Introduction

• In the year 2016, many road accidents took place across Leeds which is a city in West Yorkshire,England.
• As reported by ‘Leeds City Council’, main reasons for these accidents to occur are :
  • Number of vehicles collided.
  • Lighting conditions.
  • Weather conditions.
• Oftentimes, these traffic collisions result in injury, death and property damage.
• However, the severity of the accident rely on the reasons as mentioned above.
• This investigation intent to explore the affinity between the number of vehicles collided and the extremity of the accident.

Problem Statement

• Is there any coalition between number of vehicles collided and the severity of the accident ???

• Method used: A statistical approach called ‘Chi-square’ test has been used to inspect the categorical data and to export the coalition.

Data

• The data used in this investigation has been fetched from UK’s open government source.
• Data Source Reference :(https://data.gov.uk/dataset/6efe5505-941f-45bf-b576-4c1e09b579a1/road-traffic-accidents)
• (Copy of Leeds_RTC_2016.csv) provides the sample of 2549 accidents that took place across Leeds in the year 2016.
• The data set consists of 16 variables. This study deals with 2 variables.

Accidents_leeds <- read_csv("Copy of Leeds_RTC_2016.csv")

Data Cont.

• Mainly, the variables (Number of vehicles, severity) has been taken into consideration for the analysis. These are explained as follows:
  • Number of vehicles: The number of vehicles indulge in accident (1,2,3,4,5,…10).
  • Severity: The extrimity or the seriousness of the accident (slight,serious,fatal).
• The numeric variable (number of vehicles) has been scaled using scale() function for clear analysis.

numeric_scale <- scale(Accidents_leeds$`Number of Vehicles`)
head(numeric_scale)

##            [,1]
## [1,] 0.07626119
## [2,] 0.07626119
## [3,] 0.07626119
## [4,] 0.07626119
## [5,] 0.07626119
## [6,] 0.07626119

Descriptive Statistics and Visualisation

• All the outliers has been handled successfully for the number of vehicles variable using capping method.

Accidents_T1 <- table(Accidents_leeds$`Casualty Severity`,Accidents_leeds$`Number of Vehicles`)
knitr::kable(Accidents_T1) 

Descriptive Statistics and Visualisation Cont.

Accidents_T2 <- table(Accidents_leeds$`Casualty Severity`,Accidents_leeds$`Number of Vehicles`)%>% prop.table(margin = 1)
knitr::kable(Accidents_T2)       

Descriptive Statistics and Visualisation Cont.

barplot(Accidents_T2, main="number of vechiles colided vs Severity",ylim = c(0,0.8),ylab = "proportion of Severity",xlab="Number of vechiles collided", col=c("black","red","Green"),beside=TRUE)

legend("topright", 
       legend = rownames(Accidents_T2), 
       fill = 1:6, ncol = 3,
       cex = 0.75)

Decsriptive Statistics Cont.

• Detailed summary statistics like mean,SD,median of severity are as follows:

Accidents_leeds$`Number of Vehicles`<- as.numeric(Accidents_leeds$`Number of Vehicles`)


Accidents_leeds %>% group_by(`Casualty Severity`) %>% summarise(Min = min(`Number of Vehicles`,na.rm = TRUE),
                                           Q1 = quantile(`Number of Vehicles`,probs = .25,na.rm = TRUE),
                                           Median = median(`Number of Vehicles`, na.rm = TRUE),
                                           Q3 = quantile(`Number of Vehicles`,probs = .75,na.rm = TRUE),
                                           Max = max(`Number of Vehicles`,na.rm = TRUE),
                                           Mean = mean(`Number of Vehicles`, na.rm = TRUE),
                                           SD = sd(`Number of Vehicles`, na.rm = TRUE),
                                           n = n(),
                                           Missing = sum(is.na(`Number of Vehicles`))) -> table1
knitr::kable(table1)

Hypothesis Testing

• Applying Chi-square Test of Association for our investigation.
• Hypothesis for the Chi-square test of association between severity and number of vehicles collided:
  • H0: There is no association between casualty severity and number of vechiles collided(independent).
  • HA: There is an association between casualty severity and number of vechiles collided.
• Decision Rules:
  • Reject H0, if p-Value < 0.05.
  • else, fail to reject H0.
• Conclusion:
  • The analysis is statistically siginificant if H0 is rejected.
  • Otherwise, the process is not statistically significant.

