1 Preliminary Notions. - 1. 1 Introduction. - 1. 2 Sufficiency. - 1. 3 Complete Sufficient Statistics. - 1. 4 Exponential Families of Distributions. - 1. 5 Invariance. - 1. 6 Maximum Likelihood Estimation. - 1. 7 Unbiased Estimation. - 1. 8 Least Squares Estimation. - 1. 9 Interval Estimation. - Exercises. - 2 Notions in significance testing of hypotheses. - 2. 1 Introduction. - 2. 2 Test Statistics and Test Variables. - 2. 3 Definition of p-Value. - 2. 4 Generalized Likelihood Ratio Method. - 2. 5 Invariance in Significance Testing. - 2. 6 Unbiasedness and Similarity. - 2. 7 Interval Estimation and Fixed-Level Testing. - Exercises. - 3 Review of Special Distributions. - 3. 1 Poisson and Binomial Distributions. - 3. 2 Point Estimation and Interval Estimation. - 3. 3 Significance Testing of Parameters. - 3. 4 Bayesian Inference. - 3. 5 The Normal Distribution. - 3. 6 Inferences About the Mean. - 3. 7 Inferences About the Variance. - 3. 8 Quantiles of a Normal Distribution. - 3. 9 Conjugate Prior and Posterior Distributions. - 3. 10 Bayesian Inference About the Mean and the Variance. - Exercises. - 4 Exact Nonparametric Methods. - 4. 1 Introduction. - 4. 2 The Sign Test. - 4. 3 The Signed Rank Test and the Permutation Test. - 4. 4 The Rank Sum Test and Allied Tests. - 4. 5 Comparing k Populations. - 4. 6 Contingency Tables. - 4. 7 Testing the Independence of Criteria of Classification. - 4. 8 Testing the Homogeneity of Populations. - Exercises. - 5 Generalized p-Values. - 5. 1 Introduction. - 5. 2 Generalized Test Variables. - 5. 3 Definition of Generalized p-Values. - 5. 4 Frequency Interpretations and Generalized Fixed-Level Tests. - 5. 5 Invariance. - 5. 6 Comparing the Means of Two Exponential Distributions. - 5. 7 Unbiasedness and Similarity. - 5. 7 Comparing the Means of an Exponential Distribution and a Normal Distribution. - Exercises. - 6 Generalized Confidence Intervals. - 6. 1 Introduction. - 6. 2 Generalized Definitions. - 6. 3 Frequency Interpretations and Repeated Sampling Properties. - 6. 4 Invariance in Interval Estimation. - 6. 5 Interval Estimation of the Difference Between Two Exponential Means. - 6. 6 Similarity in Interval Estimation. - 6. 7 Generalized Confidence Intervals Based on p-Values. - 6. 8 Resolving an Undesirable Feature of Confidence Intervals. - 6. 9 Bayesian and Conditional Confidence Intervals. - Exercises. - 7 Comparing Two Normal Populations. - 7. 1 Introduction. - 7. 2 Comparing the Means when the Variances are Equal. - 7. 3 Solving the Behrens-Fisher Problem. - 7. 4 Inferences About the Ratio of Two Variances. - 7. 5 Inferences About the Difference in Two Variances. - 7. 6 Bayesian Inference. - 7. 7 Inferences About the Reliability Parameter. - 7. 8 The Case of Known Stress Distribution. - Exercises. - 8 Analysis of Variance. - 8. 1 Introduction. - 8. 2 One-way Layout. - 8. 3 Testing the Equality of Means. - 8. 4 ANOVA with Unequal Error Variances. - 8. 5 Multiple Comparisons. - 8. 6 Testing the Equality of Variances. - 8. 7 Two-way ANOVA without Replications. - 8. 8 ANOVA in a Balanced Two-way Layout with Replications. - 8. 9 Two-way ANOVA under Heteroscedasticity. - Exercises. - 9 Mixed Models. - 9. 1 Introduction. - 9. 2 One-way Layout. - 9. 3 Testing Variance Components. - 9. 4 Confidence Intervals. - 9. 5 Two-way Layout. - 9. 6 Comparing Variance Components. - Exercises. - 10 Regression. - 10. 1 Introduction. - 10. 2 Simple Linear Regression Model. - 10. 3. Inferences about Parameters of the Simple Regression Model. - 10. 3 Multiple Linear Regression. - 10. 4 Distributions of Estimators and Significance Tests. - 10. 5 Comparing Two Regressions with Equal Variances. - 10. 6 Comparing Regressions without Common Parameters. - 10. 7 Comparison of Two General Models. - Exercises. - Appendix A. - Elements of Bayesian Inference. - A. 1 Introduction. - A. 2 The Prior Distribution. - A. 3 The Posterior Distribution. - A. 4 Bayes Estimators. - A. 5 Bayesian Interval Estimation. - A. 6 Bayesian Hypothesis Testing. - Appendix B Technical Arguments. - References. Language: English