Chương 18 - ĐO LƯỜNG LIÊN HỆ doc

18-1 Chương 18 ĐO LƯỜNG LIÊN HỆ 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 18-3 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 18-4 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) 18-5 Interpretation of Coefficients • Relationship does not imply causation • Statistical significance does not imply a relationship is practically meaningful 18-6 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 18-7 Interpretation of Coefficients • Artifact Correlations • Goodness of fit – F test – Coefficient of determination – Correlation matrix • used to display coefficients for more than two variables 18-8 Bivariate Linear Regression • Used to make simple and multiple predictions • Regression coefficients – Slope – Intercept • Error term • Method of least squares 18-9 Interpreting Linear Regression • Residuals – what remains after the line is fit or (Y i -Y i ) • Prediction and confidence bands 18-10 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 [...]... 1 8- 11 Nonparametric Measures of Association • Chi-square based measure – Phi – Cramer’s V – Contingency coefficient of C • Proportional reduction in error (PRE) – Lambda – Tau 1 8- 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 1 8- 13... the other variable 1 8- 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 1 8- 14 Measures for Ordinal Data • Tests – – – – – 1 8- 15 Gamma Somer’s d Spearman’s rho Kendall’s tau b Kendall’s tau c . 1 8- 1 Chương 18 ĐO LƯỜNG LIÊN HỆ 1 8- 2 Bivariate Correlation vs. Nonparametric Measures of Association • Parametric. or 1 1 8- 12 Nonparametric Measures of Association • Chi-square based measure – Phi – Cramer’s V – Contingency coefficient of C • Proportional reduction in error (PRE) – Lambda – Tau 1 8- 13 Characteristics. two variables 1 8- 8 Bivariate Linear Regression • Used to make simple and multiple predictions • Regression coefficients – Slope – Intercept • Error term • Method of least squares 1 8- 9 Interpreting