What time of day and day of the week do most major incidents happen?

Suppose there is a pattern in the weekdays or hours where major accidents happen. In that case, this could prove a significant entry point for interventions to minimise accident casualties. This section examines the prevalence of accidents and casualties by day of the week and time of day.

What day of the week do most fatal accidents happen?

This section only examines the major accidents with at least three casualties. Figure 3 below shows the number of accidents and associated deaths for each day of the week. Weekends have markedly higher numbers of accidents and casualties. However, weekdays do have substantial numbers of accidents and fatalities as well. It is also notable but not surprising that the number of accidents correlates with the number of accidents. To this end, I do scatter plots of the number of accidents/casualties against the weekday.

(
### GRAPH 1: Number of Accidents.
accidents %>% 
  
  ## Only major accidents with casualties >= 3.
  filter(number_of_casualties >= 3) %>% 
  
  ## We want to see which day of week has more casualties.
  group_by(day_of_week) %>% 
  
  ## Summary of total deaths by day of the week.
  summarise(accidents = n()) %>% 
  
  ## plot casualties versus week day, colored by week day.
  ggplot(mapping = aes(x = day_of_week, y = accidents, 
                       
                       col = factor(day_of_week))) + 
  
  ## Scatter plot.
  geom_point(shape = 1, size = 4, stroke = 4, show.legend = FALSE) + 
  
  ## Axis labels, title and caption
  labs(x = "Day of Week", y = "Number of Accidents", 
       
       title = "Number of Major Accidents by Week Day",
       
       subtitle = "Weekends Have the Highest Number of Major Accidents",
       
       caption = "Developed by John Karuitha, 2021 Using R and ggplot2") +

#############################################################################
### GRAPH 2: Number of Casualties.

accidents %>% 
  
  ## Only major accidents with casualties >= 3.
  filter(number_of_casualties >= 3) %>% 
  
  ## We want to see which day of week has more casualties.
  group_by(day_of_week) %>% 
  
  ## Summary of total deaths by day of the week.
  summarise(casualties = sum(number_of_casualties)) %>% 
  
  ## plot casualties versus week day, colored by week day.
  ggplot(mapping = aes(x = day_of_week, y = casualties, 
                       
                       col = factor(day_of_week))) + 
  
  ## Scatter plot.
  geom_point(shape = 1, size = 4, stroke = 4, show.legend = FALSE) + 
  
  ## Axis labels, title and caption
  labs(x = "Day of Week", y = "Casualties", 
       
       title = "Casualties of Major Accidents by Week Day",
       
       subtitle = "Weekends Have the Highest Casualties from Major Accidents",
       
       caption = "Developed by John Karuitha, 2021 Using R and ggplot2")) 

Figure 3: Number of Major Accidents by Week Day

Insight 3: Weekends have the highest number of major accidents resulting in the most casualties. Typically, accidents and deaths are lowest on Mondays. Accidents and fatalities rise gradually during the week and then spike on Friday, peaking on Saturday. The numbers then reduce on Sunday (to levels only lower than Friday and Saturday) and slump back to their minimum on Monday. Still, weekdays have a significant number of fatal road accidents and fatalities, as the Table 4 shows.

accidents %>% 
  
  ## Only major accidents with casualties >= 3.
  filter(number_of_casualties >= 3) %>% 
  
  ## We want to see which day of week has more casualties.
  group_by(day_of_week) %>% 
  
  ## Summary of total deaths by day of the week.
  summarise(all_accidents = n(),
            
            percent_accidents = all_accidents/nrow(accidents) * 100,
            
            fatalities = sum(number_of_casualties),
            
            percent_fatalities = fatalities/sum(accidents %>% 
                                                  
                                                  select(number_of_casualties)) * 100) %>% 
  
  ## Make a nice table
  kbl(., booktabs = TRUE, 
      
      caption = "Table 4: Major Accidents and Fatalities by Week Day") %>% 
  
  kable_classic(latex_option = "hold_position", 
                
                full_width = FALSE, 
                
                position = "left") %>% 
  
  add_footnote(c("The weekday count starts on Sunday", "Note: We only include major accidents with more than 3 fatalities"), notation = "alphabet")

Table 4: Major Accidents and Fatalities by Week Day

day_of_week	all_accidents	percent_accidents	fatalities	percent_fatalities
Sun	687	0.7532977	2474	2.140435
Mon	614	0.6732530	2145	1.855793
Tue	621	0.6809285	2187	1.892130
Wed	632	0.6929901	2231	1.930198
Thur	645	0.7072446	2275	1.968266
Fri	798	0.8750096	2772	2.398256
Sat	820	0.8991327	2897	2.506402
a The weekday count starts on Sunday
b Note: We only include major accidents with more than 3 fatalities

What time of day do most fatal accidents happen?

