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A concise, easily accessible introduction to descriptive and inferential techniques Statistical 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…mehr
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A concise, easily accessible introduction to descriptive and inferential techniques Statistical 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. To ensure a thorough understanding of all key concepts, Statistical Inference provides numerous examples and solutions along with complete and precise answers to many fundamental questions, including: * How do we determine that a given dataset is actually a random sample? * With what level of precision and reliability can a population sample be estimated? * How are probabilities determined and are they the same thing as odds? * How can we predict the level of one variable from that of another? * What is the strength of the relationship between two variables? The book is organized to present fundamental statistical concepts first, with later chapters exploring more advanced topics and additional statistical tests such as Distributional Hypotheses, Multinomial Chi-Square Statistics, and the Chi-Square Distribution. Each chapter includes appendices and exercises, allowing readers to test their comprehension of the presented material. Statistical Inference: A Short Course is an excellent book for courses on probability, mathematical statistics, and statistical inference at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for researchers and practitioners who would like to develop further insights into essential statistical tools.
Produktdetails
- Produktdetails
- Verlag: John Wiley & Sons
- Seitenzahl: 400
- Erscheinungstermin: 6. Mai 2012
- Englisch
- ISBN-13: 9781118309780
- Artikelnr.: 37354218
- Verlag: John Wiley & Sons
- Seitenzahl: 400
- Erscheinungstermin: 6. Mai 2012
- Englisch
- ISBN-13: 9781118309780
- Artikelnr.: 37354218
MICHAEL J. PANIK, PhD, is Professor Emeritus in the Department of Economics at the University of Hartford. He has served as a consultant to the Connecticut Department of Motor Vehicles as well as a variety of healthcare organizations. Dr. Panik has published numerous journal articles in the areas of economics, mathematics, and applied econometrics.
Preface xv 1 The Nature of Statistics 1 1.1 Statistics Defined 1 1.2 The
Population and the Sample 2 1.3 Selecting a Sample from a Population 3 1.4
Measurement Scales 4 1.5 Let us Add 6 Exercises 7 2 Analyzing Quantitative
Data 9 2.1 Imposing Order 9 2.2 Tabular and Graphical Techniques: Ungrouped
Data 9 2.3 Tabular and Graphical Techniques: Grouped Data 11 Exercises 16
Appendix 2.A Histograms with Classes of Different Lengths 18 3 Descriptive
Characteristics of Quantitative Data 22 3.1 The Search for Summary
Characteristics 22 3.2 The Arithmetic Mean 23 3.3 The Median 26 3.4 The
Mode 27 3.5 The Range 27 3.6 The Standard Deviation 28 3.7 Relative
Variation 33 3.8 Skewness 34 3.9 Quantiles 36 3.10 Kurtosis 38 3.11
Detection of Outliers 39 3.12 So What Do We Do with All This Stuff? 41
Exercises 47 Appendix 3.A Descriptive Characteristics of Grouped Data 51
3.A.1 The Arithmetic Mean 52 3.A.2 The Median 53 3.A.3 The Mode 55 3.A.4
The Standard Deviation 57 3.A.5 Quantiles (Quartiles, Deciles, and
Percentiles) 58 4 Essentials of Probability 61 4.1 Set Notation 61 4.2
Events within the Sample Space 63 4.3 Basic Probability Calculations 64 4.4
Joint, Marginal, and Conditional Probability 68 4.5 Sources of
Probabilities 73 Exercises 75 5 Discrete Probability Distributions and
Their Properties 81 5.1 The Discrete Probability Distribution 81 5.2 The
Mean, Variance, and Standard Deviation of a Discrete Random Variable 85 5.3
The Binomial Probability Distribution 89 5.3.1 Counting Issues 89 5.3.2 The
Bernoulli Probability Distribution 91 5.3.3 The Binomial Probability
Distribution 91 Exercises 96 6 The Normal Distribution 101 6.1 The
Continuous Probability Distribution 101 6.2 The Normal Distribution 102 6.3
Probability as an Area Under the Normal Curve 104 6.4 Percentiles of the
Standard Normal Distribution and Percentiles of the Random Variable X 114
Exercises 116 Appendix 6.A The Normal Approximation to Binomial
Probabilities 120 7 Simple Random Sampling and the Sampling Distribution of
the Mean 122 7.1 Simple Random Sampling 122 7.2 The Sampling Distribution
of the Mean 123 7.3 Comments on the Sampling Distribution of the Mean 127
