695 lines
34 KiB
Markdown
695 lines
34 KiB
Markdown
# Analysis of Income, Geographical Location, and Voting Behaviour in Finland
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## Introduction
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### The research question
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This report investigates how citizens' voting behaviour is potentially influenced by their income and geographical location in Finland.
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### The materials used
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Two datasets are used in this investigation:
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\+ `tulot2017.csv`: This dataset contains information about how much people earn from wages and investments, how much those earnings are subject to taxation, how much taxes are paid, and how much people get to keep after taxation. This information is recorded on a per municipality basis, based on data collected in 2017 by Statistics Finland.
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\+ `ek2023.csv`: This dataset contains information about how much support each political party receives in each municipality, in terms of percentages of total votes in the corresponding municipality. This data is collected in 2019 by Statistics Finland.
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### How the research is carried out
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\- First, we explore the datasets to get a preliminary understanding of what they contain.
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\- Second, we perform some visualisations to identify potential trends and correlations.
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\- Third, based on the trends identified in the previous step, we formulate hypotheses and perform relevant tests and/or analyses for these hypotheses. To avoid p-hacking, we pre-establish that our significance level for any statistical test is 0.01.
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\- Finally, we report and summarise our findings.
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## Data Exploration and Environment Setup
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Let us first have a look at our datasets in order to understand them.
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The first dataset, `tulot2017.csv`, has the following structure:
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```R
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> income <- read.csv("tulot2017.csv", encoding = "latin1")
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> str(income)
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'data.frame': 312 obs. of 10 variables:
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$ Alue : chr "KOKO MAA" "Akaa" "Alajärvi" "Alavieska" ...
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$ Tulonsaajia : int 4634226 13751 8156 2140 9908 7147 3945 3183 450 879 ...
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$ Tulot : int 29962 27702 23775 24389 23917 27254 33659 28693 31794 28671 ...
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$ Mediaanitulot : int 24433 23848 19594 20505 20125 22062 26476 26134 25075 26057 ...
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$ Ansiotulot : int 27801 26421 21962 22459 21981 24447 29008 27235 27725 25954 ...
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$ Pääomatulot : int 2161 1281 1813 1930 1937 2807 4652 1458 4068 2717 ...
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$ Verot : int 6453 5657 4463 4605 4436 5561 7461 5889 5949 4997 ...
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$ Valtionvero : int 1796 1131 913 966 953 1487 2533 1135 2285 1452 ...
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$ Kunnallisvero : int 3997 3867 2985 3038 2911 3454 4183 4073 3054 2985 ...
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$ Tulot_miinus_verot: int 23509 22045 19312 19784 19482 21693 26198 22804 25844 23674 ...
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```
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The meanings of the fields are as follows:
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\- **Alue**: Consists of the different municipalities of Finland.
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\- **Tulonsaajia**: Number of taxable income recipients. Essentially, this field records how many people are earning money and are subject to taxation in each of the above municipalities.
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\- **Tulot**: Average taxable income, in euros. This field records the average per capita income of people in each municipality, prior to taxation.
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\- **Mediaanitulot**: Median taxable income, in euros. This fields records the median income of people in each municipality, prior to taxation.
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\- **Ansiotulot**: Average earned income, in euros. This field records the average per capita income from work, i.e. wage labour, of people in each municipality, prior to taxation. In other words, this is the average amount of money people are paid by working as an employee for an employer.
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\- **Pääomatulot**: Average investment income, in euros. This field records the average per capita income from capital investments in each municipality, prior to taxation. Investment income is income not earned by working, i.e. performing wage labour, but by investing money/capital in stocks, bonds, index funds, real estates, and so on.
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\- **Verot**: Average total of all taxes, in euros. This field records the total amount of taxes people pay on average in each of the municipality.
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\- **Valtionvero**: Average state tax, in euros. This field records the amount of state tax people pay on average in each of the municipalities. State tax contributes to the total amount of taxes above.
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\- **Kunnallisvero**: Average municipal tax, in euros. This field records the amount of municipal tax people pay on average in each of the municipalities. Municipal tax contributes to the total amount of taxes above.
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\- **Tulot_miinus_verot**: Average income after tax, in euros. This field records how much money people actually get to keep on average in each of the municipalities after all the different types of taxes.
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The second dataset, `ek2023.csv`, has the following structure:
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```R
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> finland <- read.csv("ek2023.csv", encoding = "latin1")
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> str(finland)
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'data.frame': 293 obs. of 25 variables:
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$ Alue : chr "Helsinki" "Askola" "Espoo" "Hanko" ...
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$ SDP : num 20.9 16.4 16.9 28.5 23.7 25.2 11 24.7 17.6 8.1 ...
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$ PS : num 11.3 30.8 12.5 16.6 20 24.9 10.7 21.4 25.7 7.9 ...
