| Description |
1 online resource (xviii, 378 pages) : illustrations |
| Contents |
880-01 Statistical Inference: A SHORT COURSE; Contents; Preface; 1 The Nature of Statistics; 1.1 Statistics Defined; 1.2 The Population and the Sample; 1.3 Selecting a Sample from a Population; 1.4 Measurement Scales; 1.5 Let us Add; Exercises; 2 Analyzing Quantitative Data; 2.1 Imposing Order; 2.2 Tabular and Graphical Techniques: Ungrouped Data; 2.3 Tabular and Graphical Techniques: Grouped Data; Exercises; Appendix 2.A Histograms with Classes of Different Lengths; 3 Descriptive Characteristics of Quantitative Data; 3.1 The Search for Summary Characteristics; 3.2 The Arithmetic Mean |
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880-01/(S Machine generated contents note: 1. Nature of Statistics -- 1.1. Statistics Defined -- 1.2. Population and the Sample -- 1.3. Selecting a Sample from a Population -- 1.4. Measurement Scales -- 1.5. Let us Add -- Exercises -- 2. Analyzing Quantitative Data -- 2.1. Imposing Order -- 2.2. Tabular and Graphical Techniques: Ungrouped Data -- 2.3. Tabular and Graphical Techniques: Grouped Data -- Exercises -- Appendix 2.A Histograms with Classes of Different Lengths -- 3. Descriptive Characteristics of Quantitative Data -- 3.1. Search for Summary Characteristics -- 3.2. Arithmetic Mean -- 3.3. Median -- 3.4. Mode -- 3.5. Range -- 3.6. Standard Deviation -- 3.7. Relative Variation -- 3.8. Skewness -- 3.9. Quantiles -- 3.10. Kurtosis -- 3.11. Detection of Outliers -- 3.12. So What Do We Do with All This Stuff-- Exercises -- Appendix 3.A Descriptive Characteristics of Grouped Data -- 3.A.1. Arithmetic Mean -- 3.A.2. Median -- 3.A.3. Mode -- 3.A.4. Standard Deviation -- 3.A.5. Quantiles (Quartiles, Deciles, and Percentiles) -- 4. Essentials of Probability -- 4.1. Set Notation -- 4.2. Events within the Sample Space -- 4.3. Basic Probability Calculations -- 4.4. Joint, Marginal, and Conditional Probability -- 4.5. Sources of Probabilities -- Exercises -- 5. Discrete Probability Distributions and Their Properties -- 5.1. Discrete Probability Distribution -- 5.2. Mean, Variance, and Standard Deviation of a Discrete Random Variable -- 5.3. Binomial Probability Distribution -- 5.3.1. Counting Issues -- 5.3.2. Bernoulli Probability Distribution -- 5.3.3. Binomial Probability Distribution -- Exercises -- 6. Normal Distribution -- 6.1. Continuous Probability Distribution -- 6.2. Normal Distribution -- 6.3. Probability as an Area Under the Normal Curve -- 6.4. Percentiles of the Standard Normal Distribution and Percentiles of the Random Variable X -- Exercises -- Appendix 6.A Normal Approximation to Binomial Probabilities -- 7. Simple Random Sampling and the Sampling Distribution of the Mean -- 7.1. Simple Random Sampling -- 7.2. Sampling Distribution of the Mean -- 7.3. Comments on the Sampling Distribution of the Mean -- 7.4. Central Limit Theorem -- Exercises -- Appendix 7.A Using a Table of Random Numbers -- Appendix 7.B Assessing Normality via the Normal Probability Plot -- Appendix 7.C Randomness, Risk, and Uncertainty -- 7.C.1. Introduction to Randomness -- 7.C.2. Types of Randomness -- 7.C.2.1. Type I Randomness -- 7.C.2.2. Type II Randomness -- 7.C.2.3. Type III Randomness -- 7.C.3. Pseudo-Random Numbers -- 7.C.4. Chaotic Behavior -- 7.C.5. Risk and Uncertainty -- 8. Confidence Interval Estimation of μ -- 8.1. Error Bound on X as an Estimator of μ -- 8.2. Confidence Interval for the Population Mean μ (σ Known) -- 8.3. Sample Size Requirements Formula -- 8.4. Confidence Interval for the Population Mean μ (σ Unknown) -- Exercises -- Appendix 8.A Confidence Interval for the Population Median MED -- 9. Sampling Distribution of a Proportion and its Confidence Interval Estimation -- 9.1. Sampling Distribution of a Proportion -- 9.2. Error Bound on p as an Estimator for p -- 9.3. Confidence Interval for the Population Proportion (of Successes) p -- 9.4. Sample Size Requirements Formula -- Exercises -- Appendix 9.A Ratio Estimation -- 10. Testing Statistical Hypotheses -- 10.1. What is a Statistical Hypothesis-- 10.2. Errors in Testing -- 10.3. Contextual Framework of Hypothesis Testing -- 10.3.1. Types of Errors in a Legal Context -- 10.3.2. Types of Errors in a Medical Context -- 