I found only one other possible source of data for gun ownership, a proxy measure from internet news, The Daily Beast, which, from 2011-2012, tracked the number of NICS background checks for firearms by state. The primary problem with this data is that each state can create its own policies for tracking and reporting background checks, so it is difficult to compare between state rates. For example, they mention that Kentucky mandates monthly checks for concealed weapons, creating a presumably inflated number, and indeed, the largest of background checks relative to the other states. Further, this is only a measure of background checks, which neither considers illegal weapons, nor whether the individual actually purchased the weapon. One might propose that both of these are random sources of error, equally distributed through states. However, given the vast differences between states, I doubt this can be considered equally distributed variance. There is a 0.38 correlation between the 2001 BRFSS gun ownershp study, and the 2012 Daily Beast background checks data. This is a moderate correlation, indicating that the data may have some reasonable level of consistency in predicting actual gun ownership, especially if combined into an index score.
A third source of estimation about guns is gun laws themselves, while, as above, not a measure of gun ownership as such, but one might presume that a breadth of gun safety laws would be associated with fewer guns. A 2010 report from Mayors Against Guns, Trace the Guns, tracked 10 different specific laws across all states. In the data provided below, I compiled this list into an index score from 0-10, with 10 being the maximum number of gun-safety laws, and 0 being none. There is a -0.36 correlation between gun laws and number of background checks, and -0.73 correlation between gun laws and gun ownership The first correlation is moderate, indicating that the more gun safety laws that a state has enacted, the fewer background checks that were reported. This could indicate either greater subversion of gun laws where they are more tightly regulated, or less interest in purchasing guns in states with more gun safety laws. The latter correlation is quite strong, indicating that in states with more gun safety laws, far fewer people admitted to owning guns in the 2001 CDC survey, than in states where there were fewer gun safety laws. Combined, these three measures are reasonably consistent with each other, although clearly problems exist in attempting to use these to determine actual gun prevalence rates in states.
Firearm death data is more reliable, although problems still exist. The FBI tracks national crime data as it is reported by states, and hosts that data publicly at the Bureau of Justice Statistics Web site. Critics are concerned that this data includes both suicide and self-defense data. I do not know if this assertion is true. However, regarding self-defense, Gary Kleck, a well-known pro-gun activist and researcher, indicates that multiple studies provide a range of 6-12% of firearm homicides that were likely "justifiable" homicides. A second source of firearm death data, from the CDC Web site, filters out suicide data, thus includes only "true homicide" rates, although it likely includes self-defense. However, given the relatively small representation of self-defense homicides, the impact on the data is likely marginal. In the data provided below, I used the total firearm homicides from 2006-2010, to control for specific, outlier years of high or low homicide rates. There is a 0.96 correlation between the 2011 FBI homicide rates, and the 2006-10 CDC firearm homicide rates. This indicates an incredibly high level of consistency between these two separate data sources, thus a substantial likelihood of reliability that these measures accurately represent non-suicide, firearm homicide rates.
Measuring criminally-inflicted death is one approach to the gun safety discussion. However, what seems more relevant are the total number of gun deaths, not just homicide. In terms of a direct, linear correlation, there is no clear relationship between gun ownership, background checks, or gun laws, and firearm homicide (correlations less than abs(0.15)). However, the picture changes dramatically when you combine all firearm deaths: homicide, suicide, and accidental deaths. In this case, correlations for each of the three gun-prevalence measures range from 0.25 for the number of background checks, 0.69 for gun ownership rates, and -0.68 for gun laws (Graph 1). So while there is only a small relationship between the number of background checks and firearm death per state, there is a very strong positive relationship between measured gun ownership rates and firearm death (i.e., as gun ownership goes up, so do firearm deaths), and a very strong negative relationship between gun safety laws and firearm deaths (i.e., as states enact more gun safety laws, firearm deaths go down).
Graph 1: All Firearm Deaths, 2006-2010 vs. Gun Ownership, 2001
Despite the poor bivariate linear relationship between gun-prevalence variables and firearm homicide, controlling for other variables generates a far stronger relationship. Specifically, both poverty and inequality contribute to firearm homicide rates, and controlling for these at the state level allows a strong relationship to appear (I also tested for 2010 urbanization but there seems to be little relationship at the state-level). Explaining the 4-variable relationship is complicated (see below). However, the 3-variable relationship between poverty, gun ownership and firearm homicides is easy to show visually with a scatterplot (Graph 2). Below you can see two trendlines, one for state poverty levels below 15% (blue), and the other for poverty levels above 15% (green). The negative slope of the line representing wealthier states indicates that higher gun ownership rates are related to lower levels of firearm homicide rates (35 states). The positive slope of the line for poorer states indicates that higher rates of gun ownership are related to higher rates of firearm homicide (15 states).
