18-1

18-2McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc.,All Rights

Reserved.

Part FourANALYSIS AND

PRESENTATION OF DATA

18-3

Chapter EighteenMEASURES OF ASSOCIATION

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

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

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)

18-7

Interpretation of Coefficients

• Relationship does not imply causation

• Statistical significance does not imply a relationship is practically meaningful

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

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

18-10

Bivariate Linear Regression

• Used to make simple and multiple predictions

• Regression coefficients– Slope – Intercept

• Error term

• Method of least squares

18-11

Interpreting Linear Regression

• Residuals– what remains after the line is fit or (Yi-Yi)

• Prediction and confidence bands

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

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

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

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

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

18-17

Measures for Ordinal Data

• Tests– Gamma– Somer’s d– Spearman’s rho– Kendall’s tau b– Kendall’s tau c