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