Book ChapterDOI
Measures of Association for Cross Classifications III: Approximate Sampling Theory
Leo A. Goodman,William Kruskal +1 more
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In this paper, the authors derived large sample normal distributions with their associated standard errors for various measures of association and various methods of sampling and explained how the large sample normality may be used to test hypotheses about the measures and about differences between them, and to construct corresponding confidence intervals.Abstract:
The population measures of association for cross classifications, discussed in the authors' prior publications, have sample analogues that are approximately normally distributed for large samples. (Some qualifications and restrictions are necessary.) These large sample normal distributions with their associated standard errors, are derived for various measures of association and various methods of sampling. It is explained how the large sample normality may be used to test hypotheses about the measures and about differences between them, and to construct corresponding confidence intervals. Numerical results are given about the adequacy of the large sample normal approximations. In order to facilitate extension of the large sample results to other measures of association, and to other modes of sampling, than those treated here, the basic manipulative tools of large sample theory are explained and illustrated.read more
Citations
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Book ChapterDOI
Randomized Block Designs: Ordinal Data
TL;DR: In this paper, the multivariate randomized block permutation procedures (MRBP) developed in Chap. 8 for analyzing randomized-block data at the ordinal level of measurement were used.
Journal ArticleDOI
Rao's statistic for the analysis of uniform association in cross-classifications
TL;DR: A new measure for the analysis of association in cross-classifications having ordered categories is introduced in terms of the odd-ratios in 2 × 2 subtables formed from adjacent rows and adjacent columns based on the family of divergences introduced by Burbea and Rao.
Journal ArticleDOI
Simple Approximations to Null Sampling Variances Goodman and Kruskal's Gamma, Kendall's Tau, and Somers's dxy
TL;DR: In this paper, simple formulas involving the sample size and the number of rows and columns in the cross-classification have been found to closely approximate formulas suitable for significance testing under a wide variety of circumstances.
Individual Survival Distributions: A More Effective Tool for Survival Prediction
TL;DR: This paper motivates an alternative class of tools that can learn a model which provides an individual survival distribution which gives survival probabilities across all.
Book ChapterDOI
Regression Analysis of Interval Data
TL;DR: In this article, multi-response permutation procedures are used to analyze regression residuals generated by ordinary least squares (OLS) and least absolute deviation (LAD) regression models, and experimental designs presented and analyzed in Chap. 4 include one-way randomized, oneway randomized with a covariate, one way randomized-block, two-way randomization, twoway randomized block, two way factorial, Latin square, split-plot, and two-factor nested designs.
References
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Book
Measures of association for cross classifications
Leo A. Goodman,William Kruskal +1 more
TL;DR: In this article, a number of alternative measures are considered, almost all based upon a probabilistic model for activity to which the cross-classification may typically lead, and only the case in which the population is completely known is considered, so no question of sampling or measurement error appears.
Book ChapterDOI
A Class of Statistics with Asymptotically Normal Distribution
TL;DR: In this article, the authors considered the problem of estimating a U-statistic of the population characteristic of a regular functional function, where the sum ∑″ is extended over all permutations (α 1, α m ) of different integers, 1 α≤ (αi≤ n, n).
Journal ArticleDOI
Ordinal Measures of Association
TL;DR: The three measures considered at length are the quadrant measure, Kendall's tau, and Spearman's rho as mentioned in this paper, with emphasis on the probabilistic and operational interpretations of their population values.
Journal ArticleDOI
The Central Limit Theorem for Dependent Random Variables
TL;DR: The central limit theorem has been extended to the case of dependent random variables by several authors (Bruns, Markoff, S. Bernstein, P. Levy, and Loeve) as mentioned in this paper.