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May 12, 2015
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18-2McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc.,All Rights
Reserved.
Part FourANALYSIS AND
PRESENTATION OF DATA
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Chapter EighteenMEASURES OF ASSOCIATION
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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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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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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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Interpretation of Coefficients
• Relationship does not imply causation
• Statistical significance does not imply a relationship is practically meaningful
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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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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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Bivariate Linear Regression
• Used to make simple and multiple predictions
• Regression coefficients– Slope – Intercept
• Error term
• Method of least squares
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Interpreting Linear Regression
• Residuals– what remains after the line is fit or (Yi-Yi)
• Prediction and confidence bands
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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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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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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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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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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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Measures for Ordinal Data
• Tests– Gamma– Somer’s d– Spearman’s rho– Kendall’s tau b– Kendall’s tau c