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Measures of Association

Chapter 18. Measures of Association. Deepak Khazanchi. Bivariate Correlation vs. Nonparametric Measures of Association. Parametric correlation requires two continuous variables measured on an interval or ratio scale

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Measures of Association

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  1. Chapter 18 Measures of Association Deepak Khazanchi

  2. 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 variables

  3. Bivariate Correlation Analysis • Pearson correlation coefficient • r symbolized the coefficient's 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 distribution

  4. 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)

  5. Interpretation of Coefficients • Relationship does not imply causation • Statistical significance does not imply a relationship is practically meaningful

  6. 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 reciprocally

  7. Interpretation of Coefficients • Artifact Correlations • Goodness of fit • F test • Coefficient of determination • Correlation matrix • used to display coefficients for more than two variables

  8. Bivariate Linear Regression • Used to make simple and multiple predictions • Regression coefficients • Slope • Intercept • Error term • Method of least squares

  9. Interpreting Linear Regression • Residuals • what remains after the line is fit or (Yi-Yi) • Prediction and confidence bands ^

  10. 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 function

  11. 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 1

  12. 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 variable

  13. Measures for Ordinal Data • No assumption of bivariate normal distribution • Most based on concordant/discordant pairs • Values range from +1.0 to -1.0

  14. Measures for Ordinal Data • Tests • Gamma • Somer’s d • Spearman’s rho • Kendall’s tau b • Kendall’s tau c

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