NCJ Number
47084
Date Published
1977
Length
252 pages
Annotation
METHODS ARE DESCRIBED FOR ANALYZING THE MOST COMMON WAY OF DISPLAYING AND STUDYING NOMINAL AND ORDINAL VARIABLES.
Abstract
CLASSIFICATIONS IN THE FORM OF NOMINAL AND ORDINAL VARIABLES ARE COMMON AND THE PURPOSE HERE IS TO PROVIDE AN INTUITIVE, NONRIGOROUS DESCRIPTION OF TECHNIQUES USED IN THEIR ANALYSIS. DISCUSSION OF THE ANALYSIS OF TWO-WAY TABLES IS UNDERTAKEN WITH A SHORT REVIEW OF THE CHI-SQUARE TEST FOR INDEPENDENCE, AND EXAMINATION OF RESIDUALS, PARTITIONING CHI-SQUARE, AND THE ANALYSIS OF SQUARE TABLES. MEASURES OF ASSOCIATION FOR NOMINAL DATA ARE DISCUSSED INCLUDING MEASURES OF AGREEMENT, OF PROPORTIONAL-REDUCTION-IN-ERROR, OF VARIOUS TABULAR MATRICES, AND OF PREDICTION LOGIC. MEASURES OF ASSOCIATION FOR ORDINAL DATA ARE ALSO EXAMINED REGARDING CORRELATION COEFFICIENTS, ALTERNATIVE INTERPRETATIONS, STANDARD ERRORS, AND STATISTICAL TESTS. AN INTRODUCTION TO MULTIVARIATE ANALYSIS OF CROSS-CLASSIFICATION IS PROVIDED, WITH ATTENTION TO TEST-FACTOR STRATIFICATION AND COEFFICIENTS OF PARTIAL ASSOCIATION FOR NOMINAL AND ORDINAL DATA. LOG-LINEAR MODELS ARE DEALT WITH IN DETAIL: MODELS FOR TWO-WAY AND THREE-WAY TABLES ARE OUTLINED, AND AN ALTERNATIVE VIEW OF LINEAR MODELS AND THE EFFECTS OF COLLAPSING VARIABLES ARE DISCUSSED; FORMULAS FOR CALCULATING EXPECTED FREQUENCIES, ESTIMATION BY ITERATION, AND PARTITIONING MODELS ARE ALSO EXAMINED. REGRESSION ANALYSIS OF CROSS-CLASSIFICATIONS IS CONSIDERED WITH REGARD TO CATEGORICAL VARIABLES AND THE GRIZZLE, STARMER, AND KOCH APPROACH TO WEIGHTED LEAST SQUARES. DATA SOURCES, AND A BRIEF INTRODUCTION TO VECTORS, MATRICES, ANND THE DISTRIBUTION OF CHI-SQUARE ARE PROVIDED IN APPENDIXES. REFERENCES AND AN INDEX ARE INCLUDED. (KBL)