10.3.3. Types of Errors in a Processing or Control Context -- 10.3.4. Types of Errors in a Sports Context -- 10.4. Selecting a Test Statistic -- 10.5. Classical Approach to Hypothesis Testing -- 10.6. Types of Hypothesis Tests -- 10.7. Hypothesis Tests for μ (σ Known) -- 10.8. Hypothesis Tests for μ (σ Unknown and n Small) -- 10.9. Reporting the Results of Statistical Hypothesis Tests -- 10.10. Hypothesis Tests for the Population Proportion (of Successes) p -- Exercises -- Appendix 10.A Assessing the Randomness of a Sample -- Appendix 10.B Wilcoxon Signed Rank Test (of a Median) -- Appendix 10.C Lilliefors Goodness-of-Fit Test for Normality -- 11. Comparing Two Population Means and Two Population Proportions -- 11.1. Confidence Intervals for the Difference of Means when Sampling from Two Independent Normal Populations -- 11.1.1. Sampling from Two Independent Normal Populations with Equal and Known Variances -- 11.1.2. Sampling from Two Independent Normal Populations with Unequal but Known Variances -- 11.1.3. Sampling from Two Independent Normal Populations with Equal but Unknown Variances -- 11.1.4. Sampling from Two Independent Normal Populations with Unequal and Unknown Variances -- 11.2. Confidence Intervals for the Difference of Means when Sampling from Two Dependent Populations: Paired Comparisons -- 11.3. Confidence Intervals for the Difference of Proportions when Sampling from Two Independent Binomial Populations -- 11.4. Statistical Hypothesis Tests for the Difference of Means when Sampling from Two Independent Normal Populations -- 11.4.1. Population Variances Equal and Known -- 11.4.2. Population Variances Unequal but Known -- 11.4.3. Population Variances Equal and Unknown -- 11.4.4. Population Variances Unequal and Unknown (an Approximate Test) -- 11.5. Hypothesis Tests for the Difference of Means when Sampling from Two Dependent Populations: Paired Comparisons -- 11.6. Hypothesis Tests for the Difference of Proportions when Sampling from Two Independent Binomial Populations -- Exercises -- Appendix 11.A Runs Test for Two Independent Samples -- Appendix 11.B Mann-Whitney (Rank Sum) Test for Two Independent Populations -- Appendix 11.C Wilcoxon Signed Rank Test when Sampling from Two Dependent Populations: Paired Comparisons -- 12. Bivariate Regression and Correlation -- 12.1. Introducing an Additional Dimension to our Statistical Analysis -- 12.2. Linear Relationships -- 12.2.1. Exact Linear Relationships -- 12.3. Estimating the Slope and Intercept of the Population Regression Line -- 12.4. Decomposition of the Sample Variation in Y -- 12.5. Mean, Variance, and Sampling Distribution of the Least Squares Estimators β0 and β1 -- 12.6. Confidence Intervals for β0 and β1 -- 12.7. Testing Hypotheses about β0 and β1 -- 12.8. Predicting the Average Value of Y given X -- 12.9. Prediction of a Particular Value of Y given X -- 12.10. Correlation Analysis -- 12.10.1. Case A: X and Y Random Variables -- 12.10.1.1. Estimating the Population Correlation Coefficient ρ -- 12.10.1.2. Inferences about the Population Correlation Coefficient ρ -- 12.10.2. Case B: X Values Fixed, Y a Random Variable -- Exercises -- Appendix 12.A Assessing Normality (Appendix 7.B Continued) -- Appendix 12.B On Making Causal Inferences -- 12.B.1. Introduction -- 12.B.2. Rudiments of Experimental Design -- 12.B.3. Truth Sets, Propositions, and Logical Implications -- 12.B.4. Necessary and Sufficient Conditions -- 12.B.5. Causality Proper -- 12.B.6. Logical Implications and Causality -- 12.B.7. Correlation and Causality -- 12.B.8. Causality from Counterfactuals -- 12.B.9. Testing Causality -- 12.B.10. Suggestions for Further Reading -- 13. Assortment of Additional Statistical Tests -- 13.1. Distributional Hypotheses -- 13.2. Multinomial Chi-Square Statistic -- 13.3. Chi-Square Distribution -- 13.4. Testing Goodness of Fit -- 13.5. Testing Independence -- 13.6. Testing k Proportions -- 13.7. Measure of Strength of Association in a Contingency Table -- 13.8. Confidence Interval for σ2 under Random Sampling from a Normal Population -- 13.9. F Distribution -- 13.10. Applications of the F Statistic to Regression Analysis -- 13.10.1. Testing the Significance of the Regression Relationship Between X and Y -- 13.10.2. Joint Test of the Regression Intercept and Slope -- Exercises -- Appendix A -- Table A.1 Standard Normal Areas [Z is N(0,1)] -- Table A.2 Quantiles of the t Distribution (T is tv) -- Table A.3 Quantiles of the Chi-Square Distribution (X is X2v -- Table A.4 Quantiles of the F Distribution (F is Fv1,v2) -- Table A.5 Binomial Probabilities P(X;n, p) -- Table A.6 Cumulative Binomial Probabilities -- Table A.7 Quantiles of Lilliefors' Test for Normality |
