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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```MEASURES OF ASSOCIATION

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