Transcript All Along the Watchtower: Race, Morality, Security, and

Illustrations using R
B. Jones
Dept. of Political Science
UC-Davis
Data: Evaluations of AfricanAmerican House Members




Dep. Variable: Feeling thermometer
Independent Variables: Race/Ethnicity
Theory: Descriptive Representation
Some Basic Statistics
Box Plots
60
40
20
0
Feeling Thermometer
80
100
Ratings of Af.-Am. Dem. Incumbents by Race
Black
Hispanic
White
Some Statistics
> mean(imputed_if[race_respondent==1], na="TRUE")
[1] 53.64732 (White)
> mean(imputed_if[race_respondent==2], na="TRUE")
[1] 69.92394 (Af. Am.)
> mean(imputed_if[race_respondent==3], na="TRUE")
[1] 61.45159 (Latino)
Simple t-tests: mu=50
> t.test(imputed_if, mu=50, alt="greater")
One Sample t-test
data: imputed_if
t = 19.0677, df = 1080, p-value < 2.2e-16
alternative hypothesis: true mean is greater than 50
95 percent confidence interval:
61.69999 Inf
sample estimates:
mean of x
62.8056
>
t.test(imputed_if, mu=50, alt="less")
One Sample t-test
data: imputed_if
t = 19.0677, df = 1080, p-value = 1
alternative hypothesis: true mean is less than 50
95 percent confidence interval:
-Inf 63.9112
sample estimates:
mean of x
62.8056
>
t.test(imputed_if, mu=50, alt="two.sided")
One Sample t-test
data: imputed_if
t = 19.0677, df = 1080, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 50
95 percent confidence interval:
61.48784 64.12335
sample estimates:
mean of x
62.8056
Difference-in-Means Tests


Test 1: Af.-American survey respondents
compared to Latino respondents.
Hypothesis?



1-tail
2-tail
Theory suggests 1-tail


Null: mean ratings for the two groups are the same.
1-sided alternative: Af.-Am. respondents will have
higher ratings than Latino.
Difference-in-Means
> t.test(imputed_if[race_respondent==2],
imputed_if[race_respondent==3],
alt="greater")
Welch Two Sample t-test
data: imputed_if[race_respondent == 2] and
imputed_if[race_respondent == 3]
t = 4.0562, df = 143.645, p-value = 4.075e-05
alternative hypothesis: true difference in means is
greater than 0
95 percent confidence interval:
5.014392 Inf
sample estimates:
mean of x mean of y
69.92394 61.45159
Interpretation



There is a significant difference between
the two groups.
The probability of a t-score of 4.05 or
greater is nearly 0.
Suggests the difference-in-means is
probably not due to random chance
alone.
Other Contrasts

African-American vs. White


1-tail test?
Whites vs. Latinos


What is the alternative here?
What is your theory underlying this
hypothesis?
Difference-in-Means: Af.-Am. vs.
White Respondents
> t.test(imputed_if[race_respondent==2],
imputed_if[race_respondent==1],
alt="greater")
Welch Two Sample t-test
data: imputed_if[race_respondent == 2] and
imputed_if[race_respondent == 1]
t = 10.2222, df = 670.663, p-value < 2.2e-16
alternative hypothesis: true difference in means is
greater than 0
95 percent confidence interval:
13.65391 Inf
sample estimates:
mean of x mean of y
69.92394 53.64732
Difference-in-Means: White vs.
Latino
> t.test(imputed_if[race_respondent==1],
imputed_if[race_respondent==3],
alt="two.sided")
Welch Two Sample t-test
> t.test(imputed_if[race_respondent==1],
imputed_if[race_respondent==3],
alt="less")
Welch Two Sample t-test
data: imputed_if[race_respondent == 1]
and imputed_if[race_respondent ==
3]
data: imputed_if[race_respondent == 1] and
imputed_if[race_respondent == 3]
t = -3.4508, df = 188.205, p-value = 0.00069
t = -3.4508, df = 188.205, p-value = 0.000345
alternative hypothesis: true difference in
means is not equal to 0
alternative hypothesis: true difference in
means is less than 0
95 percent confidence interval:
-12.265597 -3.342931
sample estimates:
mean of x mean of y
53.64732 61.45159
95 percent confidence interval:
-Inf -4.06587
sample estimates:
mean of x mean of y
53.64732 61.45159