7.4 A Central Limit Theorem 130 Exercises 132 Appendix 7.A Using a Table of
Random Numbers 133 Appendix 7.B Assessing Normality via the Normal
Probability Plot 136 Appendix 7.C Randomness, Risk, and Uncertainty 139
7.C.1 Introduction to Randomness 139 7.C.2 Types of Randomness 142 7.C.2.1
Type I Randomness 142 7.C.2.2 Type II Randomness 143 7.C.2.3 Type III
Randomness 143 7.C.3 Pseudo-Random Numbers 144 7.C.4 Chaotic Behavior 145
7.C.5 Risk and Uncertainty 146 8 Confidence Interval Estimation of m 152
8.1 The Error Bound on X as an Estimator of m 152 8.2 A Confidence Interval
for the Population Mean m (s Known) 154 8.3 A Sample Size Requirements
Formula 159 8.4 A Confidence Interval for the Population Mean m (s Unknown)
160 Exercises 165 Appendix 8.A A Confidence Interval for the Population
Median MED 167 9 The Sampling Distribution of a Proportion and its
Confidence Interval Estimation 170 9.1 The Sampling Distribution of a
Proportion 170 9.2 The Error Bound on ^p as an Estimator for p 173 9.3 A
Confidence Interval for the Population Proportion (of Successes) p 174 9.4
A Sample Size Requirements Formula 176 Exercises 177 Appendix 9.A Ratio
Estimation 179 10 Testing Statistical Hypotheses 184 10.1 What is a
Statistical Hypothesis? 184 10.2 Errors in Testing 185 10.3 The Contextual
Framework of Hypothesis Testing 186 10.3.1 Types of Errors in a Legal
Context 188 10.3.2 Types of Errors in a Medical Context 188 10.3.3 Types of
Errors in a Processing or Control Context 189 10.3.4 Types of Errors in a
Sports Context 189 10.4 Selecting a Test Statistic 190 10.5 The Classical
Approach to Hypothesis Testing 190 10.6 Types of Hypothesis Tests 191 10.7
Hypothesis Tests for m (s Known) 194 10.8 Hypothesis Tests for m (s Unknown
and n Small) 195 10.9 Reporting the Results of Statistical Hypothesis Tests
198 10.10 Hypothesis Tests for the Population Proportion (of Successes) p
201 Exercises 204 Appendix 10.A Assessing the Randomness of a Sample 208
Appendix 10.B Wilcoxon Signed Rank Test (of a Median) 210 Appendix 10.C
Lilliefors Goodness-of-Fit Test for Normality 213 11 Comparing Two
Population Means and Two Population Proportions 217 11.1 Confidence
Intervals for the Difference of Means when Sampling from Two Independent
Normal Populations 217 11.1.1 Sampling from Two Independent Normal
Populations with Equal and Known Variances 217 11.1.2 Sampling from Two
Independent Normal Populations with Unequal but Known Variances 218 11.1.3
Sampling from Two Independent Normal Populations with Equal but Unknown
Variances 218 11.1.4 Sampling from Two Independent Normal Populations with
Unequal and Unknown Variances 219 11.2 Confidence Intervals for the
Difference of Means when Sampling from Two Dependent Populations: Paired
Comparisons 224 11.3 Confidence Intervals for the Difference of Proportions
when Sampling from Two Independent Binomial Populations 227 11.4
Statistical Hypothesis Tests for the Difference of Means when Sampling from
Two Independent Normal Populations 228 11.4.1 Population Variances Equal
and Known 229 11.4.2 Population Variances Unequal but Known 229 11.4.3
Population Variances Equal and Unknown 229 11.4.4 Population Variances
Unequal and Unknown (an Approximate Test) 230 11.5 Hypothesis Tests for the
Difference of Means when Sampling from Two Dependent Populations: Paired
Comparisons 234 11.6 Hypothesis Tests for the Difference of Proportions
when Sampling from Two Independent Binomial Populations 236 Exercises 239
Appendix 11.A Runs Test for Two Independent Samples 243 Appendix 11.B
Mann-Whitney (Rank Sum) Test for Two Independent Populations 245 Appendix
11.C Wilcoxon Signed Rank Test when Sampling from Two Dependent
Populations: Paired Comparisons 249 12 Bivariate Regression and Correlation
253 12.1 Introducing an Additional Dimension to our Statistical Analysis
253 12.2 Linear Relationships 254 12.2.1 Exact Linear Relationships 254
12.3 Estimating the Slope and Intercept of the Population Regression Line
257 12.4 Decomposition of the Sample Variation in Y 262 12.5 Mean,
Variance, and Sampling Distribution of the Least Squares Estimators ^b0 and
^b1 264 12.6 Confidence Intervals for b0 and b1 266 12.7 Testing Hypotheses
about b0 and b1 267 12.8 Predicting the Average Value of Y given X 269 12.9
The Prediction of a Particular Value of Y given X 270 12.10 Correlation
Analysis 272 12.10.1 Case A: X and Y Random Variables 272 12.10.1.1
Estimating the Population Correlation Coefficient r 274 12.10.1.2