This section examines the number of major accident casualties by the time of day. I visualize this data using an area plot. Figure () below shows the number of deaths from accidents for each hour, which leads us to another insight.

Insight 4: There are two peak times of the day when most accidents happen. The first period starts at around 0500 hours, peaking at 0800 hours followed by a sudden drop. In the second and most deadly phase, the number of casualties starts rising at 1000 hours, reaching the maximum at 1700 hours, after which there is a sharp decline.

However, lumping data together may mask heterogeneity in accidents casualties patterns between the days of the week. In the next section, I break the data into the constituent days of the week.

accidents %>% 
  
        ## Get only the major accidents        
        filter(number_of_casualties >= 3) %>% 
  
        ## Get the hour of day from the time column
        group_by(hour = hour(time)) %>% 
  
        ## Get total casualties by hour of day
        summarise(death_by_hour = sum(number_of_casualties)) %>% 
  
        ## Plot deaths against hour
        ggplot(mapping = aes(x = hour, y = death_by_hour)) + 
  
  geom_area(col = "purple", fill = "lightgray") + 
  
  labs(x = "Hour", y = "Casualties", 
       
       title = "Number of Accident Casualties by Hour")

Figure 4: Number of Accident Casualties by Hour

Are there any patterns in the time of day/ day of the week when major incidents occur?

This section examines unique patterns in the time of the day or day of the week when major accidents occur. Again, if there are regularities, then the ministry could have interventions at these days/ times to reduce incidences of fatal accidents.

Breaking down accident casualties by the time of day and day of the week.

As noted earlier, lumping together figures could mask heterogeneity in the patterns of accidents by hour of day or day of the week. In this section, I disaggregate this data revealing patterns to each day of the week.

Insight 5: Figure 5 below shows a breakdown of the casualties by the hour for each day of the week. Working days (which I define as Monday to Friday) have a similar trend that follows Insight 1.

However, Saturdays and Sundays have a markedly different pattern.

accidents %>% 
  
        ## Get only the major accidents
        filter(number_of_casualties >= 3) %>% 
  
        ## Group by time of day and day of week
        group_by(hour = hour(time), day_of_week) %>% 
  
        ## Get number of deaths by hour
        summarise(death_by_hour = sum(number_of_casualties)) %>% 
  
        ## Plot deaths against hour
        ggplot(mapping = aes(x = hour, y = death_by_hour, col = factor(hour))) + 
  
  geom_point(show.legend = FALSE) + 
  
  facet_wrap(~day_of_week, ncol = 3) + 
  
  scale_color_viridis_d() + 
  
  labs(x = "Hour", y = "Casualties", 
       
       title = "Number of Accident Casualties by Day and Hour")

Figure 5: Number of Accident Casualties by Day and Hour

Insight 6: Unlike other days of the week, accidents on Sundays have one peak period that begins around midday and peaks at 1500 hours, followed by a rapid drop.

Insight 7: Like Sunday, Saturday has one peak in the number of accident casualties. However, the peak accident period is prolonged, lasting from around 11.00 hours to 1800 hours, after which there is a gradual decline.

Where do accidents happen at weekends vs weekdays?

Major Accident Casualties versus Speed Limits

Speed is one major cause of road traffic accidents (⊕Ashraf et al. 2019Ashraf, Imran, Soojung Hur, Muhammad Shafiq, and Yongwan Park. 2019. “Catastrophic Factors Involved in Road Accidents: Underlying Causes and Descriptive Analysis.” PLoS One 14 (10): e0223473.; ⊕Rolison et al. 2018Rolison, Jonathan J, Shirley Regev, Salissou Moutari, and Aidan Feeney. 2018. “What Are the Factors That Contribute to Road Accidents? An Assessment of Law Enforcement Views, Ordinary Drivers’ Opinions, and Road Accident Records.” Accident Analysis & Prevention 115: 11–24.). This section examines the speed limits that correspond with high casualties for major accidents. Figure 6 shows a plot of major accident casualties (y-axis) versus speed limits (x-axis), faceted by day of the week.

accidents %>% 
  
        ## Get the major accidents
        filter(number_of_casualties >= 3) %>% 
  
        ## Group data by speed limit and day of week
        group_by(speed_limit, day_of_week) %>% 
  
        ## Summarise the total casualties
        summarise(casualties = sum(number_of_casualties)) %>% 
  
        ## Get the sum of casualties
        mutate(perc_casualties = casualties / sum(casualties) * 100) %>% 
        
        ## Plot speed limit versus proportion of casualties
        ggplot(mapping = aes(x = speed_limit, y = perc_casualties)) + 
  
        geom_line() + facet_wrap(~ day_of_week) +
  
        labs(x = "Speed Limit", y = "Percent Casualties", 
       
       title = "Speed Limits versus Proportion of major Accident Casualties")

