The Great Gun Debate Part One: Gun Ownership and Firearm Deaths
(To interact with the graph above and see maps showing this data, go to https://public.tableau.com/views/GunOwnershipandFirearmDeaths/GunOwnershipFirearmDeaths)
I am a researcher and statistician by trade. As such, the level of disregard given to appropriate use of facts and information makes me a little crazy. We seem so enamored with propaganda that we are choosing it above actual facts.
If you know anything about psychology, you can understand why this might be. We like to simplify things so that they make sense to us. We like to impose dichotomies to continuous variables (we like to treat shades of grey like they were black or white). We like to win, so we want to have arguments where someone is right and someone else is wrong.
Plus, we continue to make the mistake of expecting politicians and the media to provide unbiased information, when their very business is propaganda.
The gun debate is a very good example of this happening. People have strong feelings on the subject matter, and the different perspectives have been made so much more extreme by the politicians, the media, and everything in between encouraging us to hate the other side and become more and more radical in our own views.
So we’re going to take a step back and see if we can’t spend some time with the actual data. I am calling this “The Great Gun Debate Part One” because I am hoping it will generate some feedback that will give me a direction to go for Part Two, and then maybe even Parts Three through Seventy-Seven.
The one question that I wanted to see an answer for, but which I could not find, was simply: Are there more gun-related deaths in states with more guns? State-level statistics on per-capita gun ownership and per-capita gun deaths are much harder to find than you would expect.
Here’s what I found:
- An article from 2015 written by a professor at Columbia University containing estimated gun ownership rates by state for 2013. The estimates were based on a sample of 4,000 survey respondents from across the country.
- An article from Wikipedia (based on several sound sources) for firearm death rates in the U.S. by state for 2013.
Right off the bat, we have to consider the sources.
The ownership article uses extrapolation techniques to generalize 4,000 survey responses to an estimate of what percentage of each state’s population owns guns. Statisticians have come up with all kinds of complex ways to do this, and even as a statistician I recognize the danger in doing such estimating.
The information on firearm death rates comes from Wikipedia, which some people would immediately discredit. However, if you look at the citations on the article, we have information from several credible national sources. The resulting numbers indicate the estimated number of firearm related deaths (including murder, suicide, and self-defense) per 100,000 people in each state.
The first possible Part Two for this article, then, would be to look at different sources of the same (or similar) data and see if the trend we found with this data (which I will describe soon) is also apparent in the other data sources. Ideally it would be great to compare a per-capita gun ownership rate with a per-capita gun death rate. In other words, how does the average number of guns per person related to the average number of gun deaths per person?
But as I said earlier, these statistics are hard to find, and if we are being honest, even harder to find from sources that don’t have some stake in the gun debate on one side or the other. So valid, reliable, unbiased data is a big challenge for this kind of discussion.
Even moreso in recent times where the President and lots of other apparent authorities are quick to discredit information from sources that don’t share their particular slant. But I digress.
Next let’s consider how to compare these numbers. I have chosen to start with a simple linear regression. Here’s a definition:
A regression line is a straight line that attempts to predict the relationship between two points, also known as a trend line or line of best fit. Simple linear regression is a prediction when a variable (y) is dependent on a second variable (x) based on the regression equation of a given set of data.
So doing a linear regression calculation with this data means I am trying to determine whether gun ownership (x) can predict gun deaths (y).
The key word here is “predict.” The regression equation can tell us whether the percent of people in a state that own guns can consistently give us an idea of how many gun-related deaths per 100,000 people in a state likely occur. So the most that the regression equation can “prove” is whether the gun ownership percentage is a predictor of the gun death rate. It cannot tell us whether more guns actually leads to or causes more gun deaths.
All this being said, if we look again at the graphic attached to this article, we see a scatterplot with “Gun Ownership Rate” along the bottom and “Firearm Death Rate” along the side. We see a lot of dots, each representing a state, and we see the trend line along the middle.
If you look at the statistics behind the comparison, we get an R-squared value of .483 with a significance of p < .0001.
R-squared is supposed to represent the amount of variation in the data that can be explained by the proposed model, so an R-square of .483 indicates that almost half of the variation in the data can be explained by the model.
The p value indicates how likely it is that the results found are due to error, so in this case there is a .01 percent chance that the apparent relationship between these two things is purely coincidental.
So, what does this appear to tell us? States where more people own guns have higher firearm death rates.
In truth, this is where these statistics stop. They cannot tell us that having more guns causes more gun-related deaths. Life would be so much easier if they could, but they can’t, and every time someone pushes to imply that this is the case beyond what the statistics actually shows is lying.
There are two ways in which we could have a stronger indicator that having more guns leads to more deaths.
One would be if we could somehow create an actual experiment and control the number of guns people in two identical populations had, ensuring that one group had more than the other, then see over time if the firearm death rates were different for these two otherwise identical populations.
The other would be to get access to change statistics — an indicator of which states had decreasing percentages of their population owning guns, and if those same states also saw decreases in their firearm death rates.
The first option is obviously not really possible. Social and political science cannot conduct actual experiments such as this with people because it is unethical. The second option is more possible if data sources could be located that report these kinds of statistics over time.
But even with data that more directly speaks to the change in the number of guns, all we could get would be a stronger predictor. We still can’t say via the numbers that having more guns causes more gun deaths.
Keep in mind, also, that I imposed my bias in how I put this comparison together. I made gun deaths my dependent variable (y) and gun ownership my independent predictor variable (x). What happens if I flip the two in order to determine whether gun deaths can reliably predict gun ownership?
Well, as it turns out, the R squared value and the significance are the same, though the numbers leading up to them look slightly different:
In other words, we can say that the percent of a state’s population that owns a gun can reliably predict how many people in that state die in firearm-related deaths, but we can also say the number of people in a state that die in firearm-related deaths can reliably predict the percent of the population that owns guns.
“Can reliably predict” doesn’t satisfy our need to either prove that more guns equals more death, or disprove it, depending on which side of the argument we favor. Therefore we often push beyond this and start cheating. We make conjecture and pretend the statistics back it up. We slant what we present to highlight the relationship and ignore other possible explanations.
For example, one thing we could look at is suicide rate, since the Wikipedia article I used noted that suicides account for “ roughly two out of every three gun deaths.” How do suicide rates and gun-related death rates fall on the scatterplot, and what kind of R squared would we see for them? How about the percent of the population owning guns and suicide rates? Is there a connection there?
What about race, socioeconomic status, education level, rural/urban breakouts, age distribution, police officers per capita, crime rates, incarceration rates, drug use, mental health indicators, veteran population, immigrant population, gender, tourist trade, or average hair length?
Once you start considering all of the other factors that have an impact, the waters get muddy fast. And it becomes evident why it is so hard to draw a straight line from A to B on issues like this. The numbers aren’t going to give you a clean airtight answer. They aren’t that direct because the real world is not.
Does this mean that we should look at the scatterplot at the top of this article and say it doesn’t mean anything? Do we have to have definitive proof that having more guns causes more gun deaths in order to act?
I say “no.”
I have worked with research and statistics long enough to understand that the most we ever get is an indicator of what is going on. There is always more information beyond what we’ve gathered or what we have access to. The best we can hope for is to steer our ship in the direction that seems to be the safest and most direct route to our destination based on the information available to us, and make adjustments along the way as more information becomes available.
So if there is a strong statistical relationship between the percent of the population that owns firearms in a state, and how many people in that state die gun-related deaths, is it not worthwhile to consider reducing the number of people in the state that have guns to see if that can reduce the number of people dying from those guns?
End Part One.
