This book is intended as a textbook for a first course in applied statistics for students of economics, public administration and business administration. A limited knowledge of mathematics and - in one single chapter - some knowledge of elementary matrix algebra is required for understanding the text. Complicated mathematical proofs are avoided and the explanations are based on intuition and numerical examples. The aim of this book is to enable the student to understand the reasoning underlying a statistical analysis and to apply statistical methods to problems likely to be met within the…mehr
This book is intended as a textbook for a first course in applied statistics for students of economics, public administration and business administration. A limited knowledge of mathematics and - in one single chapter - some knowledge of elementary matrix algebra is required for understanding the text. Complicated mathematical proofs are avoided and the explanations are based on intuition and numerical examples. The aim of this book is to enable the student to understand the reasoning underlying a statistical analysis and to apply statistical methods to problems likely to be met within the fields of economics, public administration and business administration. The topics covered by the book are: - methods for exploratory data analysis - probability theory and standard statistical distributions - statistical inference theory - and three main areas of application: regression analysis, survey sampling and contingency tables. The treatment of exploratory data analysis, regression analysis and the analysis of contingency tables are based on the most recent theoretical developments in these areas. Most of the examples have never been presented before in English textbooks.
1. Introduction.- 1.1. Statistical methods.- 1.2. Examples.- 2. Descriptive Statistics.- 2.1. Data and variables.- 2.2. Description of the observed distribution of a categorical variable.- 2.3. Description of the observed distribution of a quantitative variable.- 2.4. Description of a grouped distribution of a quantitative variable.- 2.5. Linear relationship between two quantitative variables.- 2.6. Multiplicative and additive structures in two-way tables.- 3. Probability Theory.- 3.1. Observations and events.- 3.2. Combinations of events.- 3.3. Relative frequencies and probabilities.- 3.4. The axioms of probability theory.- 3.5. Conditional probabilities.- 3.6. Stochastic independence.- 4. Probability Distributions on the Real Line and Random Variables.- 4.1. Probability distributions on the real line.- 4.2. Random variables.- 4.3. Discrete random variables.- 4.4. Continuous random variables.- 4.5. Transformations.- 4.6. Empirical frequencies and density functions.- 5. Mean Values and Variances.- 5.1. The mean value.- 5.2. The variance.- 5.3. Theorems about mean values and variances.- 5.4. Other moments and distributional measures.- 5.5. Applications of location and dispersion measures.- 6. Special Discrete Distributions.- 6.1. The binomial distribution.- 6.2. The Poisson distribution.- 6.3. The Pascal distribution.- 6.4. The multinomial distribution.- 6.5. The hypergeometric distribution.- 7. Special Continuous Distributions.- 7.1. The normal distribution.- 7.2. The log-normal distribution.- 7.3. The exponential distribution.- 7.4. The Pareto distribution.- 7.5. The gamma distribution.- 7.6. A comparison of six distributions.- 8. Multivariate Distributions.- 8.1. Multi-dimensional random variables.- 8.2. Discrete m-dimensional random variables.- 8.3. Continuous m-dimensional random variables.- 8.4. Marginal distributions.- 8.5. Conditional distributions.- 8.6. Independent random variables.- 8.7. Mean values and variances for sums of random variables.- 8.8. The covariance and the correlation coefficient.- 8.9. The multinomial distribution.- 8.10. The distribution of sums of random variables.- 8.11. The multivariate normal distribution.- 9. The Distribution of Sample Functions and Limit Theorems.- 9.1. Introduction.- 9.2. The distribution of $$overline {rm{X}}$$ and S2 for normally distributed random variables.- 9.3. The t-distribution and the F-distribution.