/(This was originally on my Facebook, responding to someone asking me to verify or disprove a meme claiming that women in America are 40x more likely to be killed by a gun. I took the opportunity to explain how the statistics both sides rely on are flawed, and can't really be improved.)/
Okay first I don't know where they got this number. According to http://www.washingtonpost.com/.../chart-the-u-s-has-far…, the US has 20x the average murder-by-gun rate (let's say MbGR to save time). They link to the UN Office of Drug & Crime's website, http://www.unodc.org/gsh/en/data.html, but none of the research there has any information specifically pertaining to firearms.
But that's okay, I've had this argument before, so I know that they're getting their numbers from the Small Arms Survey, http://www.smallarmssurvey.org/, a group that does research into gun ownership.
Your basic argument is that more guns corresponds to a high MbGR. Before we look into that claim, I'd like to point out a few concerns I have with the Small Arms Survey. First, they have low numbers for countries like Switzerland and Israel, where military members may own guns while not actively serving. The Survey doesn't count these guns at all, meaning that certain countries have unrealistically low ownership rates.
Additionally, certain other countries have been accused of modifying their numbers by filing crimes as non-homicides that in other nations would have been. In Argentina, unless it is known to be a malicious act, a murder by gun is not counted as a homicide. And in the UK, homicides don't get counted unless there is an associated conviction. This reduces the overall homicide rate by 15%, but reduces the firearm homicide rate further, because those deaths are often associated with unsolved gang crimes. (In example, the 2012 U.S. homicide rate was 4.7 in every 100,00. Using the U.K.'s system, that would drop to 2.6.) Further, the Survey measures the number of guns per 100 people, and I feel this is a rather useless metric. Far more useful would be to measure the percentage of the population carrying guns. The issue, from both sides, is whether or not a person has access to a gun, not whether they have access to more than one gun.
If you limit yourself to "developed" or "high-income" countries, you can paint the argument that fewer guns means fewer deaths. But that's a juvenile flaw of stats, to artificially limit your scope to support your argument. The issue here is that "developed" and "high-income" aren't being explicitly defined.
If we explicitly define them, say, by following the Organization for Economic Cooperation and Development definition of "developed", the picture suddenly changes. By including all developed nations, instead of just those in western Europe, the correlation changes. A higher rate of gun ownership goes hand-in-hand with fewer murders. (I want ot point out, this is without looking at different stats that more accurately reflect the issue, as explained in paragraphs 3-5.)
If you eliminate the U.S. as an outlier, which it matches the conditions for, causes the regression line to eliminate any relation. In non-U.S. developed nations, gun ownership and homicide have no apparent correlation.
If you count the actual numbers of gun ownership in countries like Switzerland, the correlation comes back, that more guns means fewer homicides. If you count the percentage of population who own guns, instead of the number of guns per capita, this correlation grows stronger.
There's the problem of endogeniety, which arises from using this kind of cross-sectional data. Imagine high-crime countries are the ones that adopt the most stringent gun control laws. What if gun control lowered crime rates, but not by enough to reduce rates to the same levels in countries that did not adopt the law? Looking across the countries, it would falsely appear that gun control led to higher crime. In actuality, crime rates in both countries have declined. To resolve the endogeniety problem, one must examine how the high-crime areas who adopt controls change over time, not just to themselves, but to other areas who did not institute controls.
In short, statistics are complicated, but make emotionally charged image macros like yours easy. If you take a more broad look at statistics, actual available information correlates more guns with fewer homicides. But this is flawed because of the endogenious nature of gun control policy and related statistics. Hope this explains things adequately.