Inferences about the Population Correlation Coefficient r 275 12.10.2 Case
B: X Values Fixed, Y a Random Variable 277 Exercises 278 Appendix 12.A
Assessing Normality (Appendix 7.B Continued) 280 Appendix 12.B On Making
Causal Inferences 281 12.B.1 Introduction 281 12.B.2 Rudiments of
Experimental Design 282 12.B.3 Truth Sets, Propositions, and Logical
Implications 283 12.B.4 Necessary and Sufficient Conditions 285 12.B.5
Causality Proper 286 12.B.6 Logical Implications and Causality 287 12.B.7
Correlation and Causality 288 12.B.8 Causality from Counterfactuals 289
12.B.9 Testing Causality 292 12.B.10 Suggestions for Further Reading 294 13
An Assortment of Additional Statistical Tests 295 13.1 Distributional
Hypotheses 295 13.2 The Multinomial Chi-Square Statistic 295 13.3 The
Chi-Square Distribution 298 13.4 Testing Goodness of Fit 299 13.5 Testing
Independence 304 13.6 Testing k Proportions 309 13.7 A Measure of Strength
of Association in a Contingency Table 311 13.8 A Confidence Interval for s2
under Random Sampling from a Normal Population 312 13.9 The F Distribution
314 13.10 Applications of the F Statistic to Regression Analysis 316
13.10.1 Testing the Significance of the Regression Relationship Between X
and Y 316 13.10.2 A Joint Test of the Regression Intercept and Slope 317
Exercises 318 Appendix A 323 Table A.1 Standard Normal Areas [Z is N(0,1)]
323 Table A.2 Quantiles of the t Distribution (T is tv) 325 Table A.3
Quantiles of the Chi-Square Distribution (X is w2v) 327 Table A.4 Quantiles
of the F Distribution (F is Fv1;v2 ) 329 Table A.5 Binomial Probabilities
P(X;n,p) 334 Table A.6 Cumulative Binomial Probabilities 338 Table A.7
Quantiles of Lilliefors' Test for Normality 342 Solutions to Exercises 343
References 369 Index 373
Population and the Sample 2 1.3 Selecting a Sample from a Population 3 1.4
Measurement Scales 4 1.5 Let us Add 6 Exercises 7 2 Analyzing Quantitative
Data 9 2.1 Imposing Order 9 2.2 Tabular and Graphical Techniques: Ungrouped
Data 9 2.3 Tabular and Graphical Techniques: Grouped Data 11 Exercises 16
Appendix 2.A Histograms with Classes of Different Lengths 18 3 Descriptive
Characteristics of Quantitative Data 22 3.1 The Search for Summary
Characteristics 22 3.2 The Arithmetic Mean 23 3.3 The Median 26 3.4 The
Mode 27 3.5 The Range 27 3.6 The Standard Deviation 28 3.7 Relative
Variation 33 3.8 Skewness 34 3.9 Quantiles 36 3.10 Kurtosis 38 3.11
Detection of Outliers 39 3.12 So What Do We Do with All This Stuff? 41
Exercises 47 Appendix 3.A Descriptive Characteristics of Grouped Data 51
3.A.1 The Arithmetic Mean 52 3.A.2 The Median 53 3.A.3 The Mode 55 3.A.4
The Standard Deviation 57 3.A.5 Quantiles (Quartiles, Deciles, and
Percentiles) 58 4 Essentials of Probability 61 4.1 Set Notation 61 4.2
Events within the Sample Space 63 4.3 Basic Probability Calculations 64 4.4
Joint, Marginal, and Conditional Probability 68 4.5 Sources of
Probabilities 73 Exercises 75 5 Discrete Probability Distributions and
Their Properties 81 5.1 The Discrete Probability Distribution 81 5.2 The
Mean, Variance, and Standard Deviation of a Discrete Random Variable 85 5.3
The Binomial Probability Distribution 89 5.3.1 Counting Issues 89 5.3.2 The
Bernoulli Probability Distribution 91 5.3.3 The Binomial Probability
Distribution 91 Exercises 96 6 The Normal Distribution 101 6.1 The
Continuous Probability Distribution 101 6.2 The Normal Distribution 102 6.3
Probability as an Area Under the Normal Curve 104 6.4 Percentiles of the
Standard Normal Distribution and Percentiles of the Random Variable X 114
Exercises 116 Appendix 6.A The Normal Approximation to Binomial
Probabilities 120 7 Simple Random Sampling and the Sampling Distribution of
the Mean 122 7.1 Simple Random Sampling 122 7.2 The Sampling Distribution
of the Mean 123 7.3 Comments on the Sampling Distribution of the Mean 127
7.4 A Central Limit Theorem 130 Exercises 132 Appendix 7.A Using a Table of
Random Numbers 133 Appendix 7.B Assessing Normality via the Normal
Probability Plot 136 Appendix 7.C Randomness, Risk, and Uncertainty 139
7.C.1 Introduction to Randomness 139 7.C.2 Types of Randomness 142 7.C.2.1
Type I Randomness 142 7.C.2.2 Type II Randomness 143 7.C.2.3 Type III
Randomness 143 7.C.3 Pseudo-Random Numbers 144 7.C.4 Chaotic Behavior 145
7.C.5 Risk and Uncertainty 146 8 Confidence Interval Estimation of m 152
8.1 The Error Bound on X as an Estimator of m 152 8.2 A Confidence Interval
