Chương 18 - ĐO LƯỜNG LIÊN HỆ

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Parametric correlation requires two continuous variables measured on an interval or ratio scale. The coefficient does not distinguish between independent and dependent variables

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Nội dung Text: Chương 18 - ĐO LƯỜNG LIÊN HỆ

Chương 18 ĐO LƯỜNG LIÊN HỆ 18-1
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 18-2
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 18-3 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) 18-4
Interpretation of Coefficients • Relationship does not imply causation • Statistical significance does not imply a relationship is practically meaningful 18-5
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 18-6
Interpretation of Coefficients • Artifact Correlations • Goodness of fit – F test – Coefficient of determination – Correlation matrix • used to display coefficients for more than two variables 18-7
Bivariate Linear Regression • Used to make simple and multiple predictions • Regression coefficients – Slope – Intercept • Error term • Method of least squares 18-8
Interpreting Linear Regression • Residuals – what remains after the line is fit or (Yi-Yi) • Prediction and confidence bands 18-9
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 18-10
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 18-11
Nonparametric Measures of Association • Chi-square based measure – Phi – Cramer’s V – Contingency coefficient of C • Proportional reduction in error (PRE) – Lambda – Tau 18-12
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 18-13
Measures for Ordinal Data • No assumption of bivariate normal distribution • Most based on concordant/discordant pairs • Values range from +1.0 to -1.0 18-14
Measures for Ordinal Data • Tests – Gamma – Somer’s d – Spearman’s rho – Kendall’s tau b – Kendall’s tau c 18-15