U.S. Senate Voting on Taxation – Variable List -1

Tax = Percentage of times the senator voted in favor of federal tax changes

where over 50% of the benefits went to households earning less than the median family income on 76 amendments to the Tax Reform Act of 1976.

Variable List - 2

Cons = Percentage of times the senator voted for positions favored by the Americans for Constitutional Action (a conservative interest group)

Note: What assumption about vote value does using a percentage measure make?

Variable List - 3

Party = Senator’s party affiliation (1 = Democrat; 0 = Republican)

Stinc = Median household income in

the senator’s state in thousands of dollars (i.e., $20,200 = 20.2)

What is a “median”?

Descriptive Statistics in Stata

Variable | Obs Mean Std. Dev. Min Max

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

tax | 100 46.54 28.731 7 97

cons | 100 35.11 31.242 0 100

party | 100 .62 .487 0 1

stinc | 100 9.20 1.524 6.1 12.4

Recoding Tax and Conservatism

In the following exercise “Tax” and

“Conservatism” are recoded as follows:

0 – 33 = 1

34-66 = 2

67-100 = 3

Note: this procedure “costs” us much

information (i.e., 34 is the same as 66)

Cross Tabulation of Tax and Conservatism

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?

Cross Tabulation – Page 30 – 300Reader

Tolerance by Location

Tolerance Coastal Inland

High 45% 19%

(180) (97)

Low 55% 81%

(220) (403)

Cross Tabulation – Page 31 – 300Reader

Tolerance by Location – Controlling for Education

Tolerance College Grad. High Sch. Grad.

Coastal Inland Coastal Inland

High 57% 57% 10% 10%

(170) (57) (10) (40)

Low 43% 43% 90% 90%

(130) (43) (90) (360)

Cross Tabulation and Controlling – Are We Controlling for Per Capita Income?

Measures of Association -1

PURPOSE: to summarize the association between two, or more, variables.

If we used the actual percentage score for

“Tax” and “Conservatism” we would have had a 10,000 celled table (100 x 100 = 10,000) instead of the 9 celled table on the previous slide.

Measures of Association - 2

The particular measure of association we use depends upon the level of measurement of the variables.

Pearson’s Product Moment Correlation requires interval or ratio variables (a percentage is a ratio level measure).

Gamma or Kendall’s tau only require ordinal level data.

Measures of Association - 3

Association between Tax and Conservatism

Pearson’s Correlation: -.69

Gamma: -.94

Kendall’s tau-b: -.67

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 - 4

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.

DON’T WRITE THE ABOVE MATERIAL – IT’S ON PAGE 37 OF THE 300READER

California: Analysis of County Vote in 2010

Correlation between the Percentage of a County’s Population, 25 or older, Who have at least a Bachelor’s Degree and the Percentage of the Countywide Vote for: Brown = .68

Boxer = .74

Whitman (Republican Primary) = .56

Fiorina (Republican Primary) = -.44

Visualizing Variable Association

The next several slides show various correlations.

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

2010 California Ballot Initiatives

Prop. 19 (marijuana) = .74

Prop. 21 (fees for state parks) = .84

Prop. 23 (suspend global warm) = -.81

Prop. 24 (elim. bus. tax breaks) = .70

Prop. 25 (majority budget) = .72

Prop. 26 (2/3rds vote for fees) = -.79

ECOLOGICAL FALLACY?

California Classics – Correlation of Education and the Vote

Kathleen Brown (1994) = .71

Jerry Brown (1974) = .09

Edmund G. Brown (1966) = .22

Proposition 13 (1978) = -.23

Proposition 14 (1964) = -.20

What do the results above tell us?

Pro-Democratic Trend in California

The correlation between the DIFFERENCE in the percentage of the countywide presidential vote for the Democratic presidential candidate in 2008 (Obama) and the Democratic presidential candidate in 1988 (Dukakis) and county education attainment is .63 and with median household income is .64. What does this mean for redistribution under the Democrats?

Weakness of Correlation

We do not know the magnitude of the relationship. Thus, if a person’s educational attainment is positively correlated with their income (e.g., .71), we still don’t know how much additional income each additional year of education produces. Typically, that’s what we want to know! That’s why we will later use regression.