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$ KOK : num 26.4 18.8 36.8 10.8 24.5 21.2 11 23.3 15.6 39.3 ...
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$ KESK : num 1.6 15.1 2.7 1.5 3.7 5.8 0.9 6 7.9 1.7 ...
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$ VIHR : num 15.3 2.7 10.8 3.4 8.1 5.6 3.3 7.3 3.5 5.7 ...
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$ VAS : num 11.8 3.2 3.6 4.1 6 5.1 1.9 5.2 19.2 1.7 ...
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$ RKP : num 5.1 2.9 7.5 27.6 2.6 1 56 1.2 1 29.8 ...
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$ KD : num 1.9 2.5 3.1 2.8 3.8 3.8 1.9 4.2 3 2.5 ...
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$ PIR : num 0.3 0.1 0.1 0.1 0.2 0.1 0 0.1 0 0.1 ...
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$ FP : num 0.1 0.1 0.1 0 0.1 0.1 0.1 0.1 0 0 ...
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$ LIBE : num 0.9 0.2 1.3 0.3 0.8 0.5 0.3 0.7 0.3 0.6 ...
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$ SKP : num 0.2 0 0.1 0.1 0.1 0.1 0 0.1 0.1 0 ...
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$ EOP : num 0.2 0.2 0.1 0.2 0.1 0.1 0.3 0.1 0.1 0 ...
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$ SKE : num 0.1 0 0 0 0 0 0.1 0 0 0 ...
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$ AP : num 0.2 0 0 0 0 0 0 0 0 0 ...
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$ KaL : num 0 0.1 0 0 0 0 0 0 0 0 ...
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$ KL : num 0.2 0 0 0 0 0 0.1 0.1 0 0 ...
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$ KRIP : num 0.2 0.2 0.1 0.2 0.2 0.2 0.1 0.2 0.2 0.1 ...
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$ LIIKE : num 2.3 4.6 2.9 2.8 4.3 4.4 1.3 4 3.8 1.8 ...
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$ SML : num 0 0.4 0.2 0.2 0.3 0.4 0.1 0.3 0.3 0.2 ...
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$ VKK : num 0.3 0.4 0.3 0.3 0.4 0.4 0.1 0.3 0.3 0.1 ...
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$ VL : num 0.8 1.3 0.6 0.4 0.9 1.1 0.7 0.8 1.3 0.4 ...
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$ Muut : num 0 0 0 0.1 0.1 0.1 0.1 0.1 0.1 0 ...
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$ Vaalipiiri: chr "Helsinki" "Uusimaa" "Uusimaa" "Uusimaa" ...
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```
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Again, the meanings of the fields are as follows:
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\- **Alue**: Consists of the different [**municipalities**](https://en.wikipedia.org/wiki/List_of_municipalities_of_Finland) of Finland.
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\- **SDP, PS, KOK, ..., Muut**: All these fields record how much support each party receives, as measured in percent of votes in each municipality.
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\- **Vaalipiiri**: Consists of the [**electoral districts**](https://en.wikipedia.org/wiki/Electoral_districts_of_Finland) of Finland. One electoral district may comprise multiple municipalities.
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To make it easier to deal with these two datasets, we are going to merge them into one data frame called `df`. This is done by connecting the two data sets via the `Alue` field:
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```R
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> df <- merge(finland, income, by = "Alue")
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> colnames(df)
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[1] "Alue" "SDP" "PS"
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[4] "KOK" "KESK" "VIHR"
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[7] "VAS" "RKP" "KD"
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[10] "PIR" "FP" "LIBE"
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[13] "SKP" "EOP" "SKE"
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[16] "AP" "KaL" "KL"
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[19] "KRIP" "LIIKE" "SML"
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[22] "VKK" "VL" "Muut"
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[25] "Vaalipiiri" "Tulonsaajia" "Tulot"
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[28] "Mediaanitulot" "Ansiotulot" "Pääomatulot"
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[31] "Verot" "Valtionvero" "Kunnallisvero"
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[34] "Tulot_miinus_verot"
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```
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The `df` data frame will now contain all the fields from the two data sets, which is more convenient for us.
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We're also going to be using the `tidyverse` and `ggplot2` libraries:
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```R
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library(tidyverse)
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library(ggplot2)
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```
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## Trend Identification
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First, let us see if there is any correlation between income and support for a certain party. For instance, we can plot average taxable income against support for the Social Democratic Party as follows:
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```R
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ggplot(data = df, mapping = aes(x = Tulot, y = SDP)) +
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geom_point() +
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labs(
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title = "Support for the SDP against Average Taxable Income",
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x = "Average Taxable Income (euros)",
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y = "Support for the SDP (%)"
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)
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```
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Running the above code generates the below scatterplot, in which each point represents a municipality:
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<div style="display: flex; justify-content:center">
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<img src="./plots/1.png"/>
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</div>
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<br />
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As we can see, the percentages of support for the Social Democratic Party mostly fall in the 0-30% range. There seems to be a very slight positive correlation.