Figure 6: Speed Limits versus Proportion of major Accident Casualties

Insight 8: At 21% and 20%, respectively, Fridays and Saturdays account for the highest proportion of major accident casualties at the speed limit of 20 mph. Friday also has a second peak at a speed limit of 50 mph. This observation means that the accidents could result from failure to observe road limit signs. Sunday has most accidents where speed limits are between 30 and 60 mph. Other days of the week have notable peaks at around 40 mph (⊕Jacobs and Sayer 1983Jacobs, GD, and I Sayer. 1983. “Road Accidents in Developing Countries.” Accident Analysis & Prevention 15 (5): 337–53.).

I also examine the patterns of major accidents in road stretches with speed limits. In this case, I plot the number of casualties versus days of week faceted by speed limits.

Insight 9: Overall, the road stretches with a speed limit of 30 mph have the highest incident of accidents and accident casualties across all days of the week. Figure () below shows this trend.

accidents %>% 
        
        ## Create a column of major and minor accidents
        mutate(major = case_when(
                
                number_of_casualties >= 3 ~ "Major",
                
                TRUE ~ "Minor"
        )) %>% 
        
        ## Group by day of week and speed limit
        group_by(day_of_week, speed_limit) %>% 
        
        ## Summarise total casualties
        summarise(total = sum(number_of_casualties)) %>% 
        
        ## Plot day of week versus casualties
        ggplot(mapping = aes(x = day_of_week, y = total, 
                             
                             col = day_of_week, fill = day_of_week)) + 
        
        geom_col(show.legend = FALSE) +
        
        facet_wrap(~ speed_limit) + 
        
        scale_fill_viridis_d() + 
        
        labs(y = "Number of Casualties", 
             
             title = "Accident Casualties by Weekday and Speed Limit")

Figure 7: Accident Casualties by Weekday and Speed Limit

Major Accident Casualties and Weather Conditions

Another probable driver of accidents is the weather. I tabulate weather conditions against the number of major accident casualties. The results are in Table 5.

Insight 9: Table 5 below shows that about 77% of major accident casualties happen when the weather is fine (that is, fine with no high winds). In comparison, 14% occurs when raining with no high winds. Appendix 2 (Figure 12) shows a bar graph showing the proportions of accident casualties by weather condition.

accidents %>% 
  
        ## Get only the major accidents
        filter(number_of_casualties >= 3) %>% 
  
        ## Group by weather conditions
        group_by(weather_conditions) %>% 
  
        ## Get the total number of casualties
        summarise(casualties = sum(number_of_casualties)) %>% 
  
        ## Compute the proportion of casualties
        mutate(perc_casualties = casualties / sum(casualties) * 100) %>% 
  
        ## Sort by casualties
        arrange(desc(casualties)) %>% 
  
        ## Make a nice table
        kbl(., booktabs = TRUE, 
            
            caption = "Table 5: Weather Conditions and Accident Casualties") %>% 
  
        kable_classic(full_width = FALSE, position = "left")

Table 5: Weather Conditions and Accident Casualties

weather_conditions	casualties	perc_casualties
1	13093	77.1038219
2	2382	14.0274424
5	417	2.4556858
8	391	2.3025735
4	307	1.8079030
9	202	1.1895648
7	130	0.7655615
3	47	0.2767799
6	12	0.0706672

We next break down this weather data into days of the week.

Insight 10: Most accidents on any day of the week happen when the weather is fine with no high winds (Figure 8). The second riskiest weather pattern is raining with no high winds. It would follow that people are most likely to speed when the weather is clear, hence the high number of casualties.

accidents %>% 
  
        ## Get the major accidents
        filter(number_of_casualties >= 3) %>% 
  
        ## Group by weather conditions and day of the week
        group_by(weather_conditions, day_of_week) %>% 
        
        ## Summarise total casualties
        summarise(casualties = sum(number_of_casualties)) %>% 
  
        ## Create new variable for proportion of casualties
        mutate(perc_casualties = casualties / sum(casualties) * 100) %>% 
        
        ## Plot casualties versus day of week
        ggplot(mapping = aes(x = day_of_week, y = casualties, 
                       
                       fill = day_of_week)) + 
        
        geom_col(show.legend = FALSE) + 
        
        facet_wrap(~ weather_conditions) +
        
        labs(x = "Day of the Week", y = "Casualties", 
             
             title = "Casualties by Day of Week and Weather Conditions")

Figure 8: Casualties by Day of Week and Weather Conditions

What characteristics stand out in major incidents compared with other accidents?