- 9.4. The law of large numbers.- 9.5. Limit theorems.- 10. Estimation.- 10.1. The statistical model.- 10.2. Estimation.- 10.3. Maximum likelihood estimation.- 10.4. Unbiased estimators.- 10.5. Consistency.- 10.6. The properties of ML-estimators.- 11. Confidence Intervals.- 11.1. Point estimates and confidence intervals.- 11.2. Confidence intervals.- 11.3. Confidence intervals for the mean value and the variance in the normal distribution.- 11.4. Confidence intervals for the parameters in the binomial distribution and the hypergeometric distribution.- 11.5. Approximate confidence intervals.- 11.6. Concluding remarks.- 12. Testing Statistical Hypotheses.- 12.1. The statistical hypothesis.- 12.2. Significance tests.- 12.3. Construction of tests.- 12.4. Tests in discrete distributions.- 12.5. Conditional tests.- 12.6. Approximate tests.- 12.7. The power of a test.- 12.8. Hypothesis testing and interval estimation.- 13. Models and Tests Related to the Normal Distribution.- 13.1. The u-test.- 13.2. The t-test.- 13.3. The Q-test.- 13.4. The comparison of two independent normally distributed samples.- 13.5. A model for pairwise observations.- 13.6. The model for pairwise observations and the model for two independent samples.- 13.7. The analysis of variance.- 13.8. Distribution free tests.- 14. Simple Linear Regression.- 14.1. Regression analysis.- 14.2. Simple linear regression.- 14.3. Estimation of the parameters.- 14.4. Properties of the LS-estimator.- 14.5. Analysis of variance.- 14.6. Interpretation of the estimated regression parameters and R2.- 14.7. Examination of the residuals.- 14.8. Predictions.- 14.9. Experimental and non-experimental data.- 14.10. Transformations.- 14.11. Comparison of two regression lines.- 15. Multiple Linear Regression.- 15.1. The multiple linear regression model.- 15.2. Estimation of the parameters.- 15.3. Properties of the LS-estimator.- 15.4. Residual analysis.- 15.5. Hypothesis testing.- 15.6. Case analysis.- 15.7. Collinearity.- 15.8. Predictions.- 16. Heteroscedasticity and Autocorrelation.- 16.1. Heteroscedasticity.- 16.2. Autocorrelation.- 17. Survey Sampling.- 17.1. Introduction.- 17.2. Simple random sampling.- 17.3. Simple random sampling in the binary case.- 17.4. Simple random sampling m the general case.- 17.5. Stratified sampling.- 18. Applications of the Multinomial Distribution.- 18.1. Hypothesis testing in the multinomial distribution.- 18.2. Goodness-of-fit tests of discrete distributions.- 18.3. Goodness-of-fit tests of continuous distributions.- 18.4. Comparison of k Poisson distributions.- 19. Analysis of Contingency Tables.- 19.1. The test of independence.- 19.2. The test of homogeneity.- 19.3. Comparison of binomial distributions.- 19.4. The multiplicative Poisson model.- 19.5. The effect of the sampling procedure.- 19.6. Analysis of the marginals of a two-way table.- 19.7. Three-way contingency tables.- Appendix Table.- Index of Examples with Real Data.
1. Introduction.- 1.1. Statistical methods.- 1.2. Examples.- 2. Descriptive Statistics.- 2.1. Data and variables.- 2.2. Description of the observed distribution of a categorical variable.- 2.3. Description of the observed distribution of a quantitative variable.- 2.4. Description of a grouped distribution of a quantitative variable.- 2.5. Linear relationship between two quantitative variables.- 2.6. Multiplicative and additive structures in two-way tables.- 3. Probability Theory.- 3.1. Observations and events.- 3.2. Combinations of events.- 3.3. Relative frequencies and probabilities.- 3.4. The axioms of probability theory.- 3.5. Conditional probabilities.- 3.6. Stochastic independence.- 4. Probability Distributions on the Real Line and Random Variables.- 4.1. Probability distributions on the real line.- 4.2. Random variables.- 4.3. Discrete random variables.- 4.4. Continuous random variables.- 4.5. Transformations.- 4.6. Empirical frequencies and density functions.- 5. Mean Values and Variances.- 5.1. The mean value.- 5.2. The variance.- 5.3. Theorems about mean values and variances.- 5.4. Other moments and distributional measures.- 5.5. Applications of location and dispersion measures.- 6. Special Discrete Distributions.