The role of collider bias in understanding statistics on racially biased policing

Even before the recent George Floyd case, there has been much debate about the extent to which claims of systemic racism are supported by statistical evidence. For example (Ross 2015) claims that unarmed blacks are 3.5 times more likely to be shot by police than unarmed whites when adjusting for relative differences in population size. However, (Fryer 2016) - formally published later as (Fryer 2019) - found that there was no such racial disparity when the data were conditioned on people being stopped by police, and there was a similar conclusion in (Patty and Hanson 2020) that was produced in direct response to public concerns about the Floyd case. In response to Fryer, (Ross, Winterhalder, and McElreath 2018) argued that Fryer's analysis was compromised because it was essentially an example of Simpson's paradox (Simpson 1951; Bickel, Hammel, and O'Connell 1975; Fenton, Neil, and Constantinou 2019) whereby conclusions based on pooled statistics are reversed when drilling down into relevant subcategories. A new paper (Knox, Lowe, and Mummolo 2020) explains why Simpson's paradox is not the only statistical explanation for the apparently contradictory conclusions of Ross and Fryer.