First, most casualties arise from other accidents instead of major accidents, as noted earlier in Insight 1. Figure 9 visualizes this observation.

accidents %>% 
        
        ## Create a new column major
        mutate(major = case_when(
                
                number_of_casualties >= 3 ~ "Major",
                
                TRUE ~ "Minor"
        )) %>% 
        
        ## Group the data by major
        group_by(major) %>% 
        
        ## Get the total casualties
        summarise(total_casualties = sum(number_of_casualties)) %>% 
        
        ## Plot casualties against major
        ggplot(mapping = aes(x = major, y = total_casualties)) + 
        
        geom_col(col = "skyblue", fill = "darkblue") + 
        
        labs(x = "Accident Type- Major or Minor", 
             
             y = "Number of Casualties", 
             
             title = "Accident Type versus Number of Casualties")

Figure 9: Accident Type versus Number of Casualties

Insight 11: In comparison to major accidents, minor accidents are more dispersed. Figure 10 shows that major accidents concentrate in three major hotspots, whereas minor accidents concentrate in more places. Note that the figure’s colour red shows the accident concentration hotspots.

accidents %>% 
        
        ## Create a new column for major and minor accidents
        mutate(major = case_when(
                
                number_of_casualties >= 3 ~ "Major",
                
                TRUE ~ "Minor"
        )) %>% 
        
        ## Group by major/ minor accident
        group_by(major) %>% 
        
        ## Map the locations of accidents
        ggplot(mapping = aes(x = longitude, y = latitude)) + 
  
  geom_hex(alpha = 0.5) +
  
  geom_density_2d() +
  
  labs(x = "Longitude", y = "Latitude",
       
       title = "MAJOR/MINOR ACCIDENT HOT SPOTS",
       
       subtitle = "Locations of Major/ Minor Accidents in the UK",
       
       caption = "John Karuitha, 2021 Using R and ggplot2") + 
  
  theme(legend.title = element_blank()) + 
  
  scale_fill_gradient(low = "lightgray", high = "red") + 
        
        ## Facet accidents by major/minor category
        facet_wrap(~ major) 

Figure 10: Major/Minor Accidents Hotspots

Insight 12: Furthermore, major accidents fatalities appear evenly distributed across rural and urban settings. In contrast, over 2/3 of minor accidents happen in urban areas.

## The data
accidents %>% 
        
        ## Create a major/minor columns
        mutate(major = case_when(
                
                number_of_casualties >= 3 ~ "Major",
                
                TRUE ~ "Minor"
        )) %>% 
        
        ## Group by major and urban/rural area
        group_by(major, urban_or_rural_area) %>% 
        
        ## Get total of casualties
        summarise(total = sum(number_of_casualties)) %>% 
        
        ## Make a wide dataset
        pivot_wider(names_from = "major", values_from = "total") %>% 
        
        ## Make a nice table
        kbl(., booktabs = TRUE, 
      
  caption = "Table 6: Casualties in Rural/Urban Settings for Major and Minor Accidents") %>% 
        
        kable_classic(full_width = FALSE, 
                                                                                     latex_options = "hold_position", position = "left")

Table 6: Casualties in Rural/Urban Settings for Major and Minor Accidents

Next, I examine the number of casualties by speed limit for major and minor accidents. The bar chart below shows the distribution showing a significant difference between major and minor accidents. Compared to other accidents, a significantly lower proportion of casualties happen at a speed limit of 30 mph. In contrast, more accident casualties occur at the 60 mph speed limit for major accidents than minor accidents.

accidents %>% 
        
        ## Create a major/minor accidents column
        mutate(major = case_when(
                
                number_of_casualties >= 3 ~ "Major",
                
                TRUE ~ "Minor"
        )) %>% 
        
        ## Group by major and speed limit
        group_by(major, speed_limit) %>% 
        
        ## Summarise total casualties
        summarise(casualties = sum(number_of_casualties)) %>% 
        
        ungroup() %>% 
        
        group_by(major) %>% 
        
        ## Create a new column for proportion of casualties
        mutate(prop = casualties/ sum(casualties)) %>% 
        
        ## Plot prop against speed limit
        ggplot(mapping = aes(x = speed_limit, y = prop, fill = speed_limit)) + 
        
        geom_col() +
        
        scale_fill_viridis_b() +
        
        facet_wrap(~ major) + 
        
        ## Add labels and titles
        labs(x = "Speed Limit", y = "Proportion of Casualties", 
             
             title = "Speed Limits versus Proportion of Accident Casualties")

Figure 11: Speed Limits versus Proportion of Accident Casualties

On what areas would I recommend the planning team focus their brainstorming efforts to reduce major incidents?

