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
ASCAID: Using an Asymmetric Correlation Measure for Automatic Interaction Detection
TL;DR: Based upon the predictive association measure λ by Goodman and Kruskal, a new algorithm for the induction of a decision tree is proposed that cares about the asymmetric character of the classification task and enables the use of statistical inference.
Journal ArticleDOI
Inferring logit models from empirical margins using proxy data
Ju-Sung Lee,Kathleen M. Carley +1 more
TL;DR: In this paper, the authors examined several approaches for inferring logit models from empirical margins of predictor covariates and conditional margins containing the means of a binary response for each covariate margin.
Journal ArticleDOI
An analysis of multivariate ordinal polytomous data using the log‐linear probability model
TL;DR: In this paper, the gamma coefficient developed by Goodman and Kruskal is extended to a partial measure of association in the framework of the loglinear model probability model and applied to Sewell and Armer's data on educational aspirations of high school students.
Journal ArticleDOI
Comparison of Chemstrip uG, Clinitest, and Diastix Urine Test Methods in Diabetic Children
Douglas O. Sobel,Marion Balsam +1 more
TL;DR: It is concluded that Chemstrip uG is a clinically useful and acceptable method for self-monitoring of urine glucose in diabetic children.
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.