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Measures of Association Deepak Khazanchi Chapter 18.

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1 Measures of Association Deepak Khazanchi Chapter 18

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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