RPubs link information

• Rpubs link comes here: https://rpubs.com/S3905469/956849

Introduction

Car crashes occur every second all around the world, resulting in injuries and fatalities. Road traffic accidents are the tenth greatest cause of death, accounting for 2.2% of all deaths globally. Cars have been improved and made safer over time, and they are today safer than they were before. In this assignment, we will be looking at data for car crashes in South Australia. We assume that deaths caused by car accidents are more likely to increase during peak hours where there is heavy traffic during the day.

Problem Statement

There were 1,123 fatal car accidents in Australia in 2021. This represents a 2.6% increase from 2020. The number of fatalities dropped from about 1,300 annually to 1,100 annually throughout the course of the decade. To further help keep this number in decline, we will be looking at historical data for car crashes from the year 2019 that includes road deaths. We will test a hypothesis stating that deaths caused by car accidents are more likely to increase during peak hours where there is heavy traffic. We hope this analysis can help better allocate resources for Emergency Medical Services (EMS) during times of day. The use of statistical graphs and tests will be utilized in this analysis to answer the hypothesis question.

Data

The data used in this assignment was collected from the Australian open government data website. The Road Crash Data contains Details of reported road crashes and casualties in South Australia carrying 12,964 observations, 33 variables, both quantitative and qualitative. A list of all variables and the metadata can be found on the Australian open government data website.

# reading data
crash_2019 <- read.csv("2019_Crash.csv")
head(crash_2019[,c(1,3,7,11:14,23)], n = 5) -> table1
knitr::kable(table1)

Data Cont.

We will be working on few variables from this data set, mainly:

• Total.Cas: Total number of casualties as a result of a road crash
• Month: Month crash occurred
• DayNight: Time of day the crash occurred (A factor with two levels: Day, Night)

This dataset has character and numeric type variable. Our main focus is on the variable DayNight which is a “character” type variable. In this data set, the data type of DayNight should be factor. Thus, we are going to change its type from character to factor. The levels of this factor will be Day and Night to help us identify the time of day of the car crash. Also, the numeric variable Total.Cas will be used as the total casualties for a car crash. These two variables are significant to our analysis as they can help us compare the total number of casualties for car crashes by Day or Night.

data.frame(variable = names(crash_2019),
           class = sapply(crash_2019, typeof),
           first_values = sapply(crash_2019, function(x) paste0(head(x),  collapse = ", ")),
           row.names = NULL) %>% 
  kable()

crash_2019$DayNight<- factor(crash_2019$DayNight,levels = (unique(crash_2019$DayNight)),labels = c("Day","Night") ,ordered = TRUE)
crash_2019$Month = factor(crash_2019$Month, levels = month.name) # get the ordered months of year
crash_2019$CSEF.Severity <- factor(crash_2019$CSEF.Severity,levels = (unique(crash_2019$CSEF.Severity)), labels = c("Property Damage Only", "Minor Injury", "Serious Injury", "Fatal Injury"))

levels(crash_2019$DayNight)

## [1] "Day"   "Night"

# renaming the columns for easier handling
names(crash_2019)[7]<- "Deaths"
names(crash_2019)[23]<-"TimesOfDay"

Descriptive Statistics and Visualisation

After careful inspection of the variables we found no outliers or missing data. In the below figure, we can see a boxplot for Deaths by TimesOfDay and we can see a few values outside the upper fence, which we can’t simply consider as outliers because they are actual values and not recorded by mistake or as a result of any data processing error.

ggplot(crash_2019, aes(x=TimesOfDay, y=Deaths))+
geom_boxplot()

The below bar chart compares Deaths during Daytime and Night time in 2019. Overall, road deaths are more likely to happen during Daytime which is the first evidence to back our claim. We can see that the number of deaths during Daytime are more than triple the deaths during Night time.

ggplot(crash_2019, aes(x=TimesOfDay, y=Deaths)) +
geom_bar(stat="identity", fill="steelblue", width = 0.3)+
theme_minimal()+
ggtitle("The number of deaths during Daytime and Night time")

In February and March 2019, road deaths during day time are higher than any other months with more than 450 deaths per month. However, in May and June same year deaths from car crashes are highest with more than 150 deaths per month.

death_by_month <- crash_2019 %>% group_by(Month, TimesOfDay) %>% summarise(Deaths = sum(Deaths))

ggplot(death_by_month, aes(x=Month, y=Deaths, group = TimesOfDay, fill = TimesOfDay)) +
geom_bar(position="dodge", stat="identity")+
theme_minimal()+
ggtitle("The total number of deaths across months of the year during day and night")