- 6.1. The binomial distribution.- 6.2. The Poisson distribution.- 6.3. The Pascal distribution.- 6.4. The multinomial distribution.- 6.5. The hypergeometric distribution.- 7. Special Continuous Distributions.- 7.1. The normal distribution.- 7.2. The log-normal distribution.- 7.3. The exponential distribution.- 7.4. The Pareto distribution.- 7.5. The gamma distribution.- 7.6. A comparison of six distributions.- 8. Multivariate Distributions.- 8.1. Multi-dimensional random variables.- 8.2. Discrete m-dimensional random variables.- 8.3. Continuous m-dimensional random variables.- 8.4. Marginal distributions.- 8.5. Conditional distributions.- 8.6. Independent random variables.- 8.7. Mean values and variances for sums of random variables.- 8.8. The covariance and the correlation coefficient.- 8.9. The multinomial distribution.- 8.10. The distribution of sums of random variables.- 8.11. The multivariate normal distribution.- 9. The Distribution of Sample Functions and Limit Theorems.- 9.1. Introduction.- 9.2. The distribution of $$overline {rm{X}}$$ and S2 for normally distributed random variables.- 9.3. The t-distribution and the F-distribution.- 9.4. The law of large numbers.- 9.5. Limit theorems.- 10. Estimation.- 10.1. The statistical model.- 10.2. Estimation.- 10.3. Maximum likelihood estimation.- 10.4. Unbiased estimators.- 10.5. Consistency.- 10.6. The properties of ML-estimators.- 11. Confidence Intervals.- 11.1. Point estimates and confidence intervals.- 11.2. Confidence intervals.- 11.3. Confidence intervals for the mean value and the variance in the normal distribution.- 11.4. Confidence intervals for the parameters in the binomial distribution and the hypergeometric distribution.- 11.5. Approximate confidence intervals.- 11.6. Concluding remarks.- 12. Testing Statistical Hypotheses.- 12.1. The statistical hypothesis.- 12.2. Significance tests.- 12.3. Construction of tests.- 12.4. Tests in discrete distributions.- 12.5. Conditional tests.- 12.6. Approximate tests.- 12.7. The power of a test.- 12.8. Hypothesis testing and interval estimation.- 13. Models and Tests Related to the Normal Distribution.- 13.1. The u-test.- 13.2. The t-test.- 13.3. The Q-test.- 13.4. The comparison of two independent normally distributed samples.- 13.5. A model for pairwise observations.- 13.6. The model for pairwise observations and the model for two independent samples.- 13.7. The analysis of variance.- 13.8. Distribution free tests.- 14. Simple Linear Regression.- 14.1. Regression analysis.- 14.2. Simple linear regression.- 14.3. Estimation of the parameters.- 14.4. Properties of the LS-estimator.- 14.5. Analysis of variance.- 14.6. Interpretation of the estimated regression parameters and R2.- 14.7. Examination of the residuals.- 14.8. Predictions.- 14.9. Experimental and non-experimental data.- 14.10. Transformations.- 14.11. Comparison of two regression lines.- 15. Multiple Linear Regression.- 15.1. The multiple linear regression model.- 15.2. Estimation of the parameters.- 15.3. Properties of the LS-estimator.- 15.4. Residual analysis.- 15.5. Hypothesis testing.- 15.6. Case analysis.- 15.7. Collinearity.- 15.8. Predictions.- 16. Heteroscedasticity and Autocorrelation.- 16.1. Heteroscedasticity.- 16.2. Autocorrelation.- 17. Survey Sampling.- 17.1. Introduction.- 17.2. Simple random sampling.- 17.3. Simple random sampling in the binary case.- 17.4. Simple random sampling m the general case.- 17.5. Stratified sampling.- 18. Applications of the Multinomial Distribution.- 18.1. Hypothesis testing in the multinomial distribution.- 18.2. Goodness-of-fit tests of discrete distributions.- 18.3. Goodness-of-fit tests of continuous distributions.- 18.4. Comparison of k Poisson distributions.- 19. Analysis of Contingency Tables.- 19.1. The test of independence.- 19.2. The test of homogeneity.- 19.3. Comparison of binomial distributions.- 19.4. The multiplicative Poisson model.- 19.5. The effect of the sampling procedure.- 19.6. Analysis of the marginals of a two-way table.- 19.7. Three-way contingency tables.- Appendix Table.- Index of Examples with Real Data.
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