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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Nonparametric Statistics: Use and Nonuse:
TL;DR: In this article, the distinctions among parametric, non-parametric, and distribution free statistical tests are clarified. The principal circumstances prompting the use of nonparametric procedures, both rank-based and non-rank-based, are discussed.
Journal ArticleDOI
Evaluation of determination of glucose in urine with some commercially available dipsticks and tablets.
TL;DR: Of the four products, Chemstrip uG had the lowest within-technologist and technologist-to-Technologist random analytical errors and was significantly stronger in its association with the quantitative hexokinase method than was Diastix, Clinitest, or Tes-Tape.
Journal ArticleDOI
Distributions of Goodman and Kruskal's Gamma and Spearman's Rho in 2 × 2 Tables for Small and Moderate Sample Sizes
Lydia P. Gans,C. A. Robertson +1 more
TL;DR: In this paper, the distribution of Goodman and Kruskal's G in 2 × 2 tables is examined for small and moderate sample sizes, and asymptotic results relevant to the speed of convergence of G to normality are given.
Journal ArticleDOI
A measure of 2 x 2 association with stable variance and approximately normal small-sample distribution: planning cost-effective studies.
TL;DR: A measure of 2 x 2 association, Z, is developed having the property that n(Z - Z) has approximately a standard normal distribution, even for quite small sample size.
Journal ArticleDOI
Girls and Physics Education.
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.