So while there isn't a simple bivariate linear relationship between gun ownership and firearm homicide rates, there is clearly a relationship once you control for poverty, and even moreso once you also control for levels of inequality. Looking just at firearm deaths in total, you don't even have to control for poverty and inequality to demonstrate a very strong relationship between gun ownership and firearm death. (Poverty data is from the 2011 American Community Survey, 5-year estimate, as is the inequality data. Inequality here is measured by the ratio of the number of households in the state living on less than $15,000 to the number of households living on more than $100,000.)
Graph 2: Firearm Homicides, 2006-2010 vs. Gun Ownership, 2001, controlling for poverty
Linear equation for the 4-variable interaction:
Firearm Homicides = -0.073 - 0.678(Inequality) + 1.068(Poverty) - 0.258(Gun Ownership X Poverty) + 0.042(Gun Ownership)
This equation explains 47% of the variance, p<0.000, and the Gun Ownership X Poverty interaction variable is significant at p<0.042.
| State | Firearm Murder Rate | CDC Wonder, 2006-2010, Firearm Homicide (no suicide) | CDC, All Firearm Deaths, 2006-10 | Background Check Rate/Population | Gun Ownership, 2001 | TraceTheGuns, 2010, All Gun Laws Combined | Poverty, 2011 ACS, 5-year | Income Inequality: <15k:>100k, 2011 ACS, 5 year |
| Alabama | 7 | 17.1 | 8388 | 51.7 | 4 | 17.6 | 1.10452 | |
| Alaska | 0.022535211 | 3.3 | 18 | 11068 | 57.8 | 0 | 9.5 | 0.243236 |
| Arizona | 0.034730914 | 5 | 14.8 | 4944 | 31.1 | 0 | 16.2 | 0.633314 |
| Arkansas | 0.037722908 | 5.2 | 15.2 | 7968 | 55.3 | 1 | 18.4 | 1.362871 |
| California | 0.032748161 | 4.3 | 8.6 | 2842 | 21.3 | 8 | 14.4 | 0.363118 |
| Colorado | 0.014515808 | 2.1 | 10.9 | 7835 | 34.7 | 4 | 12.5 | 0.440104 |
| Connecticut | 0.026301063 | 2.4 | 5.1 | 6335 | 16.7 | 9 | 9.5 | 0.285685 |
| Delaware | 0.031180401 | 4.5 | 9.5 | 3127 | 25.5 | 5 | 11.2 | 0.385371 |
| Florida | 4.5 | 12.2 | 4081 | 24.5 | 2 | 14.7 | 0.722721 | |
| Georgia | 0.038191577 | 5.2 | 12.8 | 4447 | 40.3 | 2 | 16.5 | 0.721028 |
| Hawaii | 0.000735294 | 0.7 | 3 | 1208 | 8.7 | 9 | 10.2 | 0.311204 |
| Idaho | 0.010841837 | 1.2 | 12.3 | 8156 | 55.3 | 0 | 14.3 | 0.850145 |
| Illinois | 0.029381966 | 4.8 | 8.3 | 7937 | 20.2 | 8 | 13.1 | 0.483338 |
| Indiana | 0.028223319 | 3.8 | 11.2 | 6867 | 39.1 | 2 | 14.1 | 0.789097 |
| Iowa | 0.006237689 | 0.9 | 6.5 | 4681 | 42.8 | 7 | 11.9 | 0.709595 |
| Kansas | 0.025587101 | 2.7 | 10.5 | 6864 | 42.1 | 0 | 12.6 | 0.632461 |