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We can generalise the above code into the following function:
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```R
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plot_income_against_support <- function(income_type, party) {
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income_type_english <- ""
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if (income_type == "Tulot") {
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income_type_english <- "Average Taxable Income"
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}
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else if (income_type == "Mediaanitulot") {
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income_type_english <- "Median Taxable Income"
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}
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else if (income_type == "Ansiotulot") {
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income_type_english <- "Average Earned Income"
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}
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else if (income_type == "Pääomatulot") {
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income_type_english <- "Average Investment Income"
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}
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else if (income_type == "Tulot_miinus_verot") {
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income_type_english <- "Average Income after Tax"
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}
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ggplot(data = df, mapping = aes(x = .data[[income_type]], y = .data[[party]])) +
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geom_point() +
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geom_smooth(method = "lm") +
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labs(
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title = paste("Support for", party, "against", income_type_english),
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x = paste(income_type_english, "(euros)"),
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y = paste("Support for", party, "(%)"),
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) +
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theme_minimal()
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}
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```
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Note that we have multiple different income metrics, and plotting all of them would be excessive. We can make a reasonable assumption that the average income after tax, i.e. the amount of money people actually get to keep, is the most important income measurement, so we will focus on this type of income for now. From this point onwards, any mention of "income" without specifying the type will, by default, refer to average income after tax. Let us plot income against support for the major parties:
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```R
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> plot_income_against_support("Tulot_miinus_verot", "SDP")
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> plot_income_against_support("Tulot_miinus_verot", "PS")
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> plot_income_against_support("Tulot_miinus_verot", "KOK")
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> plot_income_against_support("Tulot_miinus_verot", "KESK")
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> plot_income_against_support("Tulot_miinus_verot", "VIHR")
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> plot_income_against_support("Tulot_miinus_verot", "VAS")
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> plot_income_against_support("Tulot_miinus_verot", "RKP")
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> plot_income_against_support("Tulot_miinus_verot", "KD")
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> plot_income_against_support("Tulot_miinus_verot", "LIIKE")
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```
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The above code generates the following nine scatterplots:
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<p align="center">
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<img src="./plots/2.png" width="30%" />
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<img src="./plots/3.png" width="30%" />
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<img src="./plots/4.png" width="30%" />
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</p>
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<p align="center">
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<img src="./plots/5.png" width="30%" />
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<img src="./plots/6.png" width="30%" />
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<img src="./plots/7.png" width="30%" />
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</p>
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<p align="center">
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<img src="./plots/8.png" width="30%" />
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<img src="./plots/9.png" width="30%" />
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<img src="./plots/10.png" width="30%" />
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</p>
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Note that we excluded the other parties because in most municipalities, their support amounts to not even 1% and thus it is difficult to notice any trend using such data.
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In the above scatterplots, we noticed the following:
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\- Support for the Finns Party mostly falls into the `0-40%` range and has a **slight negative correlation** with income.
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\- Support for the National Coalition Party mostly concentrates in the `0-30%` range and has a **quite strong positive correlation** with income.
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\- Support for the Centre Party vary vastly `from 0% to nearly 60%` and has a **quite strong negative correlation** with income.
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\- Support for the Green League mostly ranges `from 0% to 10%` and seems to **correlate positively** with income.
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\- Support for the Left Alliance mostly ranges `from 0% to 20%`, and there seems to be **no correlation** with income.
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\- Support for the Swedish People's Party is `near 0% in most municiplaities`. In the remaining few municipalties, however, their support can range from `a few percentage points` to `over 75%`. There also seems to be **no correlation** with income.
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\- Support for the Christian Democrats mostly ranges `from 0% to 10%` and **does not seem to correlate** with income.
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\- Support for Movement Now mostly ranges `from 0% to 5%` and seems to **correlate positively** with income.
