This document discusses various measures of association that can be used for different types of variable data. It describes Pearson's correlation coefficient r which measures linear association between two continuous variables. It also discusses scatterplots and interpreting correlation results, including issues of causation. Nonparametric measures are introduced for nominal data like chi-square tests and ordinal data measures based on concordant/discordant pairs like Spearman's rho and Kendall's tau. Linear regression is also covered for predicting relationships between variables.

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

3. Chapter Eighteen
MEASURES OF
ASSOCIATION
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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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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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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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7. Interpretation of Coefficients
• Relationship does not imply causation
• Statistical significance does not imply a
relationship is practically meaningful
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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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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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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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11. Interpreting Linear Regression
• Residuals
– what remains after the line is fit or (Yi-Yi)
• Prediction and confidence bands
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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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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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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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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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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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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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