| Kentucky | 0.023046785 | 3.2 | 13.2 | 58196 | 47.7 | 0 | 18.1 | 1.234068 |
| Louisiana | 0.088682991 | 10.1 | 19 | 6711 | 44.1 | 0 | 18.4 | 1.000716 |
| Maine | 0.009036145 | 1.1 | 8.6 | 6634 | 40.5 | 2 | 12.8 | 0.842797 |
| Maryland | 0.047107724 | 6.5 | 11 | 2231 | 21.3 | 8 | 9 | 0.241683 |
| Massachusetts | 0.018631643 | 1.7 | 3.5 | 3033 | 12.6 | 9 | 10.7 | 0.373835 |
| Michigan | 0.045528126 | 5 | 11.1 | 4125 | 38.4 | 7 | 15.7 | 0.755491 |
| Minnesota | 0.008107089 | 1.3 | 6.7 | 7844 | 41.7 | 5 | 11 | 0.443991 |
| Mississippi | 0.046511628 | 7.4 | 17.3 | 7082 | 55.3 | 1 | 21.6 | 1.558142 |
| Missouri | 0.046084488 | 5.3 | 13.6 | 8002 | 41.7 | 1 | 14.3 | 0.830348 |
| Montana | 0.007077856 | 1.6 | 15.3 | 12786 | 57.7 | 1 | 14.6 | 0.957503 |
| Nebraska | 0.023001095 | 2.2 | 8 | 4347 | 38.6 | 5 | 12 | 0.684228 |
| Nevada | 0.027767494 | 4.2 | 15.4 | 5047 | 33.8 | 0 | 12.9 | 0.468341 |
| New Hampshire | 0.004559271 | 0.6 | 7 | 8971 | 30 | 2 | 8 | 0.301071 |
| New Jersey | 0.030595996 | 3 | 5.1 | 938 | 12.3 | 10 | 9.4 | 0.262094 |
| New Mexico | 0.029140359 | 4 | 14.6 | 6491 | 34.8 | 0 | 19 | 0.940948 |
| New York | 0.022964186 | 2.7 | 5.1 | 1652 | 18 | 10 | 14.5 | 0.499277 |
| North Carolina | 0.035133718 | 4.6 | 12.2 | 4811 | 41.3 | 5 | 16.1 | 0.864843 |
| North Dakota | 0.008915305 | 0.6 | 8.7 | 11901 | 50.7 | 2 | 12.3 | 0.795394 |
| Ohio | 0.02981711 | 3.5 | 9.5 | 5102 | 32.4 | 1 | 14.8 | 0.812913 |
| Oklahoma | 0.03492402 | 4 | 13.9 | 9094 | 42.9 | 0 | 16.3 | 1.003063 |
| Oregon | 0.010441138 | 1.4 | 10.8 | 6398 | 39.8 | 5 | 14.8 | 0.701096 |
| Pennsylvania | 0.037002047 | 4.2 | 10.6 | 7218 | 34.7 | 5 | 12.6 | 0.629322 |
| Rhode Island | 0.004748338 | 1.6 | 4.4 | 2106 | 12.8 | 7 | 12.8 | 0.560825 |
| South Carolina | 0.048216216 | 5.5 | 13.8 | 6322 | 42.3 | 2 | 17 | 1.00953 |
| South Dakota | 0.006142506 | 0.8 | 9.1 | 9977 | 56.6 | 0 | 13.8 | 0.890987 |
| Tennessee | 0.038449417 | 5.3 | 15.2 | 7638 | 43.9 | 2 | 16.9 | 1.044275 |
| Texas | 0.027797662 | 4.1 | 10.7 | 5261 | 35.9 | 0 | 17 | 0.61675 |
| Utah | 0.009406657 | 1.1 | 9.7 | 7827 | 43.9 | 3 | 11.4 | 0.425006 |
| Vermont | 0.006389776 | 0.9 | 9.3 | 5227 | 42 | 1 | 11.3 | 0.594292 |
| Virginia | 0.02599675 | 3.5 | 10.6 | 5119 | 35.1 | 4 | 10.7 | 0.341807 |
| Washington | 0.011747212 | 1.8 | 8.9 | 7157 | 33.1 | 2 | 12.5 | 0.419157 |
| West Virginia | 0.023205613 | 2.7 | 13.9 | 11670 | 55.4 | 0 | 17.5 | 1.528704 |
| Wisconsin | 0.014067171 | 1.9 | 8.2 | 8436 | 44.4 | 2 | 12 | 0.615174 |
| Wyoming | 0.019503546 | 1.2 | 16 | 10517 | 59.7 | 2 | 10.1 | 0.456652 |
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