MEASURES OF ASSOCIATION

Overview

Association refers to a wide variety of coefficients which measure effect size (strength of relationship), defined various ways. In common usage "association" refers to measures of the strength of relationship in which at least one of the variables is a dichotomy, nominal, or ordinal.

Correlation is a type of association used when both variables are interval, is discussed in a separate "blue book" volume. All interval procedures have their own effect size measures, also treated in separate volumes.

Reliability is a type of association used to establish the consistency of a measure or to assess inter-rater similarity on a variable. It is also treated in a separate "blue book" volume.

Measures of association discussed in this volume are for dichotomous, nominal, ordinal, or mixed data. Note that with the exception of eta, when data are mixed by data level, the researcher uses a measure of association for the lower data level. For example, for nominal-by-ordinal association one would use a measure compatible with nominal-level association.

Specifically, the following measures are treated in this volume:

" Dichotomous Association (2-by-2 tables): Percent Difference, Yule's Q, Yule's Y, Risk

" Nominal Association: Phi, Contingency Coefficient, Tschuprow's T, Cramer's V, Lambda, Uncertainty Coefficient

" Nominal-by-Interval Nonlinear Association: Eta

" Ordinal Association: Gamma, Kendall's tau-b and tau-c, Somers' d

" Association for Inter-rater Agreement (rows and columns are the same variable): Kappa

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Below is the unformatted table of contents.

MEASURES OF ASSOCIATION Table of Contents Overview 5 Key Concepts and Terms 6 Significance versus association 6 Coefficients of association 6 Types of "perfect" relationship 6 Strict monotonicity 8 Strict monotonicity and the assumption of equal marginals 8 Ordered monotonicity 10 Predictive monotonicity 10 Weak monotonicity 11 Monotonicity and table size 11 Curvilinear association 12 Types of null relationship 12 Independence 13 Accord 13 Balance 14 Cleavage 14 Association with control variables 15 Effect Size Measures (Association) for Dichotomies: Percent Difference, Yule's Q, Yule's Y, Risk, Odds Ratio 17 Overview 17 Percent Difference 17 Yule's Q 18 Yule's Y 19 The Relative Risk Coefficient, RR 20 Relative risk reduction (RRR) and odds ratios 22 Nominal Association: Phi, Contingency Coefficient, Tschuprow's T, Cramer's V, Lambda, Uncertainty Coefficient 25 Overview 25 Phi 26 The Contingency Coefficient, Pearson's C 27 Tshuprow's T 29 Cramer's V 30 Lambda 30 The Uncertainty Coefficient, UC, or Theil's U 33 Nominal-by-Interval Association: Eta, the Correlation Ratio 35 Computation 35 Ordinal Association: Gamma, Kendall's tau-b and tau-c, Somers' d 38 Overview 38 Gamma 39 Kendall's tau-b 40 Kendall's tau-c 41 Somer's d 43 Association for Inter-rater Agreement (rows and columns are the same variable): Kappa 44 Cohen's kappa 44 Assumptions 45 Not assumed 45 Split of data affects association 45 Equal marginals 46 Frequently Asked Questions 46 Where does one find measures of association in SPSS? 46 Bibliography 46