Michael J. (University of Hartford) Panik,
MJ Panik
John Wiley & Sons
e druk, 2012
9781118229408
Statistical Inference – A Short Course
A Short Course
Specificaties
Gebonden, 400 blz.
|
Engels
John Wiley & Sons |
e druk, 2012
ISBN13: 9781118229408
Rubricering
Verwachte levertijd ongeveer 16 werkdagen
Samenvatting
This concise, easily accessible introduction to descriptive and inferential techniques presents 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 and provides nonparametric methods when parametric approaches might not work. To ensure a thorough understanding of all key concepts, this book provides numerous examples and solutions along with complete and precise answers to many fundamental questions. This book serves as a valuable reference for researchers and practitioners who would like to develop further insights into essential statistical tools.
Specificaties
Inhoudsopgave
<p>Preface xv</p>
<p>1 The Nature of Statistics 1</p>
<p>1.1 Statistics Defined 1</p>
<p>1.2 The Population and the Sample 2</p>
<p>1.3 Selecting a Sample from a Population 3</p>
<p>1.4 Measurement Scales 4</p>
<p>1.5 Let us Add 6</p>
<p>Exercises 7</p>
<p>2 Analyzing Quantitative Data 9</p>
<p>2.1 Imposing Order 9</p>
<p>2.2 Tabular and Graphical Techniques: Ungrouped Data 9</p>
<p>2.3 Tabular and Graphical Techniques: Grouped Data 11</p>
<p>Exercises 16</p>
<p>Appendix 2.A Histograms with Classes of Different Lengths 18</p>
<p>3 Descriptive Characteristics of Quantitative Data 22</p>
<p>3.1 The Search for Summary Characteristics 22</p>
<p>3.2 The Arithmetic Mean 23</p>
<p>3.3 The Median 26</p>
<p>3.4 The Mode 27</p>
<p>3.5 The Range 27</p>
<p>3.6 The Standard Deviation 28</p>
<p>3.7 Relative Variation 33</p>
<p>3.8 Skewness 34</p>
<p>3.9 Quantiles 36</p>
<p>3.10 Kurtosis 38</p>
<p>3.11 Detection of Outliers 39</p>
<p>3.12 So What Do We Do with All This Stuff? 41</p>
<p>Exercises 47</p>
<p>Appendix 3.A Descriptive Characteristics of Grouped Data 51</p>
<p>3.A.1 The Arithmetic Mean 52</p>
<p>3.A.2 The Median 53</p>
<p>3.A.3 The Mode 55</p>
<p>3.A.4 The Standard Deviation 57</p>
<p>3.A.5 Quantiles (Quartiles, Deciles, and Percentiles) 58</p>
<p>4 Essentials of Probability 61</p>
<p>4.1 Set Notation 61</p>
<p>4.2 Events within the Sample Space 63</p>
<p>4.3 Basic Probability Calculations 64</p>
<p>4.4 Joint, Marginal, and Conditional Probability 68</p>
<p>4.5 Sources of Probabilities 73</p>
<p>Exercises 75</p>
<p>5 Discrete Probability Distributions and Their Properties 81</p>
<p>5.1 The Discrete Probability Distribution 81</p>
<p>5.2 The Mean, Variance, and Standard Deviation of a Discrete Random Variable 85</p>
<p>5.3 The Binomial Probability Distribution 89</p>
<p>5.3.1 Counting Issues 89</p>
<p>5.3.2 The Bernoulli Probability Distribution 91</p>
<p>5.3.3 The Binomial Probability Distribution 91</p>
<p>Exercises 96</p>
<p>6 The Normal Distribution 101</p>
<p>6.1 The Continuous Probability Distribution 101</p>
<p>6.2 The Normal Distribution 102</p>
<p>6.3 Probability as an Area Under the Normal Curve 104</p>
<p>6.4 Percentiles of the Standard Normal Distribution and Percentiles of the Random Variable X 114</p>
<p>Exercises 116</p>
<p>Appendix 6.A The Normal Approximation to Binomial Probabilities 120</p>
<p>7 Simple Random Sampling and the Sampling Distribution of the Mean 122</p>
<p>7.1 Simple Random Sampling 122</p>
