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.

Variable Association - 1

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.

Variable Association - 2

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.

Variable Association - 3

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.

Social Science Models and Regression

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

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

Examining Variable Relationships - 1

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?

Examining Variable Relationships - 2

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.

Why Regression? - 1

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).

Why Regression? - 2

California Election 2010 - 1

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

Graph of .97 Correlation of Brown10 and Boxer10

2040

6080

20 40 60 80brown10

Fitted values boxer10

Graph of .74 Correlation of Coll00 and Boxer10

2040

6080

10 20 30 40 50coll00

Fitted values boxer10

Graph of -.58 Correlation of %White in 2005 and Boxer10

2040

6080

60 70 80 90 100white05

Fitted values boxer10

Graph of -.23 Correlation of %Senior in 2005 and Boxer10

2040

6080

8 10 12 14 16 18senior05

Fitted values boxer10

California Election 2010 - 1

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

Probit – State Adoption of TRAP Abortion Laws

DON’T WRITE THE NUMBERS!

Ind. Var. Coefficient St. Error

Dem. Control -.555 .260

State Ideology .003 .010

% Catholic .009 .010

% Fundamental .029 .009

Public Opinion -.825 .465

about Abortion

Probit – State Adoption of an Income Tax Over 1916-1937

DON’T WRITE THE NUMBERS!

Ind. Var. Coefficient St. Error

Liberal Control .788 .318

Real Per Capita -1.802 .892

Income

Governor -.925 .301

Election Year