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Let us now look at the correlation between different income types and support for the above parties using a `heatmap`. We can draw the heatmap using the following code:
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```R
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income_and_voting_columns <- c("Tulot", "Mediaanitulot", "Ansiotulot", "Pääomatulot", "Tulot_miinus_verot", "SDP", "PS", "KOK", "KESK", "VIHR", "VAS", "RKP", "KD", "LIIKE")
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english_names <- c("Average Taxable Income", "Median Taxable Income", "Average Earned Income", "Average Investment Income", "Average Income after Tax", "SDP", "PS", "KOK", "KESK", "VIHR", "VAS", "RKP", "KD", "LIIKE")
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cor_matrix <- cor(df[income_and_voting_columns])
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cor_data <- as.data.frame(as.table(cor_matrix))
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cor_data$Var1 <- factor(cor_data$Var1, levels = income_and_voting_columns, labels = english_names)
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cor_data$Var2 <- factor(cor_data$Var2, levels = income_and_voting_columns, labels = english_names)
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ggplot(cor_data, aes(Var1, Var2, fill = Freq)) +
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geom_tile(color = "white") +
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geom_text(aes(label = round(Freq, 2)), color = "black", size = 4) +
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scale_fill_gradient2(
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low = "blue",
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high = "red",
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mid = "white",
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midpoint = 0,
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limit = c(-1, 1),
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name = "Correlation"
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) +
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theme_minimal() +
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labs(title = "Correlation Heatmap: Income Variables vs Party Support") +
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theme(
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axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1),
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axis.title.x = element_blank(),
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axis.title.y = element_blank()
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)
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```
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This is the resulting correlation heatmap:
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<div style="display: flex; justify-content:center">
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<img src="./plots/heatmap.png"/>
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</div>
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<br />
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In the heatmap, we notice some of the previous correlations:
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\- Municipalities with `higher incomes` appear to be more likely to support the National Coalition Party or the Green League. With the exception of average investment income, the `Pearson correlation coefficient` between the support for either party and any income metric is `greater than 0.5`.
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\- Municipalities with `lower incomes` tend to support the Centre Party. With the exception of average investment income, the correlation coeffiecient between support for the party and income of any metric is `lower than -0.6`.
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Let us now look at party support by electoral district by creating a stacked bar chart to show the composition of votes in different electoral districts. Notice that we do not have the population for each municipality, so calculating the support for a certain party in each electoral district can be tricky. However, a reasonable assumption we can make is that the voting population in each municipality is roughly the same as the number of people who are working and paying tax in that municipality. Thus, we can calculate the average support for a certain party in a certain electoral district by weighing the district's constituent muncipalities by their number of taxable income recipients. We do this using the following code:
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```R
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parties <- c("SDP", "PS", "KOK", "KESK", "VIHR", "VAS", "RKP", "KD", "LIIKE")
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weighted_districts <- df %>%
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group_by(Vaalipiiri) %>%
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summarize(across(all_of(parties), ~ weighted.mean(., Tulonsaajia)))
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weighted_districts_long <- weighted_districts %>%
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pivot_longer(cols = all_of(parties), names_to = "Party", values_to = "Support")
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ggplot(weighted_districts_long, aes(x = Vaalipiiri, y = Support, fill = Party)) +
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geom_bar(stat = "identity") +
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labs(
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title = "Population-Weighted Average Voting Support by Electoral District",
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x = "Electoral District",
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y = "Weighted Average Support (%)",
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fill = "Party"
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) +
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theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
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theme_minimal()
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```
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This is the resulting stacked bar chart:
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<div style="display: flex; justify-content:center">
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<img src="./plots/stacked_bar_chart.png"/>
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</div>
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<br />
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We notice that:
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\- Support for the National Coalition Party is strongest in the electoral districts of Helsinki and Uusimaa, which are both located in Uusimaa, Finland's wealthiest and most urban region [1].
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\- Support for the Centre Party is strongest in Lapland and Oulu, the two northernmost electoral districts of Finland. Most areas in these two districts are classified as rural by the Finnish Environment Institute [2]. Interestingly, support for the Finns Party also appears to be strongest in these two districts, and both party have roughly the same level of support in both districts.
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\- The Social Democratic Party appears to have around a fifth of the votes in most electoral districts.
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\- Support for the Swedish People's Party is insubstantial in most electoral districts. However, in Vaasa, their support amounts to around 20%.
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\- No single party has a simple majority (50%) in any district. The most support a party has in one district is around 25%.
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## Formulating Hypotheses and Conducting Tests
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Based on the above observations, we want to test if there is statistical evidence for the following hypotheses:
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\- Municipalities with `higher incomes` are more likely to support the National Coalition Party or the Green League.
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\- Municipalities with `lower incomes` are more likely to support the Finns party or the Centre Party.
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\- The National Coalition Party receives stronger support in `urban areas`, while the Centre Party and Finns party receive stronger support in `rural areas`.
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\- Support for `SDP` appears to be around `20%` in most electoral districts.
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\- Municipalities in Vaasa have substantially higher support for the Swedish People's Party than municipalities in other electoral districts.
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Let us formulate each hypothesis more explicitly.
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### 1. Municipalities with higher incomes are more likely to support the National Coalition Party.
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For this hypothesis, we can perform **linear regression analysis**. Assuming that there is a linear relationship between income and support for the National Coalition Party, then:
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$Y = \beta_0 + \beta_1X$, where:
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$Y$: Support for the National Coalition Party
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$X$: Income
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$H_0$: There is no relationship between income and support for the National Coalition Party, i.e., $\beta_1 = 0$.
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$H_A$: There is a positive relationship between income and support for the National Coalition Party, i.e., $\beta_1 >0$.
