## Results and discussion

### 1. Exploring the data

To better understand temporal patterns in road traffic fatalities, the data are visualized using heat maps. These visual tools highlight which weekdays, months, and years exhibit the highest levels of accidents with fatalities.

In addition to descriptive insights, three separate models are developed to predict the expected number of accidents with fatalities. These models incorporate the categorical variables weekday, month, and year to evaluate RTS from different temporal perspectives.

- Weekday and Month as shown in Figure [2](#fig:image2),    
- Month and Year as shown in Figure [3](#fig:image3),    
- Weekday and Year as shown in Figure [4](#fig:image4).    

These visualizations help identify patterns and potential risk periods, which are crucial for traffic safety planning and policy interventions.

![](file:///C:/Users/ardok/AppData/Local/Temp/lu463409tank7.tmp/lu463409tanle_tmp_431fde2c.png)

_Heatmaps by weekday and month 2010-2018_

![](file:///C:/Users/ardok/AppData/Local/Temp/lu463409tank7.tmp/lu463409tanle_tmp_b8b862ab.png)

_Heatmaps by month and year 2010-2018_

![](file:///C:/Users/ardok/AppData/Local/Temp/lu463409tank7.tmp/lu463409tanle_tmp_fc2736cf.png)

_Heatmaps by weekday and year 2010-2018_

**Frequency of road accidents with fatalities**

Results in Table [1](#tab:poisson_parameters) shows the frequency of daily AF-s based on Estonian data from 2010 to 2018.

The highest number of days with accidents involving fatalities (AFs) was recorded in 2011, with 77 days (77 out of 365), resulting in a daily AF rate of 0.22. This represents the peak value in the observed period. By contrast, the daily AF rate had declined to 0.16 by 2018, indicating a downward trend over time.

The potential relationship between the country´s population and the fatal accident rate is explored. The findings can help to make more evidence-based decisions, when evaluating the road safety across countries.

EU average rate is 52 road fatalities per one million people (Figure 1, Table 1). Norway, Malta, Sweden and the United Kingdom are registered with the lowest rates – less than 30 road deaths per million inhabitants. Highest fatal accident ates: Bulgaria and Romania both have a fatal accident rate of 87, which is among the highest. They are followed closely by Latvia. Lowest fatal accident rates were in Norway with the rate of 21, followed by Malta (24) and Sweden (26). Germany has the highest population (82.9 million) but a below-average fatal accident rate of 39. The UK, with a population of 66.5 million, has an even lower rate.

Based on the authors´calculations and the calculate average coefficient between the fatalities and fatal accidents ( estimated as 1,09), the average fatal accident rate for the EU-28 is 48, which can serve as a benchmark for individual countries in the EU.

  

Table 1: Fatality rate and fatal accident rate in Europe, in 2018

| **Country** | **Fatality rate** | **Fatal accident rate** | **Population in 2018,mill** |
| ----------- | ----------------- | ----------------------- | --------------------------- |
| Austria     | 55                | 51                      | 8,8                         |
| Belgium     | 67                | 62                      | 11,4                        |
| Bulgaria    | 98                | 90                      | 7                           |
| Croatia     | 82                | 76                      | 4,1                         |
| Czech       | 70                | 64                      | 10,6                        |
| Cyprus      | 67                | 62                      | 1,2                         |
| Denmark     | 36                | 33                      | 5,8                         |
| Estonia     | 51                | 47                      | 1,3                         |
| Finland     | 48                | 44                      | 5,5                         |
| France      | 54                | 49                      | 67                          |
| Germany     | 43                | 39                      | 82,9                        |
| Greece      | 74                | 68                      | 10,7                        |
| Hungary     | 66                | 60                      | 9,8                         |
| Israel      | 38                | 35                      | 8,9                         |
| Italy       | 56                | 52                      | 60,4                        |
| Latvia      | 95                | 87                      | 1,9                         |
| Lithuania   | 80                | 74                      | 2,8                         |
| Luxemburg   | 64                | 59                      | 0,6                         |
| Malta       | 26                | 24                      | 0,5                         |
| Netherlands | 37                | 34                      | 17,2                        |
| Norway      | 23                | 21                      | 5,3                         |
| Poland      | 77                | 71                      | 38                          |
| Portugal    | 60                | 55                      | 10,3                        |
| Romania     | 95                | 87                      | 19,5                        |
| Serbia      | 68                | 62                      | 7                           |
| Slovakia    | 51                | 46                      | 5,4                         |
| Slovenia    | 58                | 53                      | 2,1                         |
| Spain       | 36                | 33                      | 46,7                        |
| Sweden      | 29                | 26                      | 10,2                        |
| Switzerland | 31                | 29                      | 8,5                         |
| UK          | 31                | 28                      | 66,5                        |
| EU 28       | 52                | 48                      | 513,2                       |
Source:(ETSC, 2022), authors´ elaborations