One of the major takeaways from the analysis is that most road accidents happen when the weather is clear (77%), with another 14% happening when raining but with no high winds. 91% of major accidents occur during these two weather patterns to restate the point. The first recommendation is for the ministry to pay attention when the weather is clear and when raining with no high winds. However, we cannot take the weather pattern in isolation. After considering the weather, the ministry should also jointly focus on the recommendations below.

First, while accidents are spread all over the UK, there is a need to concentrate on areas with a high concentration of significant casualties. Figure 1 shows these two hotspots, one around London and another in the central UK. The hotspot in the central UK has a further three sub-hotspots that the ministry should pay particular attention to. After separating major and minor accidents, the areas that the ministry should concentrate on to reduce fatalities from major accidents stand out better. Figure 10, panel A, shows the two regions. Again we should not take this recommendation in isolation but with the other suggestions.

Another significant regularity in the data is the high incidence of accidents at stretches with 30mph and 60mph speed limits. This recommendation draws from insight 8 and insight 9. For some reason, the speed limit of 30 mph is especially notorious for both major and minor accidents, followed by the 60 mph speed limit. Thus, the ministry should put mechanisms to enforce adherence to these speed limits.

The day of the week effect is very prominent and a major entry point to minimise major accidents. As noted earlier in insight 3 and 5, major accidents spike on Fridays, peaking on Saturday and declining on Sundays to levels below Friday and Saturday. However, over weekends, there is a significant pattern of accidents across an hour of the day, as we discuss next.

Time of day is also a significant entry point for interventions to reduce fatalities from major accidents in line with insight 4 and insight 5. The times when major accidents and accident fatalities occur vary by day of the week. For instance, on Saturdays, the worst day in terms of major accidents fatalities, we observe an extended peak between 1100 hours and 1800 hours when the ministry should effect the interventions. We would follow a similar interpretation for other days of the week.

As noted earlier, it would be a mistake to take any one of these recommendations in isolation. Each recommendation should serve to reinforce the others. Take Saturday, a day notorious for deadly road accidents, as an example. The ministry should focus efforts on the two regions in the UK (Figure ) with an unusually high concentration of major accidents. In these regions, the ministry should focus on the period between 1100 hours and 1800 hours at road stretches with a speed limit of 30 mph and 60 mph, respectively, by installing speed cameras. The ministry should intensify these interventions when the weather is clear, for instance, by having traffic corps on sight.

Conclusion

In this analysis, I examined the road accidents data from the UK. The study of the data provided some valuable insights, the major ones being;

• Accident casualties peak during weekends, Starting from Friday and falling on Sunday.
• Accidents casualties vary by time of day.
• Major accidents and accident casualties mainly happen when the weather is fine.
• Major accidents and accident casualties mainly occur in road stretches with speed limits of 30 mph and 60 mph.

The recommendations to reduce significant accidents casualties should hence draw from these insights. None of the proposals would work very well in isolation. What is needed is a package of interventions that would help lower the tide of casualties from significant accidents.

Appendix 1: Summary Statistics

accidents %>% 
  
        ## Select the relevant variables
        select(-accident_index, -accident_reference, 
         
         -accident_year, -day_of_week,
         
         -date, -time,
         
         -longitude, -latitude) %>% 
  
        ## Get summary statistics
        skimr::skim_without_charts() %>% 
  
        ## Remove redundant summary statistics
        select(-skim_type, -n_missing) %>% 
  
        ## Make a nice table
        kbl(., booktabs = TRUE, caption = "Table 7: Summary Statistics") %>% 
  
        kable_classic(full_width = TRUE, 
                
                latex_options = "hold_position", 
                
                font_size = 12)

Appendix 2: Proportion of Major/Minor Accidents by Weather Conditions

accidents %>% 
        
        mutate(major = case_when(
                
                number_of_casualties >= 3 ~ "Major",
                
                TRUE ~ "Minor"
        )) %>% 
        
        group_by(major, weather_conditions) %>% 
        
        summarise(total = sum(number_of_casualties)) %>% 
        
        ungroup() %>% 
        
        mutate(prop = total / sum(total)) %>% 
        
        ggplot(aes(x = weather_conditions, y = prop, 
                   
                   fill = major, col = major)) + 
        
        geom_col(position = "dodge") + 
        
        scale_fill_viridis_d()

Figure 12: Proportion of Major/Minor Accidents by Weather Conditions