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18-1. 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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Presentation on theme: "18-1. 18-2 McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc.,All Rights Reserved. Part Four ANALYSIS AND PRESENTATION OF DATA."— Presentation transcript:

1 18-1

2 18-2 McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc.,All Rights Reserved. Part Four ANALYSIS AND PRESENTATION OF DATA

3 18-3 Chapter Eighteen MEASURES OF ASSOCIATION

4 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

5 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

6 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)

7 18-7 Interpretation of Coefficients Relationship does not imply causation Statistical significance does not imply a relationship is practically meaningful

8 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

9 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

10 18-10 Bivariate Linear Regression Used to make simple and multiple predictions Regression coefficients –Slope –Intercept Error term Method of least squares

11 18-11 Interpreting Linear Regression Residuals –what remains after the line is fit or (Y i -Y i ) Prediction and confidence bands

12 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

13 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

14 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

15 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

16 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

17 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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