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We can create the linear regression model as follows:
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```R
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model <- lm(KOK ~ Tulot_miinus_verot, data = df)
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summary(model)
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```
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The above code outputs:
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```
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Call:
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lm(formula = KOK ~ Tulot_miinus_verot, data = df)
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Residuals:
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Min 1Q Median 3Q Max
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-14.7911 -4.1130 -0.3091 3.5252 24.9767
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Coefficients:
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Estimate Std. Error t value Pr(>|t|)
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(Intercept) -2.206e+01 2.993e+00 -7.371 1.77e-12 ***
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Tulot_miinus_verot 1.721e-03 1.393e-04 12.358 < 2e-16 ***
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---
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
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Residual standard error: 6.211 on 291 degrees of freedom
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Multiple R-squared: 0.3442, Adjusted R-squared: 0.3419
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F-statistic: 152.7 on 1 and 291 DF, p-value: < 2.2e-16
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```
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The calculated slope is `1.721e-03`, which is indeed positive. The coefficient of determination is `0.3442`, meaning `34.42%` of the variability in support for the National Coalition Party can be explained by income. We can fit the linear regression line:
|
||
|
||
```R
|
||
ggplot(data = df, mapping = aes(x = Tulot_miinus_verot, y = KOK)) +
|
||
geom_point() +
|
||
geom_smooth(method = "lm") +
|
||
labs(
|
||
title = paste("Support for KOK against Average Income after Tax"),
|
||
x = paste("Average Income after Tax (euros)"),
|
||
y = paste("Support for KOK (%)"),
|
||
) +
|
||
theme_minimal()
|
||
```
|
||
|
||
<div style="display: flex; justify-content:center">
|
||
<img src="./plots/11.png"/>
|
||
</div>
|
||
<br />
|
||
|
||
Indeed, the line has a clear positive slope.
|
||
|
||
The `two-sided p-value` is less than `2e-16`, which is extremely small, so the `one-sided p-value` would also be lower than any commonly used threshold, and as such we reject $H_0$ and accept $H_A$. In other words, there is significant statistical evidence to suggest that municipalities with higher income are more likely to support the National Coalition Party.
|
||
|
||
### 2. Municipalities with higher incomes are more likely to support the Green League.
|
||
|
||
Again, we can perform **linear regression analysis**.
|
||
|
||
$H_0$: There is no relationship between income and support for the Green League, i.e., $\beta_1 = 0$.
|
||
$H_A$: There is a positive relationship between income and support for Green League, i.e., $\beta_1 >0$.
|
||
|
||
We create and summarise the linear regression model:
|
||
```R
|
||
model <- lm(VIHR ~ Tulot_miinus_verot, data = df)
|
||
summary(model)
|
||
```
|
||
|
||
The above code outputs:
|
||
```
|
||
Call:
|
||
lm(formula = VIHR ~ Tulot_miinus_verot, data = df)
|
||
|
||
Residuals:
|
||
Min 1Q Median 3Q Max
|
||
-8.2786 -1.0822 -0.3528 0.6284 9.2370
|
||
|
||
Coefficients:
|
||
Estimate Std. Error t value Pr(>|t|)
|
||
(Intercept) -7.186e+00 8.838e-01 -8.131 1.24e-14 ***
|
||
Tulot_miinus_verot 4.815e-04 4.112e-05 11.710 < 2e-16 ***
|
||
---
|
||
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
|
||
|
||
Residual standard error: 1.834 on 291 degrees of freedom
|
||
Multiple R-squared: 0.3203, Adjusted R-squared: 0.3179
|
||
F-statistic: 137.1 on 1 and 291 DF, p-value: < 2.2e-16
|
||
```
|
||
|
||
The calculated slope is `4.815e-04`, which is positive. The coefficient of determination is `0.3203`, meaning that roughly `32%` of the variability in support for the Green League can be explained by income. Again, we can fit the linear regression line:
|
||
<div style="display: flex; justify-content:center">
|
||
<img src="./plots/12.png"/>
|
||
</div>
|
||
<br />
|
||
|
||
Again, since the `two-sided p-value` is less than `2e-16`, which is extremely small, the `one-sided p-value` would also be lower than any commonly used threshold, so we reject $H_0$ and accept $H_A$. In other words, there is significant statistical evidence to suggest that there is a positive relationship between a municipality's average income after taxes and their support for the Green League.
|
||
|
||
### 3. Municipalities with lower incomes are more likely to support the Finns Party.
|
||
|
||
$H_0$: There is no relationship between income and support for the Finns Party, i.e., $\beta_1 = 0$.
|
||
$H_A$: There is a negative relationship between income and support for the Finns Party, i.e., $\beta_1 < 0$.
