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1. 1. 18-1
3. 3. Chapter Eighteen MEASURES OF ASSOCIATION18-3
4. 4. Bivariate Correlation vs. Nonparametric Measures of Association • Parametric correlation requires two continuous variables measured on an interval or ratio scale • The coefficient does not distinguish between independent and dependent variables18-4
5. 5. Bivariate Correlation Analysis Pearson correlation coefficient – r symbolized the coefficients estimate of linear association based on sampling data – Correlation coefficients reveal the magnitude and direction of relationships – Coefficient’s sign (+ or -) signifies the direction of the relationship • Assumptions of r Linearity Bivariate normal distribution18-5
6. 6. Bivariate Correlation Analysis Scatterplots – Provide a means for visual inspection of data • the direction of a relationship • the shape of a relationship • the magnitude of a relationship (with practice)18-6
7. 7. Interpretation of Coefficients • Relationship does not imply causation • Statistical significance does not imply a relationship is practically meaningful18-7
8. 8. Interpretation of Coefficients • Suggests alternate explanations for correlation results – X causes Y. . . or – Y causes X . . . or – X & Y are activated by one or more other variables . . . or – X & Y influence each other reciprocally18-8
9. 9. Interpretation of Coefficients • Artifact Correlations • Goodness of fit – F test – Coefficient of determination – Correlation matrix • used to display coefficients for more than two variables18-9
10. 10. Bivariate Linear Regression • Used to make simple and multiple predictions • Regression coefficients – Slope – Intercept • Error term • Method of least squares18-10
11. 11. Interpreting Linear Regression • Residuals – what remains after the line is fit or (Yi-Yi) • Prediction and confidence bands18-11
12. 12. Interpreting Linear Regression • Goodness of fit – Zero slope • Y completely unrelated to X and no systematic pattern is evident • constant values of Y for every value of X • data are related, but represented by a nonlinear function18-12
13. 13. Nonparametric Measures of Association • Measures for nominal data – When there is no relationship at all, coefficient is 0 – When there is complete dependency, the coefficient displays unity or 118-13
14. 14. Nonparametric Measures of Association • Chi-square based measure – Phi – Cramer’s V – Contingency coefficient of C • Proportional reduction in error (PRE) – Lambda – Tau18-14
15. 15. Characteristics of Ordinal Data • Concordant- subject who ranks higher on one variable also ranks higher on the other variable • Discordant- subject who ranks higher on one variable ranks lower on the other variable18-15
16. 16. Measures for Ordinal Data • No assumption of bivariate normal distribution • Most based on concordant/discordant pairs • Values range from +1.0 to -1.018-16
17. 17. Measures for Ordinal Data • Tests – Gamma – Somer’s d – Spearman’s rho – Kendall’s tau b – Kendall’s tau c18-17