Historical background

US elections is an old story about Republican’s and Democrat’s ambitions, voters, taxes and budget deficit. For more see: https://en.wikipedia.org/wiki/United_States_elections,_2018

The problem

I found some interesting data about 2018 US Congress election: https://www.bbc.com/news/world-us-canada-46267519

Let’s explore the data.

uscongress<-read.csv(file = "uscongress.csv",header = T)
uscongress
##    Year  President Party House Senate
## 1  1958 Eisenhower   Rep   -48    -13
## 2  1962    Kennedy   Dem    -4      3
## 3  1966    Johnson   Dem   -47     -4
## 4  1970      Nixon   Rep   -12      2
## 5  1974       Ford   Rep   -48     -5
## 6  1978     Carter   Dem   -15     -3
## 7  1982     Reagan   Rep   -26      1
## 8  1986     Reagan   Rep    -5     -8
## 9  1990     HWBush   Rep    -8     -1
## 10 1994    Clinton   Dem   -52     -8
## 11 1998    Clinton   Dem     5      0
## 12 2002      WBush   Rep     8      2
## 13 2006      WBush   Rep   -30     -6
## 14 2010      Obama   Dem   -63     -6
## 15 2014      Obama   Dem   -13     -9
## 16 2018      Trump   Rep   -37      2
summary(uscongress)
##       Year           President Party       House            Senate       
##  Min.   :1958   Clinton   :2   Dem:7   Min.   :-63.00   Min.   :-13.000  
##  1st Qu.:1973   Obama     :2   Rep:9   1st Qu.:-47.25   1st Qu.: -6.500  
##  Median :1988   Reagan    :2           Median :-20.50   Median : -3.500  
##  Mean   :1988   WBush     :2           Mean   :-24.69   Mean   : -3.312  
##  3rd Qu.:2003   Carter    :1           3rd Qu.: -7.25   3rd Qu.:  1.250  
##  Max.   :2018   Eisenhower:1           Max.   :  8.00   Max.   :  3.000  
##                 (Other)   :6
boxplot(House~Party,col=c("blue","red"),data = uscongress,main="US House of representatives", ylab="Seats")

boxplot(Senate~Party,col=c("blue","red"),data = uscongress,main="US Senate", ylab="Seats")

cols <- c("blue", "red")[(uscongress$Party=="Rep")+1]  
barplot(uscongress$House,names.arg=uscongress$President,col=cols,main = "US House change by president",cex.names = 0.7,ylab = "Seats",legend.text = c("Democrat", "Republican"),las=2) 

barplot(uscongress$Senate,names.arg=uscongress$President,col=cols,main = "US Senate change by president",cex.names = 0.7,ylab = "Seats",legend.text = c("Democrat", "Republican"),las=2)

Research question

Our goal is to check out if there is any difference between Republican’s and Democrat’s presidents as far as changes in Congress are concerned during midterms. So we got null hypothesis H0 : there is no difference between Republicans and Democrats. The alternative hypothesis H1 : there is difference between Republicans and Democrats.

Normal distribution test

library(fitdistrplus)
## Loading required package: MASS
## Loading required package: survival
## Loading required package: npsurv
## Loading required package: lsei
library(nortest)
plotdist(uscongress$House, histo = TRUE, demp = TRUE, col="grey", pch=16)

shapiro.test(uscongress$House)
## 
##  Shapiro-Wilk normality test
## 
## data:  uscongress$House
## W = 0.9395, p-value = 0.343
ad.test(uscongress$House)
## 
##  Anderson-Darling normality test
## 
## data:  uscongress$House
## A = 0.41041, p-value = 0.3026
plotdist(uscongress$Senate, histo = TRUE, demp = TRUE, col="grey", pch=16)

shapiro.test(uscongress$Senate)
## 
##  Shapiro-Wilk normality test
## 
## data:  uscongress$Senate
## W = 0.93688, p-value = 0.3125
ad.test(uscongress$Senate)
## 
##  Anderson-Darling normality test
## 
## data:  uscongress$Senate
## A = 0.38167, p-value = 0.3569

According to the obtained results distribution passed the test for normality. So we can apply classical Student test.

Student test

we have two independent samples (D, P) for the changes in House and Senate seats. In fact we don’t know the future that is why our data is a sample not a population.

t.test(House~Party,data = uscongress,exact=F)
## 
##  Welch Two Sample t-test
## 
## data:  House by Party
## t = -0.34274, df = 10.811, p-value = 0.7384
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -30.56789  22.34567
## sample estimates:
## mean in group Dem mean in group Rep 
##         -27.00000         -22.88889
t.test(Senate~Party,data = uscongress,exact=F)
## 
##  Welch Two Sample t-test
## 
## data:  Senate by Party
## t = -0.3995, df = 13.975, p-value = 0.6956
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -6.167301  4.230793
## sample estimates:
## mean in group Dem mean in group Rep 
##         -3.857143         -2.888889

So we can’t reject null hypothesis.

Conclusion

  1. There is no difference between Republicans and Democrats in changes of seats in Congress through out modern time history.
  2. The mean loss of seats in House of representatives for Democrats is less than for Republicans.
  3. On the contrary the mean loss of seats in Senate for Republicans is less than for Democrats.
  4. The results above prove balance of power for both parties in Congress through out modern time history of the USA.