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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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**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 • The coefficient does not distinguish between independent and dependent variables**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**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)**Interpretation of Coefficients**• Relationship does not imply causation • Statistical significance does not imply a relationship is practically meaningful**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**Interpretation of Coefficients**• Artifact Correlations • Goodness of fit • F test • Coefficient of determination • Correlation matrix • used to display coefficients for more than two variables**Bivariate Linear Regression**• Used to make simple and multiple predictions • Regression coefficients • Slope • Intercept • Error term • Method of least squares**Interpreting Linear Regression**• Residuals • what remains after the line is fit or (Yi-Yi) • Prediction and confidence bands ^**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**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**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**Measures for Ordinal Data**• No assumption of bivariate normal distribution • Most based on concordant/discordant pairs • Values range from +1.0 to -1.0**Measures for Ordinal Data**• Tests • Gamma • Somer’s d • Spearman’s rho • Kendall’s tau b • Kendall’s tau c

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