<p>7.2 The Sampling Distribution of the Mean 123</p>
<p>7.3 Comments on the Sampling Distribution of the Mean 127</p>
<p>7.4 A Central Limit Theorem 130</p>
<p>Exercises 132</p>
<p>Appendix 7.A Using a Table of Random Numbers 133</p>
<p>Appendix 7.B Assessing Normality via the Normal Probability Plot 136</p>
<p>Appendix 7.C Randomness, Risk, and Uncertainty 139</p>
<p>7.C.1 Introduction to Randomness 139</p>
<p>7.C.2 Types of Randomness 142</p>
<p>7.C.2.1 Type I Randomness 142</p>
<p>7.C.2.2 Type II Randomness 143</p>
<p>7.C.2.3 Type III Randomness 143</p>
<p>7.C.3 Pseudo–Random Numbers 144</p>
<p>7.C.4 Chaotic Behavior 145</p>
<p>7.C.5 Risk and Uncertainty 146</p>
<p>8 Confidence Interval Estimation of m 152</p>
<p>8.1 The Error Bound on X as an Estimator of m 152</p>
<p>8.2 A Confidence Interval for the Population Mean m (s Known) 154</p>
<p>8.3 A Sample Size Requirements Formula 159</p>
<p>8.4 A Confidence Interval for the Population Mean m (s Unknown) 160</p>
<p>Exercises 165</p>
<p>Appendix 8.A A Confidence Interval for the Population Median MED 167</p>
<p>9 The Sampling Distribution of a Proportion and its Confidence Interval Estimation 170</p>
<p>9.1 The Sampling Distribution of a Proportion 170</p>
<p>9.2 The Error Bound on ^p as an Estimator for p 173</p>
<p>9.3 A Confidence Interval for the Population Proportion (of Successes) p 174</p>
<p>9.4 A Sample Size Requirements Formula 176</p>
<p>Exercises 177</p>
<p>Appendix 9.A Ratio Estimation 179</p>
<p>10 Testing Statistical Hypotheses 184</p>
<p>10.1 What is a Statistical Hypothesis? 184</p>
<p>10.2 Errors in Testing 185</p>
<p>10.3 The Contextual Framework of Hypothesis Testing 186</p>
<p>10.3.1 Types of Errors in a Legal Context 188</p>
<p>10.3.2 Types of Errors in a Medical Context 188</p>
<p>10.3.3 Types of Errors in a Processing or Control Context 189</p>
<p>10.3.4 Types of Errors in a Sports Context 189</p>
<p>10.4 Selecting a Test Statistic 190</p>
<p>10.5 The Classical Approach to Hypothesis Testing 190</p>
<p>10.6 Types of Hypothesis Tests 191</p>
<p>10.7 Hypothesis Tests for m (s Known) 194</p>
<p>10.8 Hypothesis Tests for m (s Unknown and n Small) 195</p>
<p>10.9 Reporting the Results of Statistical Hypothesis Tests 198</p>
<p>10.10 Hypothesis Tests for the Population Proportion (of Successes) p 201</p>
<p>Exercises 204</p>
<p>Appendix 10.A Assessing the Randomness of a Sample 208</p>
<p>Appendix 10.B Wilcoxon Signed Rank Test (of a Median) 210</p>
<p>Appendix 10.C Lilliefors Goodness–of–Fit Test for Normality 213</p>
<p>11 Comparing Two Population Means and Two Population Proportions 217</p>
<p>11.1 Confidence Intervals for the Difference of Means when Sampling from Two Independent Normal Populations 217</p>
<p>11.1.1 Sampling from Two Independent Normal Populations with Equal and Known Variances 217</p>
<p>11.1.2 Sampling from Two Independent Normal Populations with Unequal but Known Variances 218</p>
<p>11.1.3 Sampling from Two Independent Normal Populations with Equal but Unknown Variances 218</p>
<p>11.1.4 Sampling from Two Independent Normal Populations with Unequal and Unknown Variances 219</p>
<p>11.2 Confidence Intervals for the Difference of Means when Sampling from Two Dependent Populations: Paired Comparisons 224</p>
<p>11.3 Confidence Intervals for the Difference of Proportions when Sampling from Two Independent Binomial Populations 227</p>
