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NOMINAL MEASURES OF
ASSOCIATION
► Statistics clarify the causal context of social
phenomena. One precondition for an X Y causal
relationship is that 2 variables be empirically associated. Measures of association determine if 2 variables are empirically associated.
► For nominal level variable, we can use measures of
association that are extensions of chi-square. These
chi-square or “delta” based measures of association
are: Phi-coeffient, Cramer’s V, and the Contingency
Coefficient.
ORDINAL MEASURES OF ASSOCIATION
►For variables measured at the ORDINAL level,
we can use two alternative measures of association: Spearman’s rank -order correlation coefficient (Spearman’s r), and Goodman’s and Kruskal’s Gamma coefficient (Gamma).
►When ordinal level variables have been ranked
on a given characteristic use Spearman’s r …
Interpreting Spearman’s r
► Spearman’s r shows the level of
agreement or consistency in the rankings
of two variables X and Y.
►If X and Y are ranked identically, then
Spearman’s r will be 1.0. A positive sign
indicates that as rankings increase in X
they increase in Y.
►If X and Y are ranked oppositely, then
Spearman’s r will take a value of -1.0. A
negative sign would indicate that as
rankings increase in X, they decrease in
Y.
Goodman’s and Kruskal’s
Gamma
►Variables measured in ordinal
categories such as low / medium/ high, produce a large number of tied ranks. In such cases, when two ordinal variables are crosstabulated (e.g., in a 2 x 2; 2 x 3; 3 x 4 table), the Gamma coefficient (G) is the appropriate measure of association.
