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18-1
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18-2 McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc.,All Rights Reserved. Part Four ANALYSIS AND PRESENTATION OF DATA
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18-3 Chapter Eighteen MEASURES OF ASSOCIATION
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18-4 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
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18-5 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
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18-6 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)
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18-7 Interpretation of Coefficients Relationship does not imply causation Statistical significance does not imply a relationship is practically meaningful
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18-8 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
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18-9 Interpretation of Coefficients Artifact Correlations Goodness of fit –F test –Coefficient of determination –Correlation matrix used to display coefficients for more than two variables
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18-10 Bivariate Linear Regression Used to make simple and multiple predictions Regression coefficients –Slope –Intercept Error term Method of least squares
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18-11 Interpreting Linear Regression Residuals –what remains after the line is fit or (Y i -Y i ) Prediction and confidence bands
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18-12 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
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18-13 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
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18-14 Nonparametric Measures of Association Chi-square based measure –Phi –Cramer’s V –Contingency coefficient of C Proportional reduction in error (PRE) –Lambda –Tau
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18-15 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
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18-16 Measures for Ordinal Data No assumption of bivariate normal distribution Most based on concordant/discordant pairs Values range from +1.0 to -1.0
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18-17 Measures for Ordinal Data Tests – Gamma – Somer’s d – Spearman’s rho – Kendall’s tau b – Kendall’s tau c
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