|
||
|
||
We again perform **linear regression analysis**:
|
||
```R
|
||
model <- lm(PS ~ Tulot_miinus_verot, data = df)
|
||
summary(model)
|
||
```
|
||
|
||
The above code outputs:
|
||
```
|
||
Call:
|
||
lm(formula = PS ~ Tulot_miinus_verot, data = df)
|
||
|
||
Residuals:
|
||
Min 1Q Median 3Q Max
|
||
-23.5736 -3.1454 0.0858 3.6998 27.6090
|
||
|
||
Coefficients:
|
||
Estimate Std. Error t value Pr(>|t|)
|
||
(Intercept) 39.4438263 3.2467606 12.149 < 2e-16 ***
|
||
Tulot_miinus_verot -0.0006924 0.0001511 -4.583 6.8e-06 ***
|
||
---
|
||
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
|
||
|
||
Residual standard error: 6.737 on 291 degrees of freedom
|
||
Multiple R-squared: 0.06732, Adjusted R-squared: 0.06412
|
||
F-statistic: 21.01 on 1 and 291 DF, p-value: 6.804e-06
|
||
```
|
||
|
||
The calculated slope is `-0.0006924`, which is indeed negative. The coefficient of determination is `0.06732`, indicating that `6.7%` of of the variability in support for the Finns Party can be explained by income. Since the `two-sided p-value`, `6.8e-06`, is incredibly small, we reject the null nypothesis and conclude that there is a negative relationship between income and support for the Finns Party. However, since both the slope of the linear regression line and the coeffiecient of determination are small, this negative relationship is not a strong one. In other words, the effect of income on the support for the Finns Party is negative but limited.
|
||
|
||
### 4. Municipalities with lower incomes are more likely to support the Centre Party.
|
||
|
||
$H_0$: There is no relationship between income and support for the Centre Party, i.e., $\beta_1 = 0$.
|
||
$H_A$: There is a negative relationship between income and support for the Centre Party, i.e., $\beta_1 < 0$.
|
||
|
||
We perform linear regression analysis:
|
||
```R
|
||
model <- lm(KESK ~ Tulot_miinus_verot, data = df)
|
||
summary(model)
|
||
```
|
||
|
||
The above code outputs:
|
||
```
|
||
Call:
|
||
lm(formula = KESK ~ Tulot_miinus_verot, data = df)
|
||
|
||
Residuals:
|
||
Min 1Q Median 3Q Max
|
||
-25.681 -6.390 -0.056 6.163 50.077
|
||
|
||
Coefficients:
|
||
Estimate Std. Error t value Pr(>|t|)
|
||
(Intercept) 89.5518042 4.9520159 18.08 <2e-16 ***
|
||
Tulot_miinus_verot -0.0031380 0.0002304 -13.62 <2e-16 ***
|
||
---
|
||
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
|
||
|
||
Residual standard error: 10.28 on 291 degrees of freedom
|
||
Multiple R-squared: 0.3893, Adjusted R-squared: 0.3872
|
||
F-statistic: 185.5 on 1 and 291 DF, p-value: < 2.2e-16
|
||
```
|
||
|
||
The coefficient of determination is `0.3893`, indicating that `38.93%` of the variability in support for the Centre Party can be explained by income after taxes. The two-sided p-value is extremely small (less than < 2e-16), so the one-sded p-value is even smaller, and we again reject the null hypothesis. Indeed, plotting the linear regression line shows a clear downwards trend:
|
||
|
||
<div style="display: flex; justify-content:center">
|
||
<img src="./plots/13.png"/>
|
||
</div>
|
||
<br />
|
||
|
||
### 5. The National Coalition Party receives stronger support from urban areas.
|
||
|
||
Before we can start testing this hypothesis, we need to classify municipalities as either urban or rural. We shall use the list at https://en.wikipedia.org/wiki/List_of_urban_areas_in_Finland_by_population as reference; any municipality included in this list will be considered urban and every other municipality will be considered rural.
