The outcome test: equal hit rates do not certify equal thresholds

Each group is a list with guilt probabilities q, weights w and a threshold t; a person is stopped when \(q > t\). The stop rate and the hit rate (mean guilt among the stopped) are returned. Different signal laws and thresholds can give equal hit rates (Research.P2.OutcomeTest.infra_marginality) and equal thresholds can give unequal ones (equal_thresholds_unequal_hits); only under one signal law with a strictly increasing conditional mean do equal hit rates pin equal thresholds (uniform_equal_hits_equal_thresholds).

Usage

morie_outcome_test(groups)

Arguments

groups

A named list of lists, each with q, w and t.

Value

A data frame with one row per group: threshold, stop_rate, hit_rate.

References

Bowling B, Phillips C (2007). Disproportionate and discriminatory. Modern Law Review 70(6).

Examples

morie_outcome_test(list(A = list(q = c(0.3, 0.9), w = c(1, 1), t = 0.5),
                        B = list(q = 0.9, w = 1, t = 0.2)))
#>   threshold stop_rate hit_rate
#> A       0.5       0.5      0.9
#> B       0.2       1.0      0.9