for the Population Mean m (s Known) 154 8.3 A Sample Size Requirements
Formula 159 8.4 A Confidence Interval for the Population Mean m (s Unknown)
160 Exercises 165 Appendix 8.A A Confidence Interval for the Population
Median MED 167 9 The Sampling Distribution of a Proportion and its
Confidence Interval Estimation 170 9.1 The Sampling Distribution of a
Proportion 170 9.2 The Error Bound on ^p as an Estimator for p 173 9.3 A
Confidence Interval for the Population Proportion (of Successes) p 174 9.4
A Sample Size Requirements Formula 176 Exercises 177 Appendix 9.A Ratio
Estimation 179 10 Testing Statistical Hypotheses 184 10.1 What is a
Statistical Hypothesis? 184 10.2 Errors in Testing 185 10.3 The Contextual
Framework of Hypothesis Testing 186 10.3.1 Types of Errors in a Legal
Context 188 10.3.2 Types of Errors in a Medical Context 188 10.3.3 Types of
Errors in a Processing or Control Context 189 10.3.4 Types of Errors in a
Sports Context 189 10.4 Selecting a Test Statistic 190 10.5 The Classical
Approach to Hypothesis Testing 190 10.6 Types of Hypothesis Tests 191 10.7
Hypothesis Tests for m (s Known) 194 10.8 Hypothesis Tests for m (s Unknown
and n Small) 195 10.9 Reporting the Results of Statistical Hypothesis Tests
198 10.10 Hypothesis Tests for the Population Proportion (of Successes) p
201 Exercises 204 Appendix 10.A Assessing the Randomness of a Sample 208
Appendix 10.B Wilcoxon Signed Rank Test (of a Median) 210 Appendix 10.C
Lilliefors Goodness-of-Fit Test for Normality 213 11 Comparing Two
Population Means and Two Population Proportions 217 11.1 Confidence
Intervals for the Difference of Means when Sampling from Two Independent
Normal Populations 217 11.1.1 Sampling from Two Independent Normal
Populations with Equal and Known Variances 217 11.1.2 Sampling from Two
Independent Normal Populations with Unequal but Known Variances 218 11.1.3
Sampling from Two Independent Normal Populations with Equal but Unknown
Variances 218 11.1.4 Sampling from Two Independent Normal Populations with
Unequal and Unknown Variances 219 11.2 Confidence Intervals for the
Difference of Means when Sampling from Two Dependent Populations: Paired
Comparisons 224 11.3 Confidence Intervals for the Difference of Proportions
when Sampling from Two Independent Binomial Populations 227 11.4
Statistical Hypothesis Tests for the Difference of Means when Sampling from
Two Independent Normal Populations 228 11.4.1 Population Variances Equal
and Known 229 11.4.2 Population Variances Unequal but Known 229 11.4.3
Population Variances Equal and Unknown 229 11.4.4 Population Variances
Unequal and Unknown (an Approximate Test) 230 11.5 Hypothesis Tests for the
Difference of Means when Sampling from Two Dependent Populations: Paired
Comparisons 234 11.6 Hypothesis Tests for the Difference of Proportions
when Sampling from Two Independent Binomial Populations 236 Exercises 239
Appendix 11.A Runs Test for Two Independent Samples 243 Appendix 11.B
Mann-Whitney (Rank Sum) Test for Two Independent Populations 245 Appendix
11.C Wilcoxon Signed Rank Test when Sampling from Two Dependent
Populations: Paired Comparisons 249 12 Bivariate Regression and Correlation
253 12.1 Introducing an Additional Dimension to our Statistical Analysis
253 12.2 Linear Relationships 254 12.2.1 Exact Linear Relationships 254
12.3 Estimating the Slope and Intercept of the Population Regression Line
257 12.4 Decomposition of the Sample Variation in Y 262 12.5 Mean,
Variance, and Sampling Distribution of the Least Squares Estimators ^b0 and
^b1 264 12.6 Confidence Intervals for b0 and b1 266 12.7 Testing Hypotheses
about b0 and b1 267 12.8 Predicting the Average Value of Y given X 269 12.9
The Prediction of a Particular Value of Y given X 270 12.10 Correlation
Analysis 272 12.10.1 Case A: X and Y Random Variables 272 12.10.1.1
Estimating the Population Correlation Coefficient r 274 12.10.1.2
Inferences about the Population Correlation Coefficient r 275 12.10.2 Case
B: X Values Fixed, Y a Random Variable 277 Exercises 278 Appendix 12.A
Assessing Normality (Appendix 7.B Continued) 280 Appendix 12.B On Making
Causal Inferences 281 12.B.1 Introduction 281 12.B.2 Rudiments of
Experimental Design 282 12.B.3 Truth Sets, Propositions, and Logical
Implications 283 12.B.4 Necessary and Sufficient Conditions 285 12.B.5
Causality Proper 286 12.B.6 Logical Implications and Causality 287 12.B.7
Correlation and Causality 288 12.B.8 Causality from Counterfactuals 289