|
||
|
||
```R
|
||
urban_areas <- c(
|
||
"Helsinki", "Tampere", "Turku", "Oulu", "Jyväskylä", "Lahti", "Kuopio", "Pori",
|
||
"Joensuu", "Vaasa", "Lappeenranta", "Rovaniemi", "Seinäjoki", "Hämeenlinna",
|
||
"Porvoo", "Kotka", "Kouvola", "Hyvinkää", "Mikkeli", "Kokkola", "Rauma", "Lohja",
|
||
"Kajaani", "Salo", "Riihimäki", "Imatra", "Kemi", "Forssa", "Jakobstad",
|
||
"Savonlinna", "Kirkkonummi", "Raahe", "Varkaus", "Valkeakoski", "Tornio",
|
||
"Hamina", "Iisalmi", "Mariehamn", "Nummela", "Heinola", "Ilmajoki", "Kurikka",
|
||
"Pieksämäki", "Ylivieska", "Jämsä", "Nastola", "Mäntsälä", "Siilinjärvi", "Lapua",
|
||
"Uusikaupunki", "Vammala", "Söderkulla", "Pargas", "Orimattila", "Loimaa", "Ekenäs",
|
||
"Kauhajoki", "Äänekoski", "Paimio", "Toijala", "Kuusamo", "Laukaa", "Karis",
|
||
"Kankaanpää", "Nurmijärvi", "Turenki", "Mänttä", "Karkkila", "Hanko",
|
||
"Rajamäki", "Muurame", "Muhos", "Loviisa", "Lieksa", "Joutseno", "Kyröskoski",
|
||
"Parola", "Lauttakylä", "Laihia", "Kalajoki", "Iin Hamina", "Jokela", "Eura",
|
||
"Orivesi", "Veikkola", "Kyläsaari", "Pihlava", "Vuokatti", "Keuruu", "Valkeala",
|
||
"Myllykoski", "Kiiminki", "Laitila", "Toivala", "Vuorela", "Kauhava", "Vuores",
|
||
"Nivala", "Oulainen", "Kuhmo", "Liminka", "Viiala", "Suonenjoki"
|
||
)
|
||
|
||
df$Type <- ifelse(df$Alue %in% urban_areas, "urban", "rural")
|
||
```
|
||
|
||
Let us denote $\mu_{urban}$ as the mean level of support (for the National Coalition Party, in this case) across all urban municipalities and $\mu_{rural}$ as the mean level of support for the party across all rural municipalities.
|
||
|
||
$H_0$: There is no difference in support for the National Coalition Party between urban and rural municipalities, i.e. $\mu_{urban} = \mu_{rural}$.
|
||
$H_A$: Support for the National Coalition Party is greater in urban municipalities, i.e., $\mu_{urban} > \mu_{rural}$.
|
||
|
||
We can use a **2-sample t-test** in this case:
|
||
|
||
```R
|
||
urban_support <- df$KOK[df$Type == "urban"]
|
||
rural_support <- df$KOK[df$Type == "rural"]
|
||
|
||
result <- t.test(urban_support, rural_support, alternative = "greater", conf.level = 0.99)
|
||
|
||
print(result)
|
||
```
|
||
The test code outputs:
|
||
```
|
||
Welch Two Sample t-test
|
||
|
||
data: urban_support and rural_support
|
||
t = 3.9402, df = 168.36, p-value = 5.954e-05
|
||
alternative hypothesis: true difference in means is greater than 0
|
||
99 percent confidence interval:
|
||
1.384947 Inf
|
||
sample estimates:
|
||
mean of x mean of y
|
||
17.22877 13.80000
|
||
```
|
||
|
||
The p-value, 5.954e-05, is much smaller than any common significance value. The calculated average support for the National Coalition Party across urban municipalities, 17.23%, is also reasonably higher than the average support for the party across rural municipalities, 13.8%. The 99% confidence interval does not contain zero either. Thus, we reject the null hypothesis.
|
||
|
||
### 6. The Centre Party receives stronger support from rural areas.
|
||
|
||
$H_0$: There is no difference in support for the Centre Party between urban and rural municipalities, i.e. $\mu_{urban} = \mu_{rural}$.j
|
||
$H_A$: Support for the Centre Party is greater in rural municipalities, i.e., $\mu_{urban} < \mu_{rural}$.
|
||
|
||
Again, let us use a **2-sample t-test**.
|
||
|
||
```R
|
||
urban_support <- df$KESK[df$Type == "urban"]
|
||
rural_support <- df$KESK[df$Type == "rural"]
|
||
|
||
result <- t.test(urban_support, rural_support, alternative = "less", conf.level = 0.99)
|
||
|
||
print(result)
|
||
```
|
||
|
||
The test code outputs:
|
||
```
|
||
Welch Two Sample t-test
|
||
|
||
data: urban_support and rural_support
|
||
t = -4.824, df = 147.37, p-value = 1.738e-06
|
||
alternative hypothesis: true difference in means is less than 0
|
||
99 percent confidence interval:
|
||
-Inf -3.868026
|
||
sample estimates:
|
||
mean of x mean of y
|
||
16.93836 24.48636
|
||
```
|
||
|
||
The average support for the Centre Party across urban municipalities is about 16.94%, but in rural municipalities the figure is much higher at 24.49%. Since the 99% confidence interval does not include zero and the p-value, 1.738e-06, is much less than our significance level of 0.01, we reject the null hypothesis.
|
||
|
||
### 7. PS receives stronger support from rural areas.
|
||
|
||
We also use a **2-sample t-test** in this case.
