Preface to the Sixth Edition |
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xv | |
Author Biographies |
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xix | |
1 Introduction and Fundamentals |
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1 | (28) |
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1 | (6) |
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1.2 Fundamental Statistical Concepts |
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7 | (20) |
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8 | (2) |
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1.2.2 Moments of Linear Combinations of Random Variables |
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10 | (1) |
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1.2.3 Probability Functions |
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10 | (4) |
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1.2.4 Distributions of Functions of Random Variables Using the Method of Jacobians |
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14 | (1) |
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1.2.5 Chebyshev's Inequality |
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15 | (1) |
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1.2.6 Central Limit Theorem |
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15 | (1) |
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1.2.7 Point and Interval Estimation |
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16 | (1) |
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17 | (3) |
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20 | (1) |
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21 | (1) |
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22 | (2) |
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24 | (1) |
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1.2.13 Continuity Correction |
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25 | (2) |
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1.3 Computers and Nonparametrics |
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27 | (2) |
2 Order Statistics, Quantiles, and Coverages |
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29 | (52) |
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29 | (1) |
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30 | (3) |
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2.3 Empirical Distribution Function |
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33 | (4) |
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2.3.1 Empirical Quantile Function |
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36 | (1) |
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2.4 Statistical Properties of Order Statistics |
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37 | (2) |
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2.4.1 Cumulative Distribution Function of X(r) |
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37 | (1) |
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2.4.2 Probability Density Function of X(r) |
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37 | (2) |
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2.5 Probability Integral Transformation |
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39 | (2) |
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2.6 Joint Distribution of Order Statistics |
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41 | (6) |
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2.7 Distributions of the Median and Range |
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47 | (4) |
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2.7.1 Distribution of the Median |
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47 | (2) |
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2.7.2 Distribution of the Range |
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49 | (2) |
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2.8 Exact Moments of Order Statistics |
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51 | (5) |
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2.8.1 kth Moment about the Origin |
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51 | (1) |
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2.8.2 Covariance between X(r) and X(s) |
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52 | (4) |
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2.9 Large-Sample Approximations to the Moments of Order Statistics |
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56 | (3) |
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2.10 Asymptotic Distribution of Order Statistics |
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59 | (4) |
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2.11 Tolerance Intervals, Prediction Intervals, and Coverages |
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63 | (9) |
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2.11.1 Tolerance Intervals |
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63 | (3) |
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2.11.2 Prediction Intervals |
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66 | (3) |
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2.11.3 One-Sample Coverages |
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69 | (1) |
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2.11.4 Two-Sample Coverages |
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70 | (1) |
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2.11.5 Ranks, Block Frequencies, and Placements |
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71 | (1) |
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72 | (1) |
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72 | (9) |
3 Tests of Randomness |
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81 | (26) |
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81 | (1) |
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3.2 Tests Based on the Total Number of Runs |
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82 | (9) |
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3.2.1 Exact Null Distribution of R |
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82 | (3) |
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3.2.2 Moments of the Null Distribution of R |
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85 | (3) |
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3.2.3 Asymptotic Null Distribution |
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88 | (1) |
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89 | (1) |
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89 | (2) |
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3.3 Tests Based on the Length of the Longest Run |
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91 | (3) |
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94 | (6) |
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98 | (2) |
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3.5 A Test Based on Ranks |
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100 | (2) |
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102 | (1) |
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103 | (4) |
4 Tests of Goodness of Fit |
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107 | (60) |
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107 | (1) |
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4.2 The Chi-Square Goodness-of-Fit Test |
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108 | (9) |
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4.3 The Kolmogorov-Smirnov (K-S) One-Sample Statistic |
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117 | (8) |
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4.4 Applications of the Kolmogorov-Smirnov (K-S) One-Sample Statistics |
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125 | (10) |
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131 | (2) |
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133 | (1) |
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4.4.3 Determination of Sample Size |
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134 | (1) |
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4.5 Lilliefors's Test for Normality |
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135 | (5) |
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4.6 Lilliefors's Test for the Exponential Distribution |
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140 | (4) |
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4.7 Anderson-Darling (A-D) Test |
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144 | (8) |
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4.8 Visual Analysis of Goodness of Fit |
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152 | (4) |
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156 | (3) |
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159 | (8) |
5 One-Sample and Paired-Sample Procedures |
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167 | (80) |
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167 | (1) |
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5.2 Confidence Interval for a Population Quantile |
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168 | (6) |
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5.3 Hypothesis Testing for a Population Quantile |
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174 | (5) |
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5.4 The Sign Test and Confidence Interval for the Median |
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179 | (24) |
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181 | (1) |
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5.4.2 Normal Approximations |
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181 | (1) |
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182 | (1) |
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182 | (4) |
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186 | (3) |
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5.4.6 Sample Size Determination |
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189 | (3) |
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5.4.7 Confidence Interval for the Median |
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192 | (1) |
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193 | (1) |
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5.4.9 Paired-Sample Procedures |
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193 | (1) |