12.B.9 Testing Causality 292 12.B.10 Suggestions for Further Reading 294 13
An Assortment of Additional Statistical Tests 295 13.1 Distributional
Hypotheses 295 13.2 The Multinomial Chi-Square Statistic 295 13.3 The
Chi-Square Distribution 298 13.4 Testing Goodness of Fit 299 13.5 Testing
Independence 304 13.6 Testing k Proportions 309 13.7 A Measure of Strength
of Association in a Contingency Table 311 13.8 A Confidence Interval for s2
under Random Sampling from a Normal Population 312 13.9 The F Distribution
314 13.10 Applications of the F Statistic to Regression Analysis 316
13.10.1 Testing the Significance of the Regression Relationship Between X
and Y 316 13.10.2 A Joint Test of the Regression Intercept and Slope 317
Exercises 318 Appendix A 323 Table A.1 Standard Normal Areas [Z is N(0,1)]
323 Table A.2 Quantiles of the t Distribution (T is tv) 325 Table A.3
Quantiles of the Chi-Square Distribution (X is w2v) 327 Table A.4 Quantiles
of the F Distribution (F is Fv1;v2 ) 329 Table A.5 Binomial Probabilities
P(X;n,p) 334 Table A.6 Cumulative Binomial Probabilities 338 Table A.7
Quantiles of Lilliefors' Test for Normality 342 Solutions to Exercises 343
References 369 Index 373
Preface xv 1 The Nature of Statistics 1 1.1 Statistics Defined 1 1.2 The
Population and the Sample 2 1.3 Selecting a Sample from a Population 3 1.4
Measurement Scales 4 1.5 Let us Add 6 Exercises 7 2 Analyzing Quantitative
Data 9 2.1 Imposing Order 9 2.2 Tabular and Graphical Techniques: Ungrouped
Data 9 2.3 Tabular and Graphical Techniques: Grouped Data 11 Exercises 16
Appendix 2.A Histograms with Classes of Different Lengths 18 3 Descriptive
Characteristics of Quantitative Data 22 3.1 The Search for Summary
Characteristics 22 3.2 The Arithmetic Mean 23 3.3 The Median 26 3.4 The
Mode 27 3.5 The Range 27 3.6 The Standard Deviation 28 3.7 Relative
Variation 33 3.8 Skewness 34 3.9 Quantiles 36 3.10 Kurtosis 38 3.11
Detection of Outliers 39 3.12 So What Do We Do with All This Stuff? 41
Exercises 47 Appendix 3.A Descriptive Characteristics of Grouped Data 51
3.A.1 The Arithmetic Mean 52 3.A.2 The Median 53 3.A.3 The Mode 55 3.A.4
The Standard Deviation 57 3.A.5 Quantiles (Quartiles, Deciles, and
Percentiles) 58 4 Essentials of Probability 61 4.1 Set Notation 61 4.2
Events within the Sample Space 63 4.3 Basic Probability Calculations 64 4.4
Joint, Marginal, and Conditional Probability 68 4.5 Sources of
Probabilities 73 Exercises 75 5 Discrete Probability Distributions and
Their Properties 81 5.1 The Discrete Probability Distribution 81 5.2 The
Mean, Variance, and Standard Deviation of a Discrete Random Variable 85 5.3
The Binomial Probability Distribution 89 5.3.1 Counting Issues 89 5.3.2 The
Bernoulli Probability Distribution 91 5.3.3 The Binomial Probability
Distribution 91 Exercises 96 6 The Normal Distribution 101 6.1 The
Continuous Probability Distribution 101 6.2 The Normal Distribution 102 6.3
Probability as an Area Under the Normal Curve 104 6.4 Percentiles of the
Standard Normal Distribution and Percentiles of the Random Variable X 114
Exercises 116 Appendix 6.A The Normal Approximation to Binomial
Probabilities 120 7 Simple Random Sampling and the Sampling Distribution of
the Mean 122 7.1 Simple Random Sampling 122 7.2 The Sampling Distribution
of the Mean 123 7.3 Comments on the Sampling Distribution of the Mean 127
7.4 A Central Limit Theorem 130 Exercises 132 Appendix 7.A Using a Table of
Random Numbers 133 Appendix 7.B Assessing Normality via the Normal
Probability Plot 136 Appendix 7.C Randomness, Risk, and Uncertainty 139
7.C.1 Introduction to Randomness 139 7.C.2 Types of Randomness 142 7.C.2.1
Type I Randomness 142 7.C.2.2 Type II Randomness 143 7.C.2.3 Type III
Randomness 143 7.C.3 Pseudo-Random Numbers 144 7.C.4 Chaotic Behavior 145
7.C.5 Risk and Uncertainty 146 8 Confidence Interval Estimation of m 152
8.1 The Error Bound on X as an Estimator of m 152 8.2 A Confidence Interval
for the Population Mean m (s Known) 154 8.3 A Sample Size Requirements
Formula 159 8.4 A Confidence Interval for the Population Mean m (s Unknown)
160 Exercises 165 Appendix 8.A A Confidence Interval for the Population
Median MED 167 9 The Sampling Distribution of a Proportion and its
Confidence Interval Estimation 170 9.1 The Sampling Distribution of a
Proportion 170 9.2 The Error Bound on ^p as an Estimator for p 173 9.3 A
Confidence Interval for the Population Proportion (of Successes) p 174 9.4
A Sample Size Requirements Formula 176 Exercises 177 Appendix 9.A Ratio
