Measures of Association for Cross Classifications

ISBN-13: 9781461299974 / Angielski / Miękka / 2011 / 146 str.

L. A. Goodman; W. H. Kruskal

Opis

In 1954, prior to the era of modem high speed computers, Leo A. Goodman and William H. Kruskal published the fmt of a series of four landmark papers on measures of association for cross classifications. By describing each of several cross classifications using one or more interpretable measures, they aimed to guide other investigators in the use of sensible data summaries. Because of their clarity of exposition, and their thoughtful statistical approach to such a complex problem, the guidance in this paper is as useful and important today as it was on its publication 25 years ago. in a cross-classification by a single number inevita- Summarizing association bly loses information. Only by the thoughtful choice of a measure of association can one hope to lose only the less important information and thus arrive at a satisfactory data summary. The series of four papers reprinted here serve as an outstanding guide to the choice of such measures and their use.

Spis treści

Measures of Association for Cross Classifications.- 1. Introduction.- 2. Four Preliminary Considerations.- 3. Conventions.- 4. Traditional Measures.- 5. Measures Based on Optimal Prediction.- 6. Measures Based upon Optimal Prediction of Order.- 7. The Generation of Measures by the Introduction of Loss Functions.- 8. Reliability Models.- 9. Proportional Prediction.- 10. Association with a Particular Category.- 11. Partial Association.- 12. Multiple Association.- 13. Sampling Problems.- 14. Concluding Remarks.- 15. References.- Measures of Association for Cross Classifications. II: Further Discussion and References.- 1. Introduction and Summary.- 2. Supplementary Discussion to Prior Paper.- 3. Work on Measures of Association in the Late Nineteenth and Early Twentieth Centuries.- 4. More Recent Publications.- 5. References.- Measures of Association for Cross Classifications III: Approximate Sampling Theory.- 1. Introduction and Summary.- 2. Notation and Preliminaries.- 3. Multinominal Sampling over the Whole Double Polytomy.- 4. Multinomial Sampling within Each Row (Column) of the Double Polytomy.- 5. Further Remarks.- 6. References.- Measures of Association for Cross Classifications IV: Simplification of Asymptotic Variances.- 1. Introduction and Summary.- 2. Multinomial Sampling over the Entire Two-Way Cross Classification.- 3. Independent Multinomial Sampling in the Rows.- 4. Use of the Results in Practice.- 5. When Does ?= 0?.- 6. Cautionary Note about Asymptotic Variances.- References.