The veil-of-darkness contrast as a sign test with an identified bias ratio

Stops of each group are counted in daylight and in darkness within the inter-twilight window, where the same people drive under both conditions. With latent exposures and dark propensities common to both conditions, the ratio of daylight to darkness odds of group \(g\) against the reference is exactly the ratio of visible-race factors \((1+\delta_g)/(1+\delta_{ref})\) (Research.P2.Veil.odds_ratio_identifies_bias): the exposures cancel, the relative bias is point-identified and its sign is the sign of the daylight-minus-darkness share difference (share_sign). A differential change of who drives by light condition, \(\kappa_g\), is observationally a bias (exposure_shift_confounds); passing it divides the ratio out.

Usage

morie_veil_of_darkness(
  day,
  night,
  reference = names(day)[1],
  exposure_shift = NULL
)

Arguments

day, night: Named counts of stops by group in daylight and in darkness.
reference: Name of the reference group.
exposure_shift: Optional named factors \(\kappa_g\) by which daylight exposure differs from darkness exposure; the bias ratio is divided by \(\kappa_g/\kappa_{ref}\).

Value

A data frame with one row per group: the two counts, the daylight and darkness shares, bias_ratio (relative visible-race factor against the reference), sign ("higher", "lower" or "equal") and, with exposure_shift, bias_ratio_adjusted.

References

Grogger J, Ridgeway G (2006). Testing for racial profiling in traffic stops from behind a veil of darkness. JASA 101(475).

Examples

morie_veil_of_darkness(day = c(white = 400, black = 200), night = c(white = 300, black = 100))
#>       group day night share_day share_night bias_ratio   sign
#> white white 400   300 0.6666667        0.75        1.0  lower
#> black black 200   100 0.3333333        0.25        1.5 higher