Descriptive Statistics and Visualisation
Eight electorates were missing plebiscite results data. This is because they are new electorates created after the plebiscite. They were excluded from analysis.
There was one significant outlier for ‘swing’. The electorate of Whitlam had a 39% swing towards the ALP. This was significantly more than the other outliers for that variable, they were in the 11-12% range. Upon further investigation it was uncovered that in 2019 a Liberal candidate did not run, where as in 2016 there had been a Liberal candidate. Therefore the swing was an artificial value and was re-coded as NA.
While the election result data distinguished the coalition votes among the Liberal and National Parties (and the Liberal National Party in QLD where they are officially amalgamated), for the purpose of this analysis we were only interested in the breakdown between ALP and the Coalition, as they are the two entities competing to gain government. Therefore, a new variable was created to reflect this, ‘tpp’ (two party preferred).
The Coalition won 81 seat, the ALP 70 in the election, but removing the new seats without plebiscite data, it was 79 for the coalition, 64 for the ALP. This is reflected in the barplot below. As these n values are larger than 30, we can confidently conduct a T test without the data being normalised.
tpp1 <- read_csv("HouseTppByDivisionDownload-24310.csv", skip=1)
marriage1 <- read_excel("australian_marriage_law_postal_survey_2017_-_response_final.xls", sheet=3, skip= 5)
marriage2 <- rename(marriage1, electorate =...1, yes_votes = Yes, yes_percentage=...3, no_votes= No, no_percentage = ...5, total_votes = Total...6, total_percentage = ...7)
tpp2 <- rename(tpp1,electorate=DivisionNm)
marriage3 <- marriage2 %>% select(electorate,yes_votes,yes_percentage,no_votes,no_percentage,total_votes)
voting1 <- tpp2 %>% left_join(marriage3)
voting1$StateAb <- voting1$StateAb%>% as.factor()
voting1$PartyAb <- voting1$PartyAb %>% as.factor()
voting1$yes_votes <- voting1$yes_votes %>% as.double()
voting1$yes_percentage <- voting1$yes_percentage %>% as.double()
voting1$no_votes <- voting1$no_votes %>% as.double()
voting1$no_percentage <- voting1$no_percentage %>% as.double()
voting1$total_votes <- voting1$total_votes %>% as.double()
voting1$Swing[148] <- NA
voting1$yes_percentage[25] <- 74.1
voting1$no_percentage [25] <- 25.9
voting1$yes_percentage[50] <- 74
voting1$no_percentage[50] <- 26
voting1$yes_percentage[92] <- 54.5
voting1$no_percentage[92] <- 45.5
voting1 <- voting1[-c(8,31,33,58,98,117,111,137), ]
voting2 <- mutate(voting1, difference = yes_percentage - no_percentage)
voting2$tpp <- voting2$PartyAb %>% fct_recode( "Coalition" = "LNP", "Coalition" = "LP", "Coalition" = "NP", "ALP" = "ALP")
seat_perc <- voting2$tpp %>% table() %>% prop.table()*100
seat_perc %>% barplot(main="Percentage of Seats Won", ylab = "Percent", ylim = c(0,60))
Decsriptive Statistics Cont.
- In the boxplot and table below we can see the statistics for the yes percentage variable grouped by ALP and Coalition electorates. The means are very close, while the ALP median is over 3% higher. ALP electorates had a much greater variance than coalition electorates, with a standard deviation of 12.61, compared to 7.76 for the Coalition. The minimum support from ALP electorates was 17.8 percentage points lower than the minimum for Coalition electorates.
voting2 %>% group_by(tpp) %>% summarise(Min = min(yes_percentage,na.rm = TRUE),
Q1 = quantile(yes_percentage,probs = .25,na.rm = TRUE),
Median = median(yes_percentage, na.rm = TRUE),
Q3 = quantile(yes_percentage,probs = .75,na.rm = TRUE),
Max = max(yes_percentage,na.rm = TRUE),
Mean = mean(yes_percentage, na.rm = TRUE),
SD = sd(yes_percentage, na.rm = TRUE),
n = n(),
Missing = sum(is.na(yes_percentage))) -> table1
knitr::kable(table1)
| ALP |
26.1 |
54.575 |
64.25 |
68.725 |
83.7 |
60.94844 |
12.613221 |
64 |
0 |
| Coalition |
43.9 |
55.150 |
61.10 |
64.700 |
80.8 |
60.90633 |
7.757632 |
79 |
0 |
voting2 %>% boxplot(yes_percentage ~ tpp, data = .,main= "Yes Support by Party Preference",ylab = "Yes Support (Percentage)", xlab = "Two Party Preferred")
Hypothesis Testing
Next we checked to see if there was a relationship between voting behaviour for either of the two political parties and voting behaviour on marriage equality, on an electorate level.
The null hypothesis was that there was not a statistically significant difference for marriage equality support between the two political party voting groups. \[H_0: \mu_1 = \mu_2 \] The alternate hypothesis was that there was a statistically significant difference. \[H_A: \mu_1 \ne \mu_2\]
As can be seen in the results below, with a P value of 0.98, the null hypothesis was failed to be rejected.
model1 <- lm(yes_percentage ~ tpp, data = voting2)
model1 %>% summary()
##
## Call:
## lm(formula = yes_percentage ~ tpp, data = voting2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -34.848 -5.856 0.794 6.752 22.752
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 60.94844 1.27706 47.726 <2e-16 ***
## tppCoalition -0.04211 1.71816 -0.025 0.98
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.22 on 141 degrees of freedom
## Multiple R-squared: 4.26e-06, Adjusted R-squared: -0.007088
## F-statistic: 0.0006006 on 1 and 141 DF, p-value: 0.9805
leveneTest(yes_percentage ~ tpp, data= voting2)
alp <-subset(voting2,tpp =="ALP")
Lib<-subset(voting2, tpp !="ALP")
yesp <-t.test(alp$yes_percentage,Lib$yes_percentage)
yesp
##
## Welch Two Sample t-test
##
## data: alp$yes_percentage and Lib$yes_percentage
## t = 0.023366, df = 99.948, p-value = 0.9814
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -3.533258 3.617475
## sample estimates:
## mean of x mean of y
## 60.94844 60.90633