Here is a detailed answer:
To see whether more cars or more licensed drivers is the problem, you can calculate the fatal car crash rates per 1000 cars and per 1000 licensed drivers in each state.
Fatal car crashes per 1000 cars = (58 / 100,000) x 1000 = 0.58
Fatal car crashes per 1000 licensed drivers = (58 / 250,000) x 1000 = 0.23
Fatal car crashes per 1000 cars = (796 / 1,000,000) x 1000 = 0.80
Fatal car crashes per 1000 licensed drivers = (796 / 2,500,000) x 1000 = 0.32
From these calculations, you can see that Virginia has a higher fatal car crash rate per 1000 cars and per 1000 licensed drivers than Vermont. This suggests that the group claiming that "more cars causes increases in fatal car crashes" might have a stronger argument.
However, these calculations only provide a starting point for understanding the issue. Other factors, such as road infrastructure, traffic volume, and driver behavior, can also affect the rate of fatal car crashes. Further analysis and investigation would be necessary to fully understand the issue.
Based on the numbers you provided, both Vermont and Virginia have the same rate of fatal car crashes per 1000 people, suggesting that population size may not be the primary factor.
However, when looking at the fatal car crash rates per 1000 cars and per 1000 licensed drivers, Virginia had a higher rate than Vermont. This suggests that the number of cars and licensed drivers could be contributing factors to the higher rate of fatal car crashes in Virginia.
Please note that we assume the fatal car crashes only include those inside the cars (not pedestrians, etc.), so only licensed (assuming only licensed people drive the cars) are involved in fatal crashes. In other words, the more the number of licensed drivers, the number of fatal crashes.
Better Approach (validating/checking the simple approach):
One way to test whether the above simple approach is correct is to try different assumptions and see if the results hold up.
For example, we could assume different numbers of cars or licensed drivers in each state and recalculate the fatal car crash rates per 1000 people, per 1000 cars, and per 1000 licensed drivers. Or do these for other states for different years of data. If the results consistently show that Virginia has a higher fatal car crash rate per 1000 cars and per 1000 licensed drivers than Vermont, it would lend support to the hypothesis that more cars and licensed drivers can lead to more fatal car crashes.
Another way to test the approach would be to compare the results to data from other sources. For example, you could compare our calculated rates to actual data on fatal car crash rates from the National Highway Traffic Safety Administration (NHTSA). If your calculated rates are similar to the actual rates, it would provide further evidence that the approach is reasonable.
Additionally, you could consider other factors that could affect the analysis, such as the types of roads and driving conditions in each state, the age and experience of drivers, and the presence of safety laws and regulations, if data is available for these. By accounting for these factors, you could refine the analysis and gain a deeper understanding of the issue.
Slightly Better Approach:
Alternatively, it is possible to create a composite/adjusted measure that takes into account the number of licensed drivers, number of cars, and population size when comparing fatal crashes.
One possible way to do this is to calculate the fatal crash rate per unit of exposure, where exposure is defined as the number of cars or licensed drivers in the state. For example, you could calculate the following measures:
- Fatal crash rate per 1000 cars
- Fatal crash rate per 1000 licensed drivers
- Fatal crash rate per 100,000 population
By using multiple measures, you can gain a more complete understanding of the factors that contribute to fatal crashes.
For example, you may find that one state has a higher fatal crash rate per 1000 cars, but a lower rate per 1000 licensed drivers, suggesting that the number of cars is a bigger factor in that state. Alternatively, you may find that one state has a higher fatal crash rate per 100,000 population, suggesting that environmental and social factors may be more important.
To create a composite measure, you could weight each of these measures based on their relative importance in causing fatal crashes, and then combine them into a single index. This could provide a more comprehensive way to compare fatal crashes between states and identify areas for improvement in road safety. However, it's important to note that creating a composite measure requires careful consideration of the underlying assumptions and weights used, as well as potential confounding factors that may affect the analysis.
More Robust Approach:
If you want to go even further, it is possible to use a more robust approach to create a compound (multi-variable) measure using the number of licensed people, number of cars, and population to compare/rank variables that affect the number of fatal crashes.
One common approach to creating such a measure is to use multiple regression analysis, which allows you to assess the relationship between multiple predictor variables (such as licensed drivers, cars, and population) and a dependent variable (such as fatal crashes) while controlling for the effects of other variables. This needs good data.
To create a regression model, you would first need to gather data on the predictor and dependent variables from multiple states, and then fit the data to a regression equation. The resulting equation would allow you to estimate the effect of each predictor variable on the dependent variable while holding the other variables constant.
For example, the regression equation might look something like this (you can add more variables to it, if needed):
Fatal crashes = $\beta_0$ + $\beta_1$ * Licensed Drivers + $\beta_2$ * Number of Cars + $\beta_3$ * Population + $\epsilon$
$\beta_0$ is the intercept, representing the expected number of fatal crashes when all predictor variables are zero
$\beta_1$, $\beta_2$, and $\beta_3$ are the regression coefficients, representing the change in expected fatal crashes associated with a one-unit increase in the corresponding predictor variable while holding the other variables constant
$\epsilon$ is the error term, representing the random variation in fatal crashes that is not explained by the predictor variables
Using this equation, you could estimate the relative importance of each predictor variable in explaining fatal crashes, and use this information to create a compound measure that ranks states based on their risk of fatal crashes.
It's important to note that creating a regression model requires careful consideration of the underlying assumptions and potential confounding factors. Moreover, the resulting model should be validated using out-of-sample data to ensure that it is robust and reliable.
Anyways, for any of these approaches, further analysis and investigation would be necessary to fully understand the issue.