Measures of Association Deepak Khazanchi Chapter 18

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