### 2. Relationship analysis

According to the path analysis results, figure 4 clearly shows that by plotting a scatter plot with the population on the x-axis and the fatal accident rate on the y-axis, there's a negative correlation between the size of a country's population and the fatal accident rate, with correlation coefficient -0,20, quantifying the negative relationship. The rate of fatal accidents in smaller countries, with population up to 5 million, is more concentrated compared to the data of bigger countries (Figure 2), which data is more dispersed. This illustrates well that it is challenging to compare the countries using road safety indicators across countries with different sizes. However, we may also conclude that a possible reason can also be that in bigger countries, road regulations are better enforced and roads in better conditions and less likely to cause fatal accidents on roads.  

The conclusion of the case above is as follows: a. The effect of product quality on customer satisfaction is 0,457 b. The effect of service quality on customer satisfaction is 0,038 c. The effect of complaint handling on customer satisfaction is 0,345 d. Effect of product quality, service quality, and complaint handling on customer satisfaction of 0,597 e. The influence of other variables beyond this model is 0.403 f. The correlation between product quality and service quality is 0.600 g. The correlation between product quality and complaint handling is 0.724 h. The correlation between service quality and complaint handling is 0.684

Table 2: Path analysis for roads fatalities



Source: (ETSC, 2022); Australian data (Australia, 2022); author's elaborations.

### Road safety: Estonian example



Figure 5: The number of fatalities and fatal accidents in Estonia, in 1990-2022
Source: (Statistics Estonia, 2023); authors'elaborations.

### Fatal road accidents

The number of fatal accidents is an essential indicator for predicting the average number of accidents fo the next year, as it follows the Poisson distribution (Jamroz, 2008; Spiegelhalter & Barnett, 2009). For this purpose, next, the test is applied to Estonian and Australian data (Australia, 2022; Estonia, 2021). Estonian data showed that there were no fatal accidents on 309 days, in Australia 17 days. One fatal accident occurred on 51 days, and two were fatal on five days (Figure 6). Thus, the average number of fatal accidents **per day** was 51/365 = 0,14 in 2015. For the validation ${chi} ^ {2}$, test was conducted (Table 6). The number of fatal road accidents in 2016 can be predicted using the average number of fatal accidents per day in 2015 (56/365=0,15)

A statistical test (${chi} ^ {2}$) shows no significant difference (p = 0.36) between the expected and observed figures. Thus, the regarded figures are Poisson distributed.



Source: (Open Data, 2022); (Estonia, 2021)

In addition to the cross-sectional analysis of Estonian data in 2015, the _daily_ number of fatal accidents in Estonia was analyzed longitudinally for 2010-2015. The most significant number of days when the fatal accidents occurred was 93 in 2011 (93/365 =0,25), showing clearly the decreasing trend of the **daily fatal accidents.** Given that fatal road accidents are statistically distributed allows us to assess longer-term trends. Figure 9 shows the number of fatal road accidents in Estonia since 2010. For each year, the observed count and a 95% confidence interval are given**.** If the confidence intervals do not overlap, one can infer there has been a significant change in the underlying risk of a road fatality (_Testing-for-Statistically-Significant-Changes_.)

![](file:///C:/Users/ardok/AppData/Local/Temp/lu463409tank7.tmp/lu463409tanle_tmp_ca6721f5.png)

Figure 9: Number of fatal crashes, 2010-2015
Source: (Statistics Estonia, 2023)

### Main results

Firstly, the number of road fatalities should not be the only relevant indicator to evaluate road safety across countries. The number of accidents is also an appropriate indicator, as some accidents have several fatalities (Benjamin et al., 2018; Spiegelhalter & Barnett, 2009).

The three indicators to be considered for evaluating road safety are: road deaths per day, road accidents with detahs per day and road accidents per day.

Based on the path analysis results road accidents with deaths per day is theemost important indicator.

Secondly, it is shown that the number of fatal accidents can be predicted using the random events theory and the Poisson distribution, while the statistical significance for the change of the road safety indicators should be applied. Several studies have showed showed that the number of fatal road accidents has a good fit for Poisson distribution (Benjamin et al., 2018; UK Public Data, 2021). Statistical chi-square test showed the significant correlation between the forecasted and observed data to predict the number of days with fatal road accidents.

It is essential to highlight that both the number of road fatalities and road fatal accidents must be taken into account; mainly the result of our research is relevant for small countries.