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194 | (9) |
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5.5 Rank Order Statistics |
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203 | (4) |
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5.6 Treatment of Ties in Rank Tests |
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207 | (2) |
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207 | (1) |
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208 | (1) |
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208 | (1) |
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5.6.4 Average Probability |
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208 | (1) |
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5.6.5 Least Favorable Statistic |
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208 | (1) |
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5.6.6 Range of Probability |
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208 | (1) |
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5.6.7 Omission of Tied Observations |
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209 | (1) |
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5.7 The Wilcoxon Signed-Rank Test and Confidence Interval |
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209 | (25) |
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5.7.1 The Problem of Zero and Tied Differences |
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216 | (1) |
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217 | (1) |
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218 | (1) |
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5.7.4 Sample Size Determination |
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219 | (2) |
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5.7.5 Confidence Interval Procedures |
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221 | (4) |
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5.7.6 Paired-Sample Procedures |
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225 | (1) |
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5.7.7 Use of Wilcoxon Statistics to Test for Symmetry |
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225 | (1) |
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226 | (8) |
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234 | (2) |
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236 | (8) |
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244 | (3) |
6 The General Two-Sample Problem |
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247 | (54) |
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247 | (5) |
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6.2 The Wald-Wolfowitz Runs Test |
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252 | (5) |
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6.2.1 The Problem of Ties |
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256 | (1) |
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256 | (1) |
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6.3 The Kolmogorov-Smirnov (K-S) Two-Sample Test |
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257 | (7) |
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6.3.1 One-Sided Alternatives |
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261 | (1) |
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262 | (1) |
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262 | (1) |
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263 | (1) |
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264 | (15) |
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271 | (3) |
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6.4.2 Confidence Interval Procedure |
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274 | (3) |
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6.4.3 Power of the Median Test |
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277 | (2) |
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6.5 The Control Median Test |
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279 | (5) |
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281 | (1) |
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6.5.2 Power of the Control Median Test |
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282 | (1) |
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282 | (1) |
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283 | (1) |
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6.6 The Mann-Whitney U Test and Confidence Interval |
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284 | (12) |
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6.6.1 The Problem of Ties |
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290 | (1) |
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6.6.2 Confidence Interval Procedure |
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291 | (2) |
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6.6.3 Sample Size Determination |
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293 | (2) |
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295 | (1) |
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296 | (1) |
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297 | (4) |
7 Linear Rank Statistics and the General Two-Sample Problem |
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301 | (14) |
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301 | (1) |
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7.2 Definition of Linear Rank Statistics |
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301 | (2) |
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7.3 Distribution Properties of Linear Rank Statistics |
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303 | (9) |
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7.4 Usefulness in Inference |
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312 | (1) |
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313 | (2) |
8 Linear Rank Tests for the Location Problem |
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315 | (24) |
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315 | (1) |
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8.2 The Wilcoxon Rank-Sum Test and Confidence Interval |
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316 | (11) |
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319 | (8) |
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327 | (6) |
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8.3.1 Terry-Hoeffding (Normal Scores) Test |
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327 | (1) |
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8.3.2 van der Waerden Test |
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328 | (4) |
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8.3.3 Percentile-Modified Rank Tests |
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332 | (1) |
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333 | (1) |
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334 | (5) |
9 Linear Rank Tests for the Scale Problem |
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339 | (34) |
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339 | (3) |
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342 | (3) |
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9.3 The Freund-Ansari-Bradley-David-Barton Tests |
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345 | (3) |
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9.4 The Siegel-Tukey Test |
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348 | (2) |
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9.5 The Klotz Normal-Scores Test |
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350 | (1) |
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9.6 The Percentile-Modified Rank Tests for Scale |
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351 | (1) |
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351 | (4) |
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9.8 Confidence Interval Procedures |
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355 | (1) |
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9.9 Other Tests for the Scale Problem |
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356 | (3) |
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359 | (8) |
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367 | (2) |
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369 | (4) |
10 Tests of the Equality of k Distributions |
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373 | (46) |
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373 | (1) |
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10.2 Extension of the Median Test |
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374 | (7) |
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10.3 Extension of the Control Median Test |
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381 | (3) |
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10.4 The Kruskal-Wallis One-Way ANOVA Test and Multiple Comparisons |
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384 | (10) |
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388 | (6) |
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10.5 Other Rank Test Statistics |
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394 | (3) |
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10.6 Tests against Ordered Alternatives |
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397 | (8) |
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401 | (4) |
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10.7 Comparisons with a Control |
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405 | (6) |
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406 | (2) |
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10.7.2 Case II: θ1 Unknown |
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408 | (2) |
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410 | (1) |
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411 | (1) |
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412 | (7) |
11 Measures of Association for Bivariate Samples |
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419 | (52) |
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11.1 Introduction: Definition of Measures of Association in a Bivariate Population |
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419 | (4) |
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11.2 Kendall's Tau Coefficient |