<p>11.4 Statistical Hypothesis Tests for the Difference of Means when Sampling from Two Independent Normal Populations 228</p>
<p>11.4.1 Population Variances Equal and Known 229</p>
<p>11.4.2 Population Variances Unequal but Known 229</p>
<p>11.4.3 Population Variances Equal and Unknown 229</p>
<p>11.4.4 Population Variances Unequal and Unknown (an Approximate Test) 230</p>
<p>11.5 Hypothesis Tests for the Difference of Means when Sampling from Two Dependent Populations: Paired Comparisons 234</p>
<p>11.6 Hypothesis Tests for the Difference of Proportions when Sampling from Two Independent Binomial Populations 236</p>
<p>Exercises 239</p>
<p>Appendix 11.A Runs Test for Two Independent Samples 243</p>
<p>Appendix 11.B Mann Whitney (Rank Sum) Test for Two Independent Populations 245</p>
<p>Appendix 11.C Wilcoxon Signed Rank Test when Sampling from Two Dependent Populations: Paired Comparisons 249</p>
<p>12 Bivariate Regression and Correlation 253</p>
<p>12.1 Introducing an Additional Dimension to our Statistical Analysis 253</p>
<p>12.2 Linear Relationships 254</p>
<p>12.2.1 Exact Linear Relationships 254</p>
<p>12.3 Estimating the Slope and Intercept of the Population Regression Line 257</p>
<p>12.4 Decomposition of the Sample Variation in Y 262</p>
<p>12.5 Mean, Variance, and Sampling Distribution of the Least Squares Estimators ^b0 and ^b1 264</p>
<p>12.6 Confidence Intervals for b0 and b1 266</p>
<p>12.7 Testing Hypotheses about b0 and b1 267</p>
<p>12.8 Predicting the Average Value of Y given X 269</p>
<p>12.9 The Prediction of a Particular Value of Y given X 270</p>
<p>12.10 Correlation Analysis 272</p>
<p>12.10.1 Case A: X and Y Random Variables 272</p>
<p>12.10.1.1 Estimating the Population Correlation Coefficient r 274</p>
<p>12.10.1.2 Inferences about the Population Correlation Coefficient r 275</p>
<p>12.10.2 Case B: X Values Fixed, Y a Random Variable 277</p>
<p>Exercises 278</p>
<p>Appendix 12.A Assessing Normality (Appendix 7.B Continued) 280</p>
<p>Appendix 12.B On Making Causal Inferences 281</p>
<p>12.B.1 Introduction 281</p>
<p>12.B.2 Rudiments of Experimental Design 282</p>
<p>12.B.3 Truth Sets, Propositions, and Logical Implications 283</p>
<p>12.B.4 Necessary and Sufficient Conditions 285</p>
<p>12.B.5 Causality Proper 286</p>
<p>12.B.6 Logical Implications and Causality 287</p>
<p>12.B.7 Correlation and Causality 288</p>
<p>12.B.8 Causality from Counterfactuals 289</p>
<p>12.B.9 Testing Causality 292</p>
<p>12.B.10 Suggestions for Further Reading 294</p>
<p>13 An Assortment of Additional Statistical Tests 295</p>
<p>13.1 Distributional Hypotheses 295</p>
<p>13.2 The Multinomial Chi–Square Statistic 295</p>
<p>13.3 The Chi–Square Distribution 298</p>
<p>13.4 Testing Goodness of Fit 299</p>
<p>13.5 Testing Independence 304</p>
<p>13.6 Testing k Proportions 309</p>
<p>13.7 A Measure of Strength of Association in a Contingency Table 311</p>
<p>13.8 A Confidence Interval for s2 under Random Sampling from a Normal Population 312</p>
<p>13.9 The F Distribution 314</p>
<p>13.10 Applications of the F Statistic to Regression Analysis 316</p>
<p>13.10.1 Testing the Significance of the Regression Relationship Between X and Y 316</p>
<p>13.10.2 A Joint Test of the Regression Intercept and Slope 317</p>
<p>Exercises 318</p>
<p>Appendix A 323</p>
<p>Table A.1 Standard Normal Areas [Z is N(0,1)] 323</p>