Hypothesis Testing Cont.

• Firstly, the chisq.test() has been used to analyse the χ2 statistic, df and p-value.

chi1<-chisq.test(table(Accidents_leeds$`Number of Vehicles`,Accidents_leeds$`Casualty Severity`))
chi1

## 
##  Pearson's Chi-squared test
## 
## data:  table(Accidents_leeds$`Number of Vehicles`, Accidents_leeds$`Casualty Severity`)
## X-squared = 56.638, df = 12, p-value = 9.185e-08

• P-VALUE:

pchisq(q=56.638,df=12,lower.tail = FALSE)

## [1] 9.186916e-08

• The P-value is less than 0.005. Therefore, null hypothesis is rejected.

Hypothesis Testing Cont.

• The observed values are as follows:

chi1$observed

##     
##      Fatal Serious Slight
##   1      5     128    494
##   2      3     169   1418
##   3      1      17    202
##   4      0       5     87
##   5      0       3     12
##   6      0       0      3
##   10     0       0      2

Hypothesis Testing Cont.

• The expected values are as follows:

chi1$expected

##     
##            Fatal     Serious      Slight
##   1  2.213809337  79.2051785  545.581012
##   2  5.613966261 200.8552373 1383.530796
##   3  0.776775206  27.7912907  191.431934
##   4  0.324833268  11.6218125   80.053354
##   5  0.052961946   1.8948607   13.052177
##   6  0.010592389   0.3789721    2.610435
##   10 0.007061593   0.2526481    1.740290

Hypothesis Testing Cont.

• On subtracting the two values:

chi1$observed - chi1$expected %>% round(2)

##     
##       Fatal Serious Slight
##   1    2.79   48.79 -51.58
##   2   -2.61  -31.86  34.47
##   3    0.22  -10.79  10.57
##   4   -0.32   -6.62   6.95
##   5   -0.05    1.11  -1.05
##   6   -0.01   -0.38   0.39
##   10  -0.01   -0.25   0.26

Hypthesis Testing Cont.

• Mathematical equations considered in the process:

\[χ2=∑(Oij−Eij)ˆ2/Eij\]

\[df=(r-1)(c-1)\]

Discussion

• It has been tested whether the number of vehicles collided in the accident can have impact on the severity of the accident.
• Chi-square test has been used because:
  • categorical data can be tested using Chi-square.
  • It can be utilized to test the relationship between factors.
• Limitation:
  • The Chi-square test does not provide the information about the relationship between variables.
  • There are less number of numeric data. With more numeric data more statistical analysis could be conducted.
• Findings:
  • Maximum number of vechiles having fatal level of casuality are either crashed alone or collided with another vechile(2 vehicle collisons).
  • Most of the accidents occured when a vehicle was crashed with other vechile or when it hit something individually.

Conclusion

• From the Chi-Square test result, p-value< 9.186916e-08, which is less than 0.05. So,the NULL hypothesis is rejected and has been concluded that the severity of the accidents is associated with the number of vehicles collided.

References

• https://astral-theory-157510.appspot.com/secured/MATH1324_Module_08.html#chi-square_test_of_association_using_r
• https://data.gov.uk/dataset/6efe5505-941f-45bf-b576-4c1e09b579a1/road-traffic-accidents
• https://consequenceofsound.files.wordpress.com/2018/10/tyler-the-creater-tesla-model-x-car-crash.png?w=807