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Benchmark tests are employed when testing for racial discrimination by police. Neil and Winship (2019) emphasize that such tests are threatened by Simpson’s paradox, but avoid analyzing the paradox causally. They consequently cannot elucidate the link between statistical quantities and discrimination hypotheses. Simpson’s paradox reveals that the s...
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Context 1
... although the treatment raises the probability of success in both subpopulations, men are more likely to recover than females even without the treatment. Figure 1 causally represents the example. The arrows indicate that Gender and Treatment are causes of success (the quantitative relationship is unspecified). ...
Context 2
... contrast, in figure 1, the effect of treatment (X) on success (Y ) is identified conditional on gender (M ), using the following formula: ...
Context 3
... whether one should condition on M -and, correspondingly, whether to consult the population or the M -partitioned subpopulations -depends on the causal model. Note that the causal model in figure 1 is statistically indistinguishable from one in which X causes M : any data generated by one model could have been generated by the other. This highlights the importance of causal information in determining whether to consider populations or subpopulations. ...
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