<p>Table A.2 Quantiles of the t Distribution (T is tv) 325</p>
<p>Table A.3 Quantiles of the Chi–Square Distribution (X is w2v) 327</p>
<p>Table A.4 Quantiles of the F Distribution (F is Fv1;v2 ) 329</p>
<p>Table A.5 Binomial Probabilities P(X;n,p) 334</p>
<p>Table A.6 Cumulative Binomial Probabilities 338</p>
<p>Table A.7 Quantiles of Lilliefors Test for Normality 342</p>
<p>Solutions to Exercises 343</p>
<p>References 369</p>
<p>Index 373</p>
<p>1 The Nature of Statistics 1</p>
<p>1.1 Statistics Defined 1</p>
<p>1.2 The Population and the Sample 2</p>
<p>1.3 Selecting a Sample from a Population 3</p>
<p>1.4 Measurement Scales 4</p>
<p>1.5 Let us Add 6</p>
<p>Exercises 7</p>
<p>2 Analyzing Quantitative Data 9</p>
<p>2.1 Imposing Order 9</p>
<p>2.2 Tabular and Graphical Techniques: Ungrouped Data 9</p>
<p>2.3 Tabular and Graphical Techniques: Grouped Data 11</p>
<p>Exercises 16</p>
<p>Appendix 2.A Histograms with Classes of Different Lengths 18</p>
<p>3 Descriptive Characteristics of Quantitative Data 22</p>
<p>3.1 The Search for Summary Characteristics 22</p>
<p>3.2 The Arithmetic Mean 23</p>
<p>3.3 The Median 26</p>
<p>3.4 The Mode 27</p>
<p>3.5 The Range 27</p>
<p>3.6 The Standard Deviation 28</p>
<p>3.7 Relative Variation 33</p>
<p>3.8 Skewness 34</p>
<p>3.9 Quantiles 36</p>
<p>3.10 Kurtosis 38</p>
<p>3.11 Detection of Outliers 39</p>
<p>3.12 So What Do We Do with All This Stuff? 41</p>
<p>Exercises 47</p>
<p>Appendix 3.A Descriptive Characteristics of Grouped Data 51</p>
<p>3.A.1 The Arithmetic Mean 52</p>
<p>3.A.2 The Median 53</p>
<p>3.A.3 The Mode 55</p>
<p>3.A.4 The Standard Deviation 57</p>
<p>3.A.5 Quantiles (Quartiles, Deciles, and Percentiles) 58</p>
<p>4 Essentials of Probability 61</p>
<p>4.1 Set Notation 61</p>
<p>4.2 Events within the Sample Space 63</p>
<p>4.3 Basic Probability Calculations 64</p>
<p>4.4 Joint, Marginal, and Conditional Probability 68</p>
<p>4.5 Sources of Probabilities 73</p>
<p>Exercises 75</p>
<p>5 Discrete Probability Distributions and Their Properties 81</p>
<p>5.1 The Discrete Probability Distribution 81</p>
<p>5.2 The Mean, Variance, and Standard Deviation of a Discrete Random Variable 85</p>
<p>5.3 The Binomial Probability Distribution 89</p>
<p>5.3.1 Counting Issues 89</p>
<p>5.3.2 The Bernoulli Probability Distribution 91</p>
<p>5.3.3 The Binomial Probability Distribution 91</p>
<p>Exercises 96</p>
<p>6 The Normal Distribution 101</p>
<p>6.1 The Continuous Probability Distribution 101</p>
<p>6.2 The Normal Distribution 102</p>
<p>6.3 Probability as an Area Under the Normal Curve 104</p>
<p>6.4 Percentiles of the Standard Normal Distribution and Percentiles of the Random Variable X 114</p>
<p>Exercises 116</p>
<p>Appendix 6.A The Normal Approximation to Binomial Probabilities 120</p>
<p>7 Simple Random Sampling and the Sampling Distribution of the Mean 122</p>
<p>7.1 Simple Random Sampling 122</p>
<p>7.2 The Sampling Distribution of the Mean 123</p>
<p>7.3 Comments on the Sampling Distribution of the Mean 127</p>
<p>7.4 A Central Limit Theorem 130</p>
<p>Exercises 132</p>
<p>Appendix 7.A Using a Table of Random Numbers 133</p>
<p>Appendix 7.B Assessing Normality via the Normal Probability Plot 136</p>
<p>Appendix 7.C Randomness, Risk, and Uncertainty 139</p>
<p>7.C.1 Introduction to Randomness 139</p>
<p>7.C.2 Types of Randomness 142</p>
