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DON’T TAKE NOTES ! MUCH OF THE FOLLOWING IS IN THE COURSEPACK!

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DON’T TAKE NOTES! MUCH OF THE FOLLOWING IS IN THE COURSEPACK!

Just follow the discussion and try to interpret the statistical results that follow.

We often want to see the degree to which two variables are associated with each other. For example, is there a relationship between a person’s level of education and the likelihood t they smoke? Yes! The association is negative: the more educated a person is the less likely they are to smoke. Had the association been positive it would have meant the more educated a person the more likely they are to smoke.

We frequently use what is termed a “measure of association” to assess the degree to which two variables are associated. Typically, such measures range between -1.0 (strongest negative association) and +1.0 (strongest positive association). A score of “0” means there is no association between the variables.

If variables are measured with a low degree of measurement error:

0 to plus/minus .25 = weak association

.26 to plus/minus .49 = moderate assoc.

.50 to plus/minus .69 = strong association

.70 to plus/minus 1.0 = very strong assoc.

What must we have in order to have a “social science model”?

Why do we typically use regression rather than measures of association?

Tax Conservatism

1 2 3

1 12.3% 76.2% 95.5%

2 40.4% 23.8% 4.5%

3 47.3% 0.0% 0.0%

What does the above data tell us?

Association between Tax and Conservatism

Pearson’s Correlation: -.69

NOTE: if percentages rather than 1-3 scale are used Pearson’s Correlation is -.80. Not using all the information reduces the association.

Measures of Association (e.g., correlation) only tell us the strength of the relationship between X and Y, NOT the MAGNITUDE of the relationship. Regression tells us the MAGNITUDE of the relationship (i.e., how MUCH the dependent variable changes for a specified amount of change in the independent variable).

Correlation of the Percent of the Countywide Vote for Barbara Boxer and Jerry Brown in 2010 with the Percentage of those 25, and Older, Who Have at Least a Bachelor’s Degree in 2000 and Median Household Income in 2008.

correlate boxer10 brown10 coll00 medinc08

(obs=58)

| boxer10 brown10 coll00 medinc08

-------------+------------------------------------

boxer10 | 1.0000

brown10 | 0.9788 1.0000

coll00 | 0.7422 0.6885 1.0000

medinc08 | 0.6022 0.5401 0.8321 1.0000

Given the correlations below, what should you expect

in the regression table on the next slide where the dependent variable is “boxer 10” (percent of county vote for Boxer in 2010)?

correlate boxer10 brown10 coll00 medinc08

(obs=58)

| boxer10 brown10 coll00 medinc08

-------------+------------------------------------

boxer10 | 1.0000

brown10 | 0.9788 1.0000

coll00 | 0.7422 0.6885 1.0000

medinc08 | 0.6022 0.5401 0.8321 1.0000

DON’T WRITE THE NUMBERS!

Ind. Var. CoefficientSt. Error

Dem. Control -.555 .260

State Ideology .003 .010

% Catholic .009 .010

% Fundamental .029 .009

Public Opinion -.825 .465

about Abortion

DON’T WRITE THE NUMBERS!

Ind. Var. CoefficientSt. Error

Liberal Control .788 .318

Real Per Capita -1.802 .892

Income

Governor -.925 .301

Election Year