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423 | (18) |
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11.2.1 Null Distribution of T |
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430 | (3) |
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11.2.2 The Large-Sample Nonnull Distribution of Kendall's Statistic |
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433 | (4) |
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437 | (2) |
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11.2.4 A Related Measure of Association for Discrete Populations |
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439 | (1) |
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11.2.5 Use of Kendall's Statistic to Test against Trend |
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440 | (1) |
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11.3 Spearman's Coefficient of Rank Correlation |
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441 | (9) |
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11.3.1 Exact Null Distribution of R |
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444 | (3) |
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11.3.2 Asymptotic Null Distribution of R |
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447 | (1) |
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11.3.3 Testing the Null Hypothesis |
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447 | (1) |
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448 | (2) |
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11.3.5 Use of Spearman's R to Test against Trend |
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450 | (1) |
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11.4 The Relations between R and T; E(R), &taj;, and ρ |
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450 | (6) |
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11.5 Another Measure of Association |
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456 | (1) |
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457 | (5) |
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462 | (2) |
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464 | (7) |
12 Measures of Association in Multiple Classifications |
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471 | (44) |
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471 | (2) |
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12.2 Friedman's Two-Way Analysis of Variance by Ranks in a kxn Table and Multiple Comparisons |
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473 | (10) |
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478 | (5) |
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12.3 Page's Test for Ordered Alternatives |
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483 | (4) |
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12.4 The Coefficient of Concordance for k Sets of Rankings of n Objects |
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487 | (9) |
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12.4.1 Relationship between W and Rank Correlation |
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489 | (1) |
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12.4.2 Tests of Significance Based on W |
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490 | (2) |
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12.4.3 Estimation of the True Preferential Order of Objects |
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492 | (1) |
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493 | (1) |
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493 | (3) |
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12.5 The Coefficient of Concordance for k Sets of Incomplete Rankings |
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496 | (6) |
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12.5.1 Tests of Significance Based on W |
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499 | (2) |
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501 | (1) |
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501 | (1) |
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12.6 Kendall's Tau Coefficient for Partial Correlation |
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502 | (4) |
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505 | (1) |
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506 | (1) |
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507 | (8) |
13 Asymptotic Relative Efficiency |
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515 | (26) |
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515 | (3) |
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13.2 Theoretical Bases for Calculating the ARE |
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518 | (5) |
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13.3 Examples of the Calculation of Efficacy and ARE |
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523 | (15) |
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13.3.1 One-Sample and Paired-Sample Problems |
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523 | (6) |
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13.3.2 Two-Sample Location Problems |
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529 | (5) |
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13.3.3 Two-Sample Scale Problems |
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534 | (4) |
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538 | (1) |
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539 | (2) |
14 Analysis of Count Data |
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541 | (34) |
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541 | (1) |
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541 | (8) |
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14.2.1 Contingency Coefficient |
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546 | (3) |
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14.3 Some Special Results for 2xk Contingency Tables |
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549 | (4) |
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553 | (5) |
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558 | (7) |
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14.6 Analysis of Multinomial Data |
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565 | (4) |
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14.6.1 Ordered Categories |
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567 | (2) |
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569 | (1) |
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569 | (6) |
15 Summary |
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575 | (6) |
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575 | (2) |
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577 | (4) |
Appendix of Tables |
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581 | (58) |
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Table A Normal Distribution |
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582 | (1) |
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Table B Chi-Square Distribution |
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583 | (1) |
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Table C Cumulative Binomial Distribution |
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584 | (13) |
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Table D Total Number of Runs Distribution |
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597 | (5) |
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Table E Runs Up and Down Distribution |
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602 | (3) |
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Table F Kolmogorov-Smirnov One-Sample Statistic |
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605 | (1) |
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Table G Binomial Distribution for θ = 0.5 |
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606 | (1) |
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Table H Probabilities for the Wilcoxon Signed-Rank Statistic |
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607 | (4) |
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Table I Kolmogorov-Smirnov Two-Sample Statistic |
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611 | (3) |
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Table J Probabilities for the Wilcoxon Rank Sum Statistic |
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614 | (8) |
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Table K Kruskal-Wallis Test Statistic |
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622 | (1) |
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Table L Kendall's Tau Statistic |
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623 | (2) |
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Table M Spearman's Coefficient of Rank Correlation |
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625 | (3) |
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Table N Friedman's Analysis-of-Variance Statistic and Kendall's Coefficient of Concordance |
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628 | (1) |
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Table O Lilliefors's Test for Normal Distribution Critical Values |
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629 | (1) |
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Table P Significance Points of Txy, for Kendall's Partial Rank Correlation Coefficient |
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630 | (1) |
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Table Q Page's L Statistic |
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631 | (1) |
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Table R Critical Values and Associated Probabilities for the Jonckheere-Terpstra Test |
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632 | (3) |
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Table S Rank von Neumann Statistic |
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635 | (3) |
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Table T Lilliefors's Test for Exponential Distribution Critical Values |
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638 | (1) |
Answers to Selected Problems |
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639 | (8) |
References |
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647 | (18) |
Index |
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665 | |