Ivan Katchanovski, Ph.D. POL 242Y-Y Correlation July 7, 2008 Ivan Katchanovski, Ph.D. POL 242Y-Y

Association between Variables at Interval-ratio and Ordinal Levels Correlation: Association between variables at interval-ratio level Can be used for ordinal variables with certain assumptions Scattergrams: graphical plots of two variables Provide visual information about the existence, strength and direction of the relationship Independent variable (X): horizontal axis Dependent variable (Y): vertical axis

Scattergram: Internet use and education level

Direction of association Positive Negative No association

Correlation Coefficient (Pearson’s R) ranges between –1 (negative association) 0 (no association) and 1 (positive association) 0: no association 0-0.25: weak association 0.25-0.5: moderate association 0.5-0.75: strong association 0.75-1.0: very strong association

Statistical Significance of Correlation Statistical Significance of Correlation Coefficient (R): Statistically significant if in SPSS p(obtained)<p(critical)=.05 or .01 or .001 Statistically nonsignificant if SPSS p(obtained)>p(critical)=.05 Correlation does not always mean causation

Example Research hypothesis: The level of economic development has a positive effect on civil liberties Independent variable: the level of economic development Interval-ratio Dependent variable: civil liberties Ordinal

Example Pearson Correlation Coefficient: .753 Statistical significance Positive association in expected direction Very strong association Statistical significance SPSS: p(obtained)=.000 <p(critical)=.001=.1% Statistically significant at the .001 or .1% level Research hypothesis: supported by correlation analysis The level of economic development has a positive and statistically significant effect on civil liberties