<p>7.C.2.1 Type I Randomness 142</p>
<p>7.C.2.2 Type II Randomness 143</p>
<p>7.C.2.3 Type III Randomness 143</p>
<p>7.C.3 Pseudo–Random Numbers 144</p>
<p>7.C.4 Chaotic Behavior 145</p>
<p>7.C.5 Risk and Uncertainty 146</p>
<p>8 Confidence Interval Estimation of m 152</p>
<p>8.1 The Error Bound on X as an Estimator of m 152</p>
<p>8.2 A Confidence Interval for the Population Mean m (s Known) 154</p>
<p>8.3 A Sample Size Requirements Formula 159</p>
<p>8.4 A Confidence Interval for the Population Mean m (s Unknown) 160</p>
<p>Exercises 165</p>
<p>Appendix 8.A A Confidence Interval for the Population Median MED 167</p>
<p>9 The Sampling Distribution of a Proportion and its Confidence Interval Estimation 170</p>
<p>9.1 The Sampling Distribution of a Proportion 170</p>
<p>9.2 The Error Bound on ^p as an Estimator for p 173</p>
<p>9.3 A Confidence Interval for the Population Proportion (of Successes) p 174</p>
<p>9.4 A Sample Size Requirements Formula 176</p>
<p>Exercises 177</p>
<p>Appendix 9.A Ratio Estimation 179</p>
<p>10 Testing Statistical Hypotheses 184</p>
<p>10.1 What is a Statistical Hypothesis? 184</p>
<p>10.2 Errors in Testing 185</p>
<p>10.3 The Contextual Framework of Hypothesis Testing 186</p>
<p>10.3.1 Types of Errors in a Legal Context 188</p>
<p>10.3.2 Types of Errors in a Medical Context 188</p>
<p>10.3.3 Types of Errors in a Processing or Control Context 189</p>
<p>10.3.4 Types of Errors in a Sports Context 189</p>
<p>10.4 Selecting a Test Statistic 190</p>
<p>10.5 The Classical Approach to Hypothesis Testing 190</p>
<p>10.6 Types of Hypothesis Tests 191</p>
<p>10.7 Hypothesis Tests for m (s Known) 194</p>
<p>10.8 Hypothesis Tests for m (s Unknown and n Small) 195</p>
<p>10.9 Reporting the Results of Statistical Hypothesis Tests 198</p>
<p>10.10 Hypothesis Tests for the Population Proportion (of Successes) p 201</p>
<p>Exercises 204</p>
<p>Appendix 10.A Assessing the Randomness of a Sample 208</p>
<p>Appendix 10.B Wilcoxon Signed Rank Test (of a Median) 210</p>
<p>Appendix 10.C Lilliefors Goodness–of–Fit Test for Normality 213</p>
<p>11 Comparing Two Population Means and Two Population Proportions 217</p>
<p>11.1 Confidence Intervals for the Difference of Means when Sampling from Two Independent Normal Populations 217</p>
<p>11.1.1 Sampling from Two Independent Normal Populations with Equal and Known Variances 217</p>
<p>11.1.2 Sampling from Two Independent Normal Populations with Unequal but Known Variances 218</p>
<p>11.1.3 Sampling from Two Independent Normal Populations with Equal but Unknown Variances 218</p>
<p>11.1.4 Sampling from Two Independent Normal Populations with Unequal and Unknown Variances 219</p>
<p>11.2 Confidence Intervals for the Difference of Means when Sampling from Two Dependent Populations: Paired Comparisons 224</p>
<p>11.3 Confidence Intervals for the Difference of Proportions when Sampling from Two Independent Binomial Populations 227</p>
<p>11.4 Statistical Hypothesis Tests for the Difference of Means when Sampling from Two Independent Normal Populations 228</p>
<p>11.4.1 Population Variances Equal and Known 229</p>
<p>11.4.2 Population Variances Unequal but Known 229</p>
<p>11.4.3 Population Variances Equal and Unknown 229</p>
<p>11.4.4 Population Variances Unequal and Unknown (an Approximate Test) 230</p>
<p>11.5 Hypothesis Tests for the Difference of Means when Sampling from Two Dependent Populations: Paired Comparisons 234</p>
