Quantitative Research Methods – Introduction to Applied Statistics

Seventh meeting

• Bivariate analysis

• McCarthy, Poole & Rosenthal (2006): Polarized America: The Dance of Ideology and Unequal Riches. MIT Press
• Polarization of votes in the US congress

congress <- read.csv("congress.csv")
rep <- subset(congress, subset = (party == "Republican"))
dem <- congress[congress$party == "Democrat", ]
rep80 <- subset(rep, subset = (congress == 80))
dem80 <- subset(dem, subset = (congress == 80))
rep112 <- subset(rep, subset = (congress == 112))
dem112 <- subset(dem, subset = (congress == 112))

congress80112 <- subset(congress, subset = (congress == 80 | congress == 112))

ggplot(congress80112, aes(x=dwnom1, y=dwnom2))+
  geom_point(aes(color=party))+
  scale_color_manual(values=c("blue", "green", "red"))+
  facet_wrap(~congress)+
  labs(title="აშშ კონგრესის პოლარიზაცია",
       x="ეკონომიკური ლიბერალიზმი/კონსერვატიზმი",
       y="რასობრივი ლიბერალიზმი/კონსერვატიზმი")

dem.median <- tapply(dem$dwnom1, dem$congress, median)
rep.median <- tapply(rep$dwnom1, rep$congress, median)
median <- rbind(dem.median, rep.median)
## tapply() helps us to do calculations by group

• z-score
• \( z{x}_{i} = \frac{x_{i}-\bar{x}}{S_{x}} \), where \( \bar{x} \) stands for the mean of a districution, \( S_{x} \) - stands for the standard deviation

• Pearson's correlation:
• \( Corr(x,y) = \frac{1}{n}\Sigma\frac{x_{i}-\bar{x}}{S_{x}}*\frac{y_{i}-\bar{y}}{S_{y}} \)

gini <- read.csv("USGini.csv")

cor(gini$gini[seq(from = 2, to = nrow(gini), by = 2)],
rep.median - dem.median)