Estimation 179 10 Testing Statistical Hypotheses 184 10.1 What is a
Statistical Hypothesis? 184 10.2 Errors in Testing 185 10.3 The Contextual
Framework of Hypothesis Testing 186 10.3.1 Types of Errors in a Legal
Context 188 10.3.2 Types of Errors in a Medical Context 188 10.3.3 Types of
Errors in a Processing or Control Context 189 10.3.4 Types of Errors in a
Sports Context 189 10.4 Selecting a Test Statistic 190 10.5 The Classical
Approach to Hypothesis Testing 190 10.6 Types of Hypothesis Tests 191 10.7
Hypothesis Tests for m (s Known) 194 10.8 Hypothesis Tests for m (s Unknown
and n Small) 195 10.9 Reporting the Results of Statistical Hypothesis Tests
198 10.10 Hypothesis Tests for the Population Proportion (of Successes) p
201 Exercises 204 Appendix 10.A Assessing the Randomness of a Sample 208
Appendix 10.B Wilcoxon Signed Rank Test (of a Median) 210 Appendix 10.C
Lilliefors Goodness-of-Fit Test for Normality 213 11 Comparing Two
Population Means and Two Population Proportions 217 11.1 Confidence
Intervals for the Difference of Means when Sampling from Two Independent
Normal Populations 217 11.1.1 Sampling from Two Independent Normal
Populations with Equal and Known Variances 217 11.1.2 Sampling from Two
Independent Normal Populations with Unequal but Known Variances 218 11.1.3
Sampling from Two Independent Normal Populations with Equal but Unknown
Variances 218 11.1.4 Sampling from Two Independent Normal Populations with
Unequal and Unknown Variances 219 11.2 Confidence Intervals for the
Difference of Means when Sampling from Two Dependent Populations: Paired
Comparisons 224 11.3 Confidence Intervals for the Difference of Proportions
when Sampling from Two Independent Binomial Populations 227 11.4
Statistical Hypothesis Tests for the Difference of Means when Sampling from
Two Independent Normal Populations 228 11.4.1 Population Variances Equal
and Known 229 11.4.2 Population Variances Unequal but Known 229 11.4.3
Population Variances Equal and Unknown 229 11.4.4 Population Variances
Unequal and Unknown (an Approximate Test) 230 11.5 Hypothesis Tests for the
Difference of Means when Sampling from Two Dependent Populations: Paired
Comparisons 234 11.6 Hypothesis Tests for the Difference of Proportions
when Sampling from Two Independent Binomial Populations 236 Exercises 239
Appendix 11.A Runs Test for Two Independent Samples 243 Appendix 11.B
Mann-Whitney (Rank Sum) Test for Two Independent Populations 245 Appendix
11.C Wilcoxon Signed Rank Test when Sampling from Two Dependent
Populations: Paired Comparisons 249 12 Bivariate Regression and Correlation
253 12.1 Introducing an Additional Dimension to our Statistical Analysis
253 12.2 Linear Relationships 254 12.2.1 Exact Linear Relationships 254
12.3 Estimating the Slope and Intercept of the Population Regression Line
257 12.4 Decomposition of the Sample Variation in Y 262 12.5 Mean,
Variance, and Sampling Distribution of the Least Squares Estimators ^b0 and
^b1 264 12.6 Confidence Intervals for b0 and b1 266 12.7 Testing Hypotheses
about b0 and b1 267 12.8 Predicting the Average Value of Y given X 269 12.9
The Prediction of a Particular Value of Y given X 270 12.10 Correlation
Analysis 272 12.10.1 Case A: X and Y Random Variables 272 12.10.1.1
Estimating the Population Correlation Coefficient r 274 12.10.1.2
Inferences about the Population Correlation Coefficient r 275 12.10.2 Case
B: X Values Fixed, Y a Random Variable 277 Exercises 278 Appendix 12.A
Assessing Normality (Appendix 7.B Continued) 280 Appendix 12.B On Making
Causal Inferences 281 12.B.1 Introduction 281 12.B.2 Rudiments of
Experimental Design 282 12.B.3 Truth Sets, Propositions, and Logical
Implications 283 12.B.4 Necessary and Sufficient Conditions 285 12.B.5
Causality Proper 286 12.B.6 Logical Implications and Causality 287 12.B.7
Correlation and Causality 288 12.B.8 Causality from Counterfactuals 289
12.B.9 Testing Causality 292 12.B.10 Suggestions for Further Reading 294 13
An Assortment of Additional Statistical Tests 295 13.1 Distributional
Hypotheses 295 13.2 The Multinomial Chi-Square Statistic 295 13.3 The
Chi-Square Distribution 298 13.4 Testing Goodness of Fit 299 13.5 Testing
Independence 304 13.6 Testing k Proportions 309 13.7 A Measure of Strength
of Association in a Contingency Table 311 13.8 A Confidence Interval for s2
under Random Sampling from a Normal Population 312 13.9 The F Distribution
314 13.10 Applications of the F Statistic to Regression Analysis 316