<p>11.6 Hypothesis Tests for the Difference of Proportions when Sampling from Two Independent Binomial Populations 236</p>
<p>Exercises 239</p>
<p>Appendix 11.A Runs Test for Two Independent Samples 243</p>
<p>Appendix 11.B Mann Whitney (Rank Sum) Test for Two Independent Populations 245</p>
<p>Appendix 11.C Wilcoxon Signed Rank Test when Sampling from Two Dependent Populations: Paired Comparisons 249</p>
<p>12 Bivariate Regression and Correlation 253</p>
<p>12.1 Introducing an Additional Dimension to our Statistical Analysis 253</p>
<p>12.2 Linear Relationships 254</p>
<p>12.2.1 Exact Linear Relationships 254</p>
<p>12.3 Estimating the Slope and Intercept of the Population Regression Line 257</p>
<p>12.4 Decomposition of the Sample Variation in Y 262</p>
<p>12.5 Mean, Variance, and Sampling Distribution of the Least Squares Estimators ^b0 and ^b1 264</p>
<p>12.6 Confidence Intervals for b0 and b1 266</p>
<p>12.7 Testing Hypotheses about b0 and b1 267</p>
<p>12.8 Predicting the Average Value of Y given X 269</p>
<p>12.9 The Prediction of a Particular Value of Y given X 270</p>
<p>12.10 Correlation Analysis 272</p>
<p>12.10.1 Case A: X and Y Random Variables 272</p>
<p>12.10.1.1 Estimating the Population Correlation Coefficient r 274</p>
<p>12.10.1.2 Inferences about the Population Correlation Coefficient r 275</p>
<p>12.10.2 Case B: X Values Fixed, Y a Random Variable 277</p>
<p>Exercises 278</p>
<p>Appendix 12.A Assessing Normality (Appendix 7.B Continued) 280</p>
<p>Appendix 12.B On Making Causal Inferences 281</p>
<p>12.B.1 Introduction 281</p>
<p>12.B.2 Rudiments of Experimental Design 282</p>
<p>12.B.3 Truth Sets, Propositions, and Logical Implications 283</p>
<p>12.B.4 Necessary and Sufficient Conditions 285</p>
<p>12.B.5 Causality Proper 286</p>
<p>12.B.6 Logical Implications and Causality 287</p>
<p>12.B.7 Correlation and Causality 288</p>
<p>12.B.8 Causality from Counterfactuals 289</p>
<p>12.B.9 Testing Causality 292</p>
<p>12.B.10 Suggestions for Further Reading 294</p>
<p>13 An Assortment of Additional Statistical Tests 295</p>
<p>13.1 Distributional Hypotheses 295</p>
<p>13.2 The Multinomial Chi–Square Statistic 295</p>
<p>13.3 The Chi–Square Distribution 298</p>
<p>13.4 Testing Goodness of Fit 299</p>
<p>13.5 Testing Independence 304</p>
<p>13.6 Testing k Proportions 309</p>
<p>13.7 A Measure of Strength of Association in a Contingency Table 311</p>
<p>13.8 A Confidence Interval for s2 under Random Sampling from a Normal Population 312</p>
<p>13.9 The F Distribution 314</p>
<p>13.10 Applications of the F Statistic to Regression Analysis 316</p>
<p>13.10.1 Testing the Significance of the Regression Relationship Between X and Y 316</p>
<p>13.10.2 A Joint Test of the Regression Intercept and Slope 317</p>
<p>Exercises 318</p>
<p>Appendix A 323</p>
<p>Table A.1 Standard Normal Areas [Z is N(0,1)] 323</p>
<p>Table A.2 Quantiles of the t Distribution (T is tv) 325</p>
<p>Table A.3 Quantiles of the Chi–Square Distribution (X is w2v) 327</p>
<p>Table A.4 Quantiles of the F Distribution (F is Fv1;v2 ) 329</p>
<p>Table A.5 Binomial Probabilities P(X;n,p) 334</p>
<p>Table A.6 Cumulative Binomial Probabilities 338</p>
<p>Table A.7 Quantiles of Lilliefors Test for Normality 342</p>
<p>Solutions to Exercises 343</p>
<p>References 369</p>
<p>Index 373</p>