Happiness Levels in Eastern Europe compared to Western Europe
Are mean happiness scores higher in Western Europe than in Eastern Europe?
Felicity Draper, s3742570
Last updated: 14 October, 2020
Code for Reading Data
# Import and Preprocess Data
happy<- read.csv("2018.csv")
country_regions<- read.csv("countries_of_the_world.csv")
happy_score<- happy[, 2:3]# Subset for required columns
regions<- country_regions[, 1:2]
colnames(happy_score)<- c("Country", "Score")# Name columns
regions$Region<- str_trim(regions$Region, side = "right") # Manipulate strings to be same
regions$Country<- str_trim(regions$Country, side = "right")
happy_region<- inner_join(happy_score, regions) # merge to one data set
happy_region$Region<- str_to_title(happy_region$Region) #fix all caps
head(happy_region) # print and check
## 'data.frame': 144 obs. of 3 variables:
## $ Country: chr "Finland" "Norway" "Denmark" "Iceland" ...
## $ Score : num 7.63 7.59 7.55 7.5 7.49 ...
## $ Region : chr "Western Europe" "Western Europe" "Western Europe" "Western Europe" ...
# Filter for only East and West Europe
east<- happy_region %>% filter(Region == "Eastern Europe")
west<- happy_region %>% filter(Region == "Western Europe")
east_west<- rbind(east, west)
head(east_west)
Descriptive Statistics and Visualisation
- A boxplot is used to visualise the median values, inter-quartile range. No outliers were identified for either region.
- Median Happiness Score for Western Europe is higher than Eastern Europe.
#Box plot to show median, IQR and possible outliers
east_west %>% boxplot(Score ~ Region, data = ., main="Box Plot of Happiness Score by Region",
ylab="Region", xlab="Happiness Score", horizontal=TRUE, col = "skyblue")
Summary Statistics
# Happiness Level Statistics by Region (East or West Europe)
east_west %>% group_by(Region) %>% summarise(Min = min(Score,na.rm = TRUE),
Q1 = quantile(Score,probs = .25,na.rm = TRUE),
Median = median(Score, na.rm = TRUE),
Q3 = quantile(Score,probs = .75,na.rm = TRUE),
Max = max(Score,na.rm = TRUE),
Mean = mean(Score, na.rm = TRUE),
SD = sd(Score, na.rm = TRUE),
n = n(),
Missing = sum(is.na(Score))) -> table1
knitr::kable(table1)
| Eastern Europe |
4.586 |
5.253 |
5.620 |
6.0355 |
6.711 |
5.631182 |
0.6188673 |
11 |
0 |
| Western Europe |
5.358 |
6.558 |
6.977 |
7.4640 |
7.632 |
6.885263 |
0.6974815 |
19 |
0 |
Hypothesis Testing
- A one-tailed two sample t-test is used to analyze if there is a statistically significant difference between means
- Assumption of normality is tested using Q-Q plot
- Homogeneity of variance using Levene’s test
Hypothesis Statement
Null Hypothsis: \[H_0: \mu_1 = \mu_2 \] (There is no difference in means) Alternative Hypothesis: \[H_0: \mu_1 < \mu_2 \](The true difference in means is less than 0)
The Alternative Hypothesis can be understood as the true mean for happiness score in Eastern Europe is less than that in Western Europe.
Two-Sample t-test
- The two samples t-test has been selected as it is appropriate for comparing the difference between - two population means.
- It is assumed that the populations tested are independent of each other.
- Test will be performed with the following R-Code
# Two-sample t-test
t.test(
Score ~ Region,
data = east_west,
var.equal = TRUE,
alternative = "less"
)
##
## Two Sample t-test
##
## data: Score by Region
## t = -4.937, df = 28, p-value = 1.647e-05
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
## -Inf -0.821965
## sample estimates:
## mean in group Eastern Europe mean in group Western Europe
## 5.631182 6.885263
Results from one-tailed two-sample t-test
p-value < 0.001. As p-value < 0.05. Decision is made to reject H0.
The t-test score is -4.937. The t-critical level is found to be -1.701 using the following R-function.
qt(p = 0.05, df = 28, lower.tail = TRUE)
## [1] -1.701131
As the t-test score is more extreme then the t-critical level a decision is made to reject H0.
