Basic model -- 5.2 Properties of the method -- 5.3 Properties of residuals -- 5.4 Properties of sums of squares -- 5.5 Application to multiple regression -- Further reading -- 6 Multiple regression: Further analysis and interpretation -- 6.1 Testing the significance of subsets of explanatory variables -- 6.2 Application of the extra sum-of-squares principle to multiple regression -- 6.3 Problems of interpretation -- 6.4 Relationships between sums of squares -- 6.5 Departures from assumptions -- 6.6 Predictions from regression -- 6.7 Strategies for multiple regression analysis -- 6.8 Practical details -- Further reading on practical points -- 7 Polynomial regression -- 7.1 Introduction -- 7.2 General theory -- 7.3 Derivation of the polynomials -- 7.4 Tables of orthogonal polynomials -- 7.5 An illustrative example -- 8 The use of transformations -- 8.1 Introduction -- 8.2 One explanatory variable -- 8.3 Transformations for homogeneity of variance -- 8.4 An example -- 8.5 The Box—Cox transformation -- 8.6 Transformations of regressor variables -- 8.7 Application to bioassay data -- Further reading -- 9 Correlation -- 9.1 Definition and examples -- 9.2 Correlation or regression? -- 9.3 Estimation of ? -- 9.4 Results on the distribution of R -- 9.5 Confidence intervals and hypothesis tests for ? -- 9.6 Relationship with regression -- 9.7 Partial correlation -- 9.8 The multiple correlation coefficient -- Further reading -- 10 The analysis of variance -- 10.1 An example -- 10.2 Generalized inverses -- 10.3 Least squares using generalized inverses -- 10.4 One-way classification analysis of variance -- 10.5 A discussion of Example 10.1 -- 10.6 Two-way classification -- 10.7 A discussion of Example 10.2 -- 10.8 General method for analysis of variance -- Further reading -- 11 Designs with regressions in the treatment effects -- 11.1 One-way analysis -- 11.2 Parallel regressions -- 11.3 The two-way analysis -- 12 An analysis of data on trees -- 12.1 The data -- 12.2 Regression analyses -- 12.3 The analysis of covariance -- 12.4 Residuals -- 13 The analysis of variance: Subsidiary analyses -- 13.1 Multiple comparisons: Introduction -- 13.2 Multiple comparisons: Various techniques -- 13.3 Departures from underlying assumptions -- 13.4 Tests for heteroscedasticity -- 13.5 Residuals and outliers -- 13.6 Some points of experimental design: General points -- 13.7 Some points of experimental design: Randomized blocks -- Further reading on experimental design -- 14 Components of variance -- 14.1 Components of variance -- 14.2 Components of variance: Follow-up analysis -- 14.3 Nested classifications -- 14.4 Outline analysis of Example 14.3 -- 14.5 Nested classifications: Finite population model -- 14.6 Sampling from finite populations -- 14.7 Nested classifications with unequal numbers -- Further reading -- 15 Crossed classifications -- 15.1 Crossed classifications and interactions -- 15.2 More about interactions -- 15.3 Analysis of a two-way equally replicated design -- 15.4 An analysis of Example 15.1 -- 15.5 Unit errors -- 15.6 Random-effects models -- 15.7 Analysis of a two-way unequally replicated design -- Further reading -- 16 Further analysis of variance -- 16.1 Three-way crossed classification -- 16.2 An analysis of Example 16.1 -- Further reading -- 17 The generalized linear model -- 17.1 Introduction -- 17.2 The maximum likelihood ratio test -- 17.3 The family of probability distributions permitted -- 17.4 The generalized linear model -- 17.5 The analysis of deviance -- 17.6 Illustration using the radiation experiment data -- Further reading -- References.