In the terrible aftermath of the Las Vegas massacre people have been urgently trying to explain it. Some have put race at the centre of their explanations. Mass shootings, they argue, reveal something sinister in the heart of whiteness.

A Newsweek headline asserted

White men have committed more mass shootings than any other group.

At CNN a commentator opined that “America has silently accepted the rage of white men” and diagnosed mass shootings as “a white man’s problem”. Elle magazine told us “white men’s violence is the violence we’ve normalized” and that “white men’s rage … is burning down the world”.

There is no shortage of violence committed by white men. Their violent behaviour is sometimes viewed differently from that committed by other groups. But is it true there is a link between whiteness and mass shootings?

Mother Jones magazine has collated a database of American mass shootings that extends from 1982 to now. It contains a grievous record of 91 crimes where a shooter killed at least four victims. The race of the shooter was coded as unknown or unclear in three cases. Of the 88 remaining shootings, 51 (58%) were committed by whites.

Sure enough, the statistically typical mass shooter is a white man. But is that evidence for a meaningful link between race and this form of violence? Not if we remember that whites are statistically typical Americans.

According to the 2016 US census, 61.3% of Americans were “white alone, not Hispanic or Latino”. The proportion of white mass shooters is therefore almost exactly what we would expect it to be if whites and non-whites committed mass shootings at the same rate. Indeed it is (trivially) lower.

This graph plots the proportion of the 88 mass shooters in census-based racial groups against each group’s proportion in the US population. The dotted line represents equality between the two proportions. Groups falling above or below the line have committed mass shootings above or below the rate expected given their representation in the population. Generally speaking, groups defined by race have committed these outrages at approximately the same rate, given their relative size.

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Perhaps the surprising fact that white mass shooters are not proportionally over- represented is due to the long period covered by the Mother Jones database. Are more recent shootings whiter? The answer is no: of the 27 shootings in the past five years where the murderer’s race is recorded, 10 (37%) were committed by white men.

This is not to say mass shootings committed by white men might not be distinctive in some respects. Nor does it preclude a racial double standard in how their atrocities are reported or perceived compared to those of others. But it does indicate that mass shootings themselves are not an inherently white problem.

Illusory correlation

Why is it then, that many people see a causal connection between whiteness and mass killings? Part of the answer may come from the searing recency of the Las Vegas killings and their white perpetrator. Part of it may come from the vexed links between race, US politics and gun culture. And part of the answer may be found in the typical colour contrast between mass shootings and mass killings committed by Islamic extremists.

Another part of the answer may involve a bias in how people judge associations between two phenomena. Humans often perceive “illusory correlations” where none exist objectively. There is evidence from cognitive psychology this is especially likely when one of the two phenomena is highly prevalent.

In a study published in 1998, participants were given information about 60 fictitious patients. Each patient was described as either having or not having a made-up disease (such as van Ork’s disease) and as either having or not having a made-up symptom of the disease (such as swollen joints). Participants were then asked to judge how strongly the symptom and the disease were correlated.

Participants were assigned to several different experimental conditions, which differed in how prevalent the disease was among the fictitious patients. But when it came to the symptom, in two of these conditions there was no correlation at all between symptom and disease, meaning the symptom was equally likely to occur whether the disease was present or absent.

In the low prevalence condition the disease was present 30% of the time. The symptom was present in half of these cases and absent in the rest. In the high prevalence group the disease was present 70% of the time. Again, the symptom was present in half of the disease cases and also in half of the no disease cases.

Participants in the low prevalence condition group correctly judged that there was no relationship between symptom and disease. But those in the high prevalence group saw a correlation between symptom and disease that simply did not exist.

The likely explanation is that participants paid special attention to cases where the symptom and disease co-occurred. This happened only nine times in the low prevalence condition, but 21 times in the high prevalence condition. Seeing symptom and cause occurring together so often led people to believe they were associated, although they were not.

The analogy to race and mass shootings should be clear. The shootings are the symptom and, in the eyes of some, whiteness is the disease that causes it. There is no actual correlation between being white and being a mass shooter in the US, but because whiteness is common we see many examples where the symptom and the disease go together. As a result, mass shootings are seen as linked to whiteness.

In this case, the diagnosis is incorrect. The problem is not white men, but men. So, not race, but gender. Only two of the 91 mass shootings were perpetrated by women.