Intermediate Statistical Methods

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. 4Relationships 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 BoxCox 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 forheteroscedasticity. - 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. Language: English