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Preface to the Fifth Edition | |

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Introduction and Fundamentals | |

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Introduction | |

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Fundamental Statistical Concepts | |

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Basic Definitions | |

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Moments of Linear Combinations of Random Variables | |

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Probability Functions | |

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Distributions of Functions of Random Variables Using the Method of Jacobians | |

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Chebyshev's Inequality | |

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Central Limit Theorem | |

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Point and Interval Estimation | |

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Hypothesis Testing | |

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P Value | |

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Consistency | |

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Pitman Efficiency | |

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Randomized Tests | |

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Continuity Correction | |

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Order Statistics, Quantiles, and Coverages | |

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Introduction | |

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Quantile Function | |

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Empirical Distribution Function | |

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Empirical Quantile Function | |

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Statistical Properties of Order Statistics | |

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Cumulative Distribution Function of X<sub>(r)</sub> | |

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Probability Density Function of X<sub>(r)</sub> | |

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Probability-Integral Transformation | |

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Joint Distribution of Order Statistics | |

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Distributions of the Median and Range | |

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Distribution of the Median | |

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Distribution of the Range | |

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Exact Moments of Order Statistics | |

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kth Moment about the Origin | |

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Covariance between X<sub>(r)</sub> and X<sub>(s)</sub> | |

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Large-Sample Approximations to the Moments of Order Statistics | |

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Asymptotic Distribution of Order Statistics | |

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Tolerance Limits for Distributions and Coverages | |

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One-Sample Coverages | |

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Two-Sample Coverages | |

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Ranks, Block Frequencies, and Placements | |

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Summary | |

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Problems | |

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Tests of Randomness | |

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Introduction | |

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Tests Based on the Total Number of Runs | |

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Exact Null Distribution of R | |

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Moments of the Null Distribution of R | |

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Asymptotic Null Distribution | |

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Discussion | |

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Applications | |

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Tests Based on the Length of the Longest Run | |

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Rims Up and Down | |

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Applications | |

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A Test Based on Ranks | |

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Summary | |

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Problems | |

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Tests of Goodness of Fit | |

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Introduction | |

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The Chi-Square Goodness-of-Fit Test | |

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The Kolmogorov-Smirnov (K-S) One-Sample Statistic | |

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Applications of the Kolmogorov-Smirnov (K-S) One-Sample Statistics | |

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One-Sided Tests | |

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Confidence Bands | |

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Determination of Sample Size | |

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Lilliefors's Test for Normality | |

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Lilliefors's Test for the Exponential Distribution | |

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Anderson-Darling (A-D) Test | |

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Visual Analysis of Goodness of Fit | |

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Summary | |

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Problems | |

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One-Sample and Paired-Sample Procedures | |

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Introduction | |

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Confidence Interval for a Population Quantile | |

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Hypothesis Testing for a Population Quantile | |

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The Sign Test and Confidence Interval for the Median | |

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P value | |

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Normal Approximations | |

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Zero Differences | |

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Power Function | |

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Simulated Power | |

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Sample Size Determination | |

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Confidence Interval for the Median | |

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Problem of Zeros | |

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Paired-Sample Procedures | |

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Applications | |

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Rank-Order Statistics | |

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Treatment of Ties in Rank Tests | |

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Randomization | |

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Midranks | |

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Average Statistic | |

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Average Probability | |

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Least Favorable Statistic | |

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Range of Probability | |

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Omission of Tied Observations | |

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The Wilcoxon Signed-Rank Test and Confidence Interval | |

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The Problem of Zero and Tied Differences | |

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Power Function | |

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Simulated Power | |

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Sample Size Determination | |

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Confidence-Interval Procedures | |

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Paired-Sample Procedures | |

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Use of Wilcoxon Statistics to Test for Symmetry | |

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Applications | |

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Summary | |

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Problems | |

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The General Two-Sample Problem | |

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Introduction | |

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The Wald-Wolfowitz Runs Test | |

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The Problem of Ties | |

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Discussion | |

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The Kolmogorov-Smirnov (K-S) Two-Sample Test | |

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One-Sided Alternatives | |

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Ties | |

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Discussion | |

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Applications | |

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The Median Test | |

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Applications | |

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Confidence-Interval Procedure | |

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Power of the Median Test | |

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The Control Median Test | |

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Curtailed Sampling | |

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Power of the Control Median Test | |

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Discussion | |

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Applications | |

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The Mann-Whitney U Test and Confidence Interval | |

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The Problem of Ties | |

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Confidence-Interval Procedure | |

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Sample Size Determination | |

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Discussion | |

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Summary | |

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Problems | |

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Linear Rank Statistics and the General Two-Sample Problem | |

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Introduction | |

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Definition of Linear Rank Statistics | |

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Distribution Properties of Linear Rank Statistics | |

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Usefulness in Inference | |

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Problems | |

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Linear Rank Tests for the Location Problem | |