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3.3 The Median3.4 The Mode; 3.5 The Range; 3.6 The Standard Deviation; 3.7 Relative Variation; 3.8 Skewness; 3.9 Quantiles; 3.10 Kurtosis; 3.11 Detection of Outliers; 3.12 So What Do We Do with All This Stuff?; Exercises; Appendix 3.A Descriptive Characteristics of Grouped Data; 3.A.1 The Arithmetic Mean; 3.A.2 The Median; 3.A.3 The Mode; 3.A.4 The Standard Deviation; 3.A.5 Quantiles (Quartiles, Deciles, and Percentiles); 4 Essentials of Probability; 4.1 Set Notation; 4.2 Events within the Sample Space; 4.3 Basic Probability Calculations; 4.4 Joint, Marginal, and Conditional Probability |
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4.5 Sources of ProbabilitiesExercises; 5 Discrete Probability Distributions and Their Properties; 5.1 The Discrete Probability Distribution; 5.2 The Mean, Variance, and Standard Deviation of a Discrete Random Variable; 5.3 The Binomial Probability Distribution; 5.3.1 Counting Issues; 5.3.2 The Bernoulli Probability Distribution; 5.3.3 The Binomial Probability Distribution; Exercises; 6 The Normal Distribution; 6.1 The Continuous Probability Distribution; 6.2 The Normal Distribution; 6.3 Probability as an Area Under the Normal Curve |
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6.4 Percentiles of the Standard Normal Distribution and Percentiles of the Random Variable XExercises; Appendix 6.A The Normal Approximation to Binomial Probabilities; 7 Simple Random Sampling and the Sampling Distribution of the Mean; 7.1 Simple Random Sampling; 7.2 The Sampling Distribution of the Mean; 7.3 Comments on the Sampling Distribution of the Mean; 7.4 A Central Limit Theorem; Exercises; Appendix 7.A Using a Table of Random Numbers; Appendix 7.B Assessing Normality via the Normal Probability Plot; Appendix 7.C Randomness, Risk, and Uncertainty; 7.C.1 Introduction to Randomness |
| Summary |
A concise, easily accessible introduction to descriptive and inferential techniquesStatistical Inference: A Short Course offers a concise presentation of the essentials of basic statistics for readers seeking to acquire a working knowledge of statistical concepts, measures, and procedures. The author conducts tests on the assumption of randomness and normality, provides nonparametric methods when parametric approaches might not work. The book also explores how to determine a confidence interval for a population median while also providing coverage of ratio estimation, randomness, and causality |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Mathematical statistics -- Testbooks
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MATHEMATICS -- Probability & Statistics -- General.
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Mathematical statistics
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Estadística matemàtica.
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| Genre/Form |
Textbooks
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Textbooks.
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| Form |
Electronic book
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| LC no. |
2011047632 |
| ISBN |
9781118309780 |
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1118309782 |
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9781118309773 |
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1118309774 |
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9781118309803 |
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1118309804 |
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9781280699337 |
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1280699337 |
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9786613676313 |
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6613676314 |
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