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This is an important comment by @sndurlauf and @heckmanequation (thread) https://twitter.com/BrendanNyhan/status/1287089470152552450
Here's the key point: bias in initial contacts can lead to misleading inferences based on use of force conditional on contact:
Dan OFlaherty and I made this point in #ShadowsofDoubt as follows:
An earlier post in response to a piece by @m_sendhil in the @nytimes also discussed the issue: http://rajivsethi.blogspot.com/2015/10/threats-perceived-when-there-are-none.html
And here's a follow-up post by @StatModeling that explained the problem quite clearly: https://statmodeling.stat.columbia.edu/2015/10/21/its-all-about-the-denominator-and-rajiv-sethi-and-sendhil-mullainathan-in-a-statistical-debate-on-racial-bias-in-police-killings/
And some notes of the Fryer paper from back when it was still unpublished: http://rajivsethi.blogspot.com/2016/07/police-use-of-force-notes-on-study.html
And finally, a different problem with inferences based on data that aggregates across locations, based on Simpson's paradox: http://rajivsethi.blogspot.com/2016/07/a-fallacy-of-composition.html
Which is empirically important because scale differences across locations are so large (the table is also from #ShadowsofDoubt):
With this one in the original paper, which clearly seems to suggest that his empirical findings contradict prior claims of discrimination based on video evidence:
And this from the @nytimes report on the study:
Dan and I discussed these issues at length in #ShadowsofDoubt, here's a passage on the Fryer study:
The comments made by Officer Leon Lashley after the Gates arrest illustrate perfectly why the point made by @sndurlauf and @heckmanequation is not just logically sound but also empirically valid: http://rajivsethi.blogspot.com/2009/11/leon-lashley-and-gates-arrest.html
Further discussion of the relevance of this case in #ShadowsofDoubt:
The point is much more general of course:
