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NOMINAL MEASURES OF ASSOCIATION

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NOMINAL MEASURES OF ASSOCIATION

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    1. 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, Cramers V, and the Contingency Coefficient.

    3. THE PHI-COEFFICIENT Relationship between two nominal or one nominal-one ordinal variable, and the relationship that is crosstabulated in a 2 x 2 table, use the phi-coefficient. Phi-coefficient varies from 0 to 1 (.10-.30 is weak; .31 to .60 is moderate; .61 or more is strong). If chi-square is significant, phi is significant! Also, if you square the phi-coefficient, you get a measure of the percentage improvement in predicting Y from X.

    6. CONTINGENCY COEFFICIENT & CRAMERS V Contingency Coefficient ( C ) varies from 0 to 1the closer to 1 the stronger the association between variables. If chi-square is statistically significant, C will be statistically significant. Use C ( Contingency Coefficient ) for symmetrical crosstabulations bigger than 2 x 2 (e.g., 3 x 3; 4 x 4; 5 x 5; etc.). For asymmetrical crosstabulations (e.g., 2 x 3; 3 x 4; 4 x 5; etc.) use Cramers V.

    8. ORDINAL MEASURES OF ASSOCIATION For variables measured at the ORDINAL level, we can use two alternative measures of association: Spearmans rank-order correlation coefficient (Spearmans r), and Goodmans and Kruskals Gamma coefficient (Gamma). When ordinal level variables have been ranked on a given characteristic use Spearmans r

    13. Interpreting Spearmans r Spearmans 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 Spearmans 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 Spearmans r will take a value of -1.0. A negative sign would indicate that as rankings increase in X, they decrease in Y.

    20. Goodmans and Kruskals 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.

    23. To calculate Na, find the frequency in the upper left corner cell of the crosstabulation (f=15); and multiply it by the sum of all the cell frequencies that fall below and to the right . Repeat this procedure for all cell frequencies that have cells below and to the right.

    26. To calculate Ni, reverse the procedure and find the frequency in the upper right corner cell of the crosstabulation (f= 7); multiply it by the sum of all the cell frequencies that fall below and to the left . Repeat for all cell frequencies that have cells below and to the left .

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