Data Lab #6

July 9, 2008

Ivan Katchanovski, Ph.D.

POL 242Y-Y

Correlation: SPSS Commands• SPSS Command: Analyze-Correlate-Bivariate-Pearson

• Research Hypothesis: The level of economic development has a positive effect on the level of democracy

• Dataset: World

• Variables: – Freedom House democracy rating reversed:

• Dependent variable

• Interval-ratio

– GDP per capita ($1000): • Independent variable

• Interval-ratio2

Example: Interpretation

• Pearson Correlation Coefficient: .607– Positive association in expected direction

– 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 the level of democracy

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Scatterplot: Example

• SPSS commands: Graphs-Interactive-Scatterplot

• Assign variables:– Vertical axis box: select the dependent variable

• Freedom House democracy rating reversed

– Horizontal axis box: select the independent variable• GDP per capita ($1000)

– Double click to edit scatterplot

• Positive association between the economic development level and the democracy level

Scatterplot: SPSS Graph Example

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Correlation Matrix• Correlation Matrix: correlations of more than 2 variables

• Example: The Greatest Portuguese vote reliability check– Variables: TV vote, Poll 1, Poll 2

– TV vote is weakly correlated with Poll 1 and Poll 2

– Correlations of TV vote with Poll 1 and Poll 2 are statistically insignificant

– Poll 1 and Poll 2 are strongly correlated

– Correlation between Poll 1 and Poll 2 is statistically significant at the .05 level

• TV vote data are not reliable measure of public opinion concerning “Greatest Portuguese”

• Public opinion polls are reliable measure of public opinion concerning “Greatest Portuguese” 6

Greatest Portuguese: SPSS Correlation Matrix

TV vote Poll No 1 Poll No 2

TV vote Pearson Correlation 1 .095 -.126

Sig. (2-tailed) .795 .728N 10 10 10

Poll No 1 Pearson Correlation .095 1 .698(*)

Sig. (2-tailed) .795 .025N 10 10 10

Poll No 2 Pearson Correlation -.126 .698(*) 1

Sig. (2-tailed) .728 .025 N 10 10 10

7* Correlation is significant at the 0.05 level (2-tailed).

Correlation Matrix: Table

TV vote Poll No 1 Poll No 2TV vote

1

Poll No 1.095 1

Poll No 2-.126 .698*** 1

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Table 1. Correlation Matrix

*** Correlation is significant at the 0.001 level.