|
||
|
||
$H_0$: $\mu_{urban} = \mu_{rural}$
|
||
$H_A$: $\mu_{urban} < \mu_{rural}$
|
||
|
||
This is the test code:
|
||
```R
|
||
urban_support <- df$PS[df$Type == "urban"]
|
||
rural_support <- df$PS[df$Type == "rural"]
|
||
|
||
result <- t.test(urban_support, rural_support, alternative = "less", conf.level = 0.99)
|
||
|
||
print(result)
|
||
```
|
||
|
||
The code outputs:
|
||
```
|
||
Welch Two Sample t-test
|
||
|
||
data: urban_support and rural_support
|
||
t = -0.54051, df = 157.19, p-value = 0.2948
|
||
alternative hypothesis: true difference in means is less than 0
|
||
99 percent confidence interval:
|
||
-Inf 1.504662
|
||
sample estimates:
|
||
mean of x mean of y
|
||
24.33562 24.78500
|
||
```
|
||
|
||
The p-value, 0.2948, is not smaller than our significance level of 0.01. The average support for the Finns Party across urban municipalities is 24.34%, which is virtually the same as the average support for the party across rural municipalities. Thus, we fail to reject $H_0$.
|
||
|
||
### 8. Support for the Social Democratic Party is uniform across electoral districts at 20%.
|
||
|
||
Let us denote $\mu$ as the average support for the SDP across electoral districts.
|
||
|
||
$H_0$: $\mu = 20%$
|
||
$H_A$: $\mu \neq 20%$
|
||
|
||
We shall use a **one-sample t-test**.
|
||
|
||
This is the test code:
|
||
```R
|
||
weighted <- df %>%
|
||
group_by(Vaalipiiri) %>%
|
||
summarise(weighted_sdp_support = sum(SDP * Tulonsaajia) / sum(Tulonsaajia))
|
||
|
||
result <- t.test(weighted$weighted_sdp_support, mu = 20, conf.level = 0.99)
|
||
|
||
print(result)
|
||
```
|
||
|
||
The code outputs:
|
||
```
|
||
One Sample t-test
|
||
|
||
data: weighted$weighted_sdp_support
|
||
t = 0.16673, df = 11, p-value = 0.8706
|
||
alternative hypothesis: true mean is not equal to 20
|
||
99 percent confidence interval:
|
||
16.28294 24.13878
|
||
sample estimates:
|
||
mean of x
|
||
20.21086
|
||
```
|
||
|
||
The p-value is 0.8706, which is not less than our significance level of 0.01. Thus, we should fail to reject the null hypothesis. In other words, we cannot conclude that SDP has uniform support at 20% at every electoral district.
|
||
|
||
### 9. Municipalities in Vaasa have substantially higher support for the Swedish People's Party than municipalities in other electoral districts.
|
||
|
||
Let us denote $\mu_{Vaasa}$ as the average unweighted support for the Swedish People's party across municipalities in Vaasa and $\mu_{Other}$ as the average unweighted support for the party across municipalities in other electoral districts.
|
||
|
||
$H_0$: $\mu_{Vaasa} = \mu_{Other}$
|
||
$H_A$: $\mu_{Vaasa} > \mu_{Other}$
|
||
|
||
We shall use a **2-sample t-test**. This is the test code:
|
||
```R
|
||
vaasa <- df$RKP[df$Vaalipiiri == "Vaasa"]
|
||
other <- df$RKP[df$Vaalipiiri != "Vaasa"]
|
||
|
||
result <- t.test(vaasa, othery, alternative = "greater", conf.level = 0.99)
|
||
|
||
print(result)
|
||
```
|
||
|
||
Result:
|
||
```
|
||
Welch Two Sample t-test
|
||
|
||
data: vaasa and other
|
||
t = 3.6727, df = 39.87, p-value = 0.0003523
|
||
alternative hypothesis: true difference in means is greater than 0
|
||
99 percent confidence interval:
|
||
5.939094 Inf
|
||
sample estimates:
|
||
mean of x mean of y
|
||
19.580000 2.117391
|
||
```
|
||
|
||
The p-value is 0.0003523, much smaller than our significance level of 0.01. Thus, we reject the null hypothesis and accept the alternative hypothesis that the Swedish People's Party receives much more support in Vaasa's municipalities than municipalities in other electoral districts.
|
||
|
||
## Summary
|
||
|
||
In this report, we analysed Finnish citizens' voting behaviour by taking into account their income metrics across municipalities countrywide in addition to their geographic locations. We found statistically significant evidences, at 99% confidence, that:
|
||
\- Municipalities with higher income are more likely to support the National Coalition Party or the Green League.
|
||
\- There is a negative but very limited relationship between a municipality's income and their support for the Finns Party.
|
||
\- Municipalities with lower income are also more likely to support the Centre Party.
|
||
\- The National Coalition Party tends to receive higher support in urban municipalities.
|
||
\- The Centre Party, on the other hand, receives higher support in rural municiplaities.
|
||
\- The Swedish People's Party receives significantly more support in the municipalities of Vaasa than in the municipalities of other electoral districts.
|
||
|
||
## References
|
||
[1] https://www.statista.com/statistics/1150699/finland-gross-domestic-product-gdp-per-capita-by-region/
|
||
[2] https://www.syke.fi/en-US/Current/Updated_urbanrural_classification_Finlan(57443)
|