13.10.1 Testing the Significance of the Regression Relationship Between X
and Y 316 13.10.2 A Joint Test of the Regression Intercept and Slope 317
Exercises 318 Appendix A 323 Table A.1 Standard Normal Areas [Z is N(0,1)]
323 Table A.2 Quantiles of the t Distribution (T is tv) 325 Table A.3
Quantiles of the Chi-Square Distribution (X is w2v) 327 Table A.4 Quantiles
of the F Distribution (F is Fv1;v2 ) 329 Table A.5 Binomial Probabilities
P(X;n,p) 334 Table A.6 Cumulative Binomial Probabilities 338 Table A.7
Quantiles of Lilliefors' Test for Normality 342 Solutions to Exercises 343
References 369 Index 373
Population and the Sample 2 1.3 Selecting a Sample from a Population 3 1.4
Measurement Scales 4 1.5 Let us Add 6 Exercises 7 2 Analyzing Quantitative
Data 9 2.1 Imposing Order 9 2.2 Tabular and Graphical Techniques: Ungrouped
Data 9 2.3 Tabular and Graphical Techniques: Grouped Data 11 Exercises 16
Appendix 2.A Histograms with Classes of Different Lengths 18 3 Descriptive
Characteristics of Quantitative Data 22 3.1 The Search for Summary
Characteristics 22 3.2 The Arithmetic Mean 23 3.3 The Median 26 3.4 The
Mode 27 3.5 The Range 27 3.6 The Standard Deviation 28 3.7 Relative
Variation 33 3.8 Skewness 34 3.9 Quantiles 36 3.10 Kurtosis 38 3.11
Detection of Outliers 39 3.12 So What Do We Do with All This Stuff? 41
Exercises 47 Appendix 3.A Descriptive Characteristics of Grouped Data 51
3.A.1 The Arithmetic Mean 52 3.A.2 The Median 53 3.A.3 The Mode 55 3.A.4
The Standard Deviation 57 3.A.5 Quantiles (Quartiles, Deciles, and
Percentiles) 58 4 Essentials of Probability 61 4.1 Set Notation 61 4.2
Events within the Sample Space 63 4.3 Basic Probability Calculations 64 4.4
Joint, Marginal, and Conditional Probability 68 4.5 Sources of
Probabilities 73 Exercises 75 5 Discrete Probability Distributions and
Their Properties 81 5.1 The Discrete Probability Distribution 81 5.2 The
Mean, Variance, and Standard Deviation of a Discrete Random Variable 85 5.3
The Binomial Probability Distribution 89 5.3.1 Counting Issues 89 5.3.2 The
Bernoulli Probability Distribution 91 5.3.3 The Binomial Probability
Distribution 91 Exercises 96 6 The Normal Distribution 101 6.1 The
Continuous Probability Distribution 101 6.2 The Normal Distribution 102 6.3
Probability as an Area Under the Normal Curve 104 6.4 Percentiles of the
Standard Normal Distribution and Percentiles of the Random Variable X 114
Exercises 116 Appendix 6.A The Normal Approximation to Binomial
Probabilities 120 7 Simple Random Sampling and the Sampling Distribution of
the Mean 122 7.1 Simple Random Sampling 122 7.2 The Sampling Distribution
of the Mean 123 7.3 Comments on the Sampling Distribution of the Mean 127
7.4 A Central Limit Theorem 130 Exercises 132 Appendix 7.A Using a Table of
Random Numbers 133 Appendix 7.B Assessing Normality via the Normal
Probability Plot 136 Appendix 7.C Randomness, Risk, and Uncertainty 139
7.C.1 Introduction to Randomness 139 7.C.2 Types of Randomness 142 7.C.2.1
Type I Randomness 142 7.C.2.2 Type II Randomness 143 7.C.2.3 Type III
Randomness 143 7.C.3 Pseudo-Random Numbers 144 7.C.4 Chaotic Behavior 145
7.C.5 Risk and Uncertainty 146 8 Confidence Interval Estimation of m 152
8.1 The Error Bound on X as an Estimator of m 152 8.2 A Confidence Interval
for the Population Mean m (s Known) 154 8.3 A Sample Size Requirements
Formula 159 8.4 A Confidence Interval for the Population Mean m (s Unknown)
160 Exercises 165 Appendix 8.A A Confidence Interval for the Population
Median MED 167 9 The Sampling Distribution of a Proportion and its
Confidence Interval Estimation 170 9.1 The Sampling Distribution of a
Proportion 170 9.2 The Error Bound on ^p as an Estimator for p 173 9.3 A
Confidence Interval for the Population Proportion (of Successes) p 174 9.4
A Sample Size Requirements Formula 176 Exercises 177 Appendix 9.A Ratio
Estimation 179 10 Testing Statistical Hypotheses 184 10.1 What is a
Statistical Hypothesis? 184 10.2 Errors in Testing 185 10.3 The Contextual
Framework of Hypothesis Testing 186 10.3.1 Types of Errors in a Legal
Context 188 10.3.2 Types of Errors in a Medical Context 188 10.3.3 Types of
Errors in a Processing or Control Context 189 10.3.4 Types of Errors in a
Sports Context 189 10.4 Selecting a Test Statistic 190 10.5 The Classical
Approach to Hypothesis Testing 190 10.6 Types of Hypothesis Tests 191 10.7
Hypothesis Tests for m (s Known) 194 10.8 Hypothesis Tests for m (s Unknown