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Introduction | |

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The Wilcoxon Rank-Sum Test and Confidence Interval | |

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Applications | |

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Other Location Tests | |

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Terry-Hoeffding (Normal Scores) Test | |

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van der Waerden Test | |

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Percentile Modified Rank Tests | |

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Summary | |

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Problems | |

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Linear Rank Tests for the Scale Problem | |

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Introduction | |

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The Mood Test | |

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The Freund-Ansari-Bradley-David-Barton Tests | |

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The Siegel-Tukey Test | |

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The Klotz Normal-Scores Test | |

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The Percentile Modified Rank Tests for Scale | |

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The Sukhatme Test | |

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Confidence Interval Procedures | |

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Other Tests for the Scale Problem | |

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Applications | |

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Summary | |

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Problems | |

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Tests of the Equality of k Independent Samples | |

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Introduction | |

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Extension of the Median Test | |

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Extension of the Control Median Test | |

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The Kruskal-Wallis One-Way ANOVA Test and Multiple Comparisons | |

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Applications | |

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Other Rank-Test Statistics | |

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Tests against Ordered Alternatives | |

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Applications | |

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Comparisons with a Control | |

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Case I: ï¿½<sub>1</sub> Known | |

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Case II: ï¿½<sub>1</sub> Unknown | |

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Applications | |

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Summary | |

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Problems | |

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Measures of Association for Bivariate Samples | |

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Introduction: Definition of Measures of Association in a Bivariate Population | |

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Kendall's Tau Coefficient | |

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Null Distribution of T | |

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The Large-Sample Nonnull Distribution of Kendall's Statistic | |

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Tied Observations | |

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A Related Measure of Association for Discrete Populations | |

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Use of Kendall's Statistic to Test against Trend | |

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Spearman's Coefficient of Rank Correlation | |

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Exact Null Distribution of R | |

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Asymptotic Null Distribution of R | |

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Testing the Null Hypothesis | |

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Tied Observations | |

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Use of Spearman's R to Test against Trend | |

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The Relations between R and T; E(R), T, and ï¿½ | |

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Another Measure of Association | |

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Applications | |

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Summary | |

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Problems | |

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Measures of Association in Multiple Classifications | |

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Introduction | |

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Friedman's Two-Way Analysis of Variance by Ranks in a k x n Table and Multiple Comparisons | |

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Applications | |

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Page's Test for Ordered Alternatives | |

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The Coefficient of Concordance for k Sets of Rankings of n Objects | |

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Relationship between W and Rank Correlation | |

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Tests of Significance Based on W | |

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Estimation of the True Preferential Order of Objects | |

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Tied Observations | |

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Applications | |

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The Coefficient of Concordance for k Sets of Incomplete Rankings | |

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Tests of Significance Based on W | |

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Tied Observations | |

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Applications | |

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Kendall's Tau Coefficient for Partial Correlation | |

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Applications | |

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Summary | |

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Problems | |

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Asymptotic Relative Efficiency | |

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Introduction | |

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Theoretical Bases for Calculating the ARE | |

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Examples of the Calculation of Efficacy and ARE | |

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One-Sample and Paired-Sample Problems | |

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Two-Sample location Problems | |

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Two-Sample Scale Problems | |

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Summary | |

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Problems | |

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Analysis of Count Data | |

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Introduction | |

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Contingency Tables | |

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Contingency Coefficient | |

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Some Special Results for k x 2 Contingency Tables | |

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Fisher's Exact Test | |

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McNemar's Test | |

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Analysis of Multinomial Data | |

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Ordered Categories | |

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Summary | |

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Problems | |

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Summary | |

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Appendix of Tables | |

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Normal Distribution | |

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Chi-Square Distribution | |

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Cumulative Binomial Distribution | |

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Total Number of Runs Distribution | |

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Runs Up and Down Distribution | |

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Kolmogorov-Smirnov One-Sample Statistic | |

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Binomial Distribution for ï¿½ = 0.5 | |

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Probabilities for the Wilcoxon Signed-Rank Statistic | |

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Kolmogorov-Smirnov Two-Sample Statistic | |

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Probabilities for the Wilcoxon Rank-Sum Statistic | |

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Kruskal-Wallis Test Statistic | |

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Kendall's Tau Statistic | |

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Spearman's Coefficient of Rank Correlation | |

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Friedman's Analysis-of-Variancc Statistic and Kendall's Coefficient of Concordance | |

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Lilliefor's Test for Normal Distribution Critical Values | |

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Significance Points of T<sub>XY.Z</sub> for Kendall's Partial Rank-Correlation Coefficient | |

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Page's L Statistic | |

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Critical Values and Associated Probabilities for the Jonckheere-Terpstra Test | |

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Rank von Neumann Statistic | |

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Lilliefors's Test for Exponential Distribution Critical Values | |

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Answers to Selected Problems | |

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References | |

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Index | |