Descriptive Statistics

crash_2019 %>% group_by(TimesOfDay) %>% summarise(Min = min(Deaths,na.rm = TRUE),
                                         Q1 = quantile(Deaths,probs = .25,na.rm = TRUE),
                                         Median = median(Deaths, na.rm = TRUE),
                                         IQR = IQR(Deaths),
                                         Q3 = quantile(Deaths,probs = .75,na.rm = TRUE),
                                         Max = max(Deaths,na.rm = TRUE),
                                         Mean = mean(Deaths, na.rm = TRUE),
                                         SD = sd(Deaths, na.rm = TRUE),
                                         N = n(),
                                         Missing = sum(is.na(Deaths))) -> table2
knitr::kable(table2)

Hypothesis Testing

In order to test our hypothesis, first we need to compare the variances of Deaths by Day and Night. We will use The Levene’s test to get the p-value compared to the standard 0.05 significance level. The Levene’s test has the following statistical hypotheses: \[H_0: \sigma_1^2 = \sigma_2^2\] \[H_A: \sigma_1^2 \ne \sigma_2^2\]

leveneTest(Deaths ~ TimesOfDay, data = crash_2019)

The p-value for the Levene’s test of equal variance for car crash Deaths by TimesOfDay is statistically insignificant where p = 0.06. We find p > .05, therefore, we fail to reject H0. In other words, the variance for the two samples are equal.

Hypothesis Testing Cont.

t.test(
  Deaths ~ TimesOfDay,
  data = crash_2019,
  var.equal = TRUE,
  alternative = "two.sided"
  )

## 
##  Two Sample t-test
## 
## data:  Deaths by TimesOfDay
## t = 1.882, df = 12962, p-value = 0.05985
## alternative hypothesis: true difference in means between group Day and group Night is not equal to 0
## 95 percent confidence interval:
##  -0.001186797  0.058375118
## sample estimates:
##   mean in group Day mean in group Night 
##           0.4719033           0.4433092

The Two Sample t-test has the following statistical hypotheses: \[H_0: \mu_1 - \mu_2 = 0 \] \[H_A: \mu_1 - \mu_2 \ne 0\]

where \(\mu_1\) and \(\mu_2\) refer to the mean of Deaths by TimesOfDay for the two groups Day and Night respectively. The difference between Deaths at Day and Deaths at Night estimated by the sample was 0.4719033 - 0.4433092 = 0.0285941. In other words, \(\mu_1\) > \(\mu_2\) which means the mean for Day group is greater than the mean for Night group. Therefore, our assumption that deaths caused by car crashes are more likely to increase during rush hour which is day time is true.

Discussion

• By our estimation, deaths from car accidents are three times more likely to happen during rush hour.
• February and March are highest in deaths caused by car accidents during day time.
• May and June are highest in deaths from car crashes during night time.
• The variety of the dataset and diversity of measurements makes it challenging for us to determine which measurement we can use to conduct the investigation.
• Also, diversity of variables gives a good standing point for future investigations. For example, we can classify accidents by severity of injuries and conduct a new hypothesis testing.
• Overall, we tested our assumption about deaths caused by car crashes are more likely to happen during day time using different methods. We used visualizations to prove our assumption then we performed a scientific Two Sample t-test which further proved our hypothesis.

References

• [1]“Road Crash Data”, Data.gov.au, 2016. [Online]. Available: https://data.gov.au/dataset/ds-sa-21386a53-56a1-4edf-bd0b-61ed15f10acf/details?q=. [Accessed: 10- Oct- 2022].
• [2]“Road traffic injuries”, Who.int, 2022. [Online]. Available: https://www.who.int/news-room/fact-sheets/detail/road-traffic-injuries. [Accessed: 10- Oct- 2022].
• [3]“Road Trauma Australia—Annual Summaries”, bitre.gov.au, 2022. [Online]. Available: https://www.bitre.gov.au/publications/ongoing/road_deaths_australia_annual_summaries. [Accessed: 10- Oct- 2022].
• [4]“T-tests in R – Learn to perform & use it today itself!”, data-flair.training, 2022. [Online]. Available: https://data-flair.training/blogs/t-tests-in-r/#:~:text=What%20is%20T%2Dtests%20in%20R%20Programming%3F,normal%20distributions%20with%20equal%20variances. [Accessed: 11- Oct- 2022].