and n Small) 195 10.9 Reporting the Results of Statistical Hypothesis Tests
198 10.10 Hypothesis Tests for the Population Proportion (of Successes) p
201 Exercises 204 Appendix 10.A Assessing the Randomness of a Sample 208
Appendix 10.B Wilcoxon Signed Rank Test (of a Median) 210 Appendix 10.C
Lilliefors Goodness-of-Fit Test for Normality 213 11 Comparing Two
Population Means and Two Population Proportions 217 11.1 Confidence
Intervals for the Difference of Means when Sampling from Two Independent
Normal Populations 217 11.1.1 Sampling from Two Independent Normal
Populations with Equal and Known Variances 217 11.1.2 Sampling from Two
Independent Normal Populations with Unequal but Known Variances 218 11.1.3
Sampling from Two Independent Normal Populations with Equal but Unknown
Variances 218 11.1.4 Sampling from Two Independent Normal Populations with
Unequal and Unknown Variances 219 11.2 Confidence Intervals for the
Difference of Means when Sampling from Two Dependent Populations: Paired
Comparisons 224 11.3 Confidence Intervals for the Difference of Proportions
when Sampling from Two Independent Binomial Populations 227 11.4
Statistical Hypothesis Tests for the Difference of Means when Sampling from
Two Independent Normal Populations 228 11.4.1 Population Variances Equal
and Known 229 11.4.2 Population Variances Unequal but Known 229 11.4.3
Population Variances Equal and Unknown 229 11.4.4 Population Variances
Unequal and Unknown (an Approximate Test) 230 11.5 Hypothesis Tests for the
Difference of Means when Sampling from Two Dependent Populations: Paired
Comparisons 234 11.6 Hypothesis Tests for the Difference of Proportions
when Sampling from Two Independent Binomial Populations 236 Exercises 239
Appendix 11.A Runs Test for Two Independent Samples 243 Appendix 11.B
Mann-Whitney (Rank Sum) Test for Two Independent Populations 245 Appendix
11.C Wilcoxon Signed Rank Test when Sampling from Two Dependent
Populations: Paired Comparisons 249 12 Bivariate Regression and Correlation
253 12.1 Introducing an Additional Dimension to our Statistical Analysis
253 12.2 Linear Relationships 254 12.2.1 Exact Linear Relationships 254
12.3 Estimating the Slope and Intercept of the Population Regression Line
257 12.4 Decomposition of the Sample Variation in Y 262 12.5 Mean,
Variance, and Sampling Distribution of the Least Squares Estimators ^b0 and
^b1 264 12.6 Confidence Intervals for b0 and b1 266 12.7 Testing Hypotheses
about b0 and b1 267 12.8 Predicting the Average Value of Y given X 269 12.9
The Prediction of a Particular Value of Y given X 270 12.10 Correlation
Analysis 272 12.10.1 Case A: X and Y Random Variables 272 12.10.1.1
Estimating the Population Correlation Coefficient r 274 12.10.1.2
Inferences about the Population Correlation Coefficient r 275 12.10.2 Case
B: X Values Fixed, Y a Random Variable 277 Exercises 278 Appendix 12.A
Assessing Normality (Appendix 7.B Continued) 280 Appendix 12.B On Making
Causal Inferences 281 12.B.1 Introduction 281 12.B.2 Rudiments of
Experimental Design 282 12.B.3 Truth Sets, Propositions, and Logical
Implications 283 12.B.4 Necessary and Sufficient Conditions 285 12.B.5
Causality Proper 286 12.B.6 Logical Implications and Causality 287 12.B.7
Correlation and Causality 288 12.B.8 Causality from Counterfactuals 289
12.B.9 Testing Causality 292 12.B.10 Suggestions for Further Reading 294 13
An Assortment of Additional Statistical Tests 295 13.1 Distributional
Hypotheses 295 13.2 The Multinomial Chi-Square Statistic 295 13.3 The
Chi-Square Distribution 298 13.4 Testing Goodness of Fit 299 13.5 Testing
Independence 304 13.6 Testing k Proportions 309 13.7 A Measure of Strength
of Association in a Contingency Table 311 13.8 A Confidence Interval for s2
under Random Sampling from a Normal Population 312 13.9 The F Distribution
314 13.10 Applications of the F Statistic to Regression Analysis 316
13.10.1 Testing the Significance of the Regression Relationship Between X
and Y 316 13.10.2 A Joint Test of the Regression Intercept and Slope 317
Exercises 318 Appendix A 323 Table A.1 Standard Normal Areas [Z is N(0,1)]
323 Table A.2 Quantiles of the t Distribution (T is tv) 325 Table A.3
Quantiles of the Chi-Square Distribution (X is w2v) 327 Table A.4 Quantiles
of the F Distribution (F is Fv1;v2 ) 329 Table A.5 Binomial Probabilities
P(X;n,p) 334 Table A.6 Cumulative Binomial Probabilities 338 Table A.7
Quantiles of Lilliefors' Test for Normality 342 Solutions to Exercises 343
References 369 Index 373