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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A guide for selecting statistical techniques for analyzing social science data
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Measurement of reliability for categorical data in medical research.
TL;DR: The problem of measuring reliability of categorical measurements, particularly diagnostic categorizations, is addressed and a general model is proposed, leading to definition of reliability indices.
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An Analysis of Variance for Categorical Data, II: Small Sample Comparisons with Chi Square and other Competitors
TL;DR: In this article, the authors investigated the small sample behavior of contingency tables for Pearson's chi-square statistic (X 2), Light and Margolin's C statistic, Kullback's minimum discrimination information statistic (2I), and Goodman and Kruskal's Lambda.
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How much does it cost? Optimization of costs in sequence analysis of social science data
TL;DR: The authors provide an empirical way of determining costs for cases, frequent in the social sciences, in which theory does not clearly promote one cost scheme over another and performs well compared with other cost-setting strategies, while it alleviates the justification problem of cost schemes.
Journal ArticleDOI
Multiplicative models for square contingency tables with ordered categories
TL;DR: In this article, the diagonals-parameter symmetry model and other related multiplicative models are applied to the 4 x 4 table on unaided vision first analysed by Stuart (1953, 1955), and a possible explanation is obtained for the "strange residual pattern" noted by McCullagh (1978), both in his recent analysis of the data using the palindromic symmetry model, and in the analysis of data using quasisymmetry model as fitted by Plackett (1974, p. 61) and others.
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.