Outcome tests and veil of darkness

Three separate meanings of an outcome

any_action, arrest and outcome_linked_to_object measure different things. An action need not be an arrest, and a recorded link to the search object is a separate source field. Searchlight preserves disagreements and unknown values. Wilson intervals describe a binary outcome among searches with that outcome observed. Unknown ethnicity appears in the descriptive table.

hits <- sl_hit_rates(records, by = character())
display <- hits[hits$ethnicity_5 %in% c("Black", "White", "Unknown"), ]
knitr::kable(as.data.frame(display)[c("ethnicity_5", "outcome", "observed",
  "missing_outcome", "hit_rate", "conf_low", "conf_high")], digits = 3)

ethnicity_5	outcome	observed	missing_outcome	hit_rate	conf_low	conf_high
Black	any_action	58	0	0.379	0.266	0.508
Unknown	any_action	2226	54	0.357	0.337	0.377
White	any_action	2138	3	0.355	0.335	0.376
Black	arrest	58	0	0.190	0.109	0.309
Unknown	arrest	2226	54	0.132	0.119	0.147
White	arrest	2138	3	0.196	0.179	0.213
Black	outcome_linked_to_object	58	0	0.862	0.751	0.928
Unknown	outcome_linked_to_object	2234	46	0.941	0.931	0.950
White	outcome_linked_to_object	2141	0	0.917	0.904	0.928

Each outcome has a separate logistic comparison of Black versus White searches, with force and object fixed effects. A constant control is omitted and named in the output. Other ethnicities and unknown ethnicity are excluded only from this specified pairwise model, with counts retained in the exclusion table. An unstable, aliased or separated model withholds its Wald interval instead of printing a misleading extreme estimate.

coefficients <- attr(hits, "coefficients")
knitr::kable(coefficients[c("outcome", "odds_ratio", "conf_low", "conf_high",
  "n", "status")], digits = 3)

outcome	odds_ratio	conf_low	conf_high	n	status
any_action	1.082	0.630	1.858	2196	estimable
arrest	0.991	0.506	1.942	2196	estimable
outcome_linked_to_object	0.585	0.271	1.263	2199	estimable

knitr::kable(coefficients[c("outcome", "omitted_constant_controls")])

outcome	omitted_constant_controls
any_action	force_id
arrest	force_id
outcome_linked_to_object	force_id

knitr::kable(attr(hits, "exclusions"))

outcome	included	unknown_ethnicity	other_ethnicity	pair_missing_outcome_or_control
any_action	2196	2280	178	3
arrest	2196	2280	178	3
outcome_linked_to_object	2199	2280	178	0

Hit rates condition on being searched. Differences in selection, the distribution of unobserved risk, recording and the meaning of outcomes can all affect them. Equal hit rates need not imply equal decision thresholds, and differing hit rates do not by themselves establish discrimination. Repeated searches also challenge independent-event intervals when identifiers for clustering are unavailable. These interpretation limits are related to the outcome-test framework of Knowles, Persico and Todd (2001), doi:10.1086/318603 (open working-paper version).

A time-quality screen is mandatory

The darkness design excludes every force-month marked unreliable or lacking a timestamp audit. Source-clock midnight and London-clock midnight are both checked upstream, so a date-only UTC timestamp shifted to 01:00 in summer cannot pass. Passing this screen does not prove that times are accurate.

knitr::kable(sl_timestamp_quality(records)[c("force_id", "month",
  "gating_midnight_share", "time_reliable")], digits = 3)

force_id	month	gating_midnight_share	time_reliable
dyfed-powys	2026-05	NA	FALSE
dyfed-powys	2026-06	NA	FALSE
dyfed-powys	2026-07	NA	FALSE
west-yorkshire	2026-05	0.010	TRUE
west-yorkshire	2026-06	0.010	TRUE
west-yorkshire	2026-07	0.014	TRUE

date_only <- records[1:10, ]
day <- as.Date(date_only$date, tz = "Europe/London")
date_only$date <- as.POSIXct(paste(day, "00:00:00"), tz = "Europe/London")
date_only$date_raw <- format(date_only$date, "%Y-%m-%dT%H:%M:%S%z")
attr(date_only, "contract")$timestamps <- sl_timestamp_quality(date_only)
refused <- sl_veil_of_darkness(date_only)
#> Excluded 1 unreliable force-month(s).
knitr::kable(as.data.frame(refused)[c("odds_ratio", "n", "status")])

odds_ratio	n	status
NA	0	insufficient outcome/predictor variation

knitr::kable(attr(refused, "excluded_force_months"))

force_id	month	time_reliable
west-yorkshire	2026-05	FALSE

Local clock time, sunset and civil twilight

Solar events are calculated for the published location and date with suncalc, using Europe/London. For each distinct location and year, the annual earliest and latest evening twilight define the intertwilight clock window. This permits both daylight and darkness at comparable clock times across the year. The default defines darkness after civil dusk and removes the ambiguous sunset-to-dusk interval. twilight = "sunset" provides an explicit alternative. Missing locations are excluded, never imputed from a force centroid.

The logistic outcome is membership of the comparison ethnicity among the selected pair. Predictors include darkness, a natural spline of clock time (or a linear term with too few distinct times), weