Chương 18 - ĐO LƯỜNG LIÊN HỆ doc

Bivariate Correlation vs.. Nonparametric Measures of Association • Parametric correlation requires two continuous variables measured on an interval or ratio scale • The coefficient does

Chương 18

ĐO LƯỜNG LIÊN HỆ

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

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

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)

Interpretation of Coefficients

• Relationship does not imply causation

• Statistical significance does not imply a

relationship is practically meaningful

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

Interpretation of Coefficients

• Artifact Correlations

• Goodness of fit

– F test – Coefficient of determination – Correlation matrix

• used to display coefficients for more

than two variables

Bivariate Linear Regression

• Used to make simple and multiple

predictions

• Regression coefficients

– Slope – Intercept

• Error term

Interpreting Linear Regression

• Residuals

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

• Prediction and confidence bands

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

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

Nonparametric Measures of Association

– Contingency coefficient of C

• Proportional reduction in error (PRE)

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

Measures for Ordinal Data

• No assumption of bivariate normal

distribution

• Most based on concordant/discordant

pairs

• Values range from +1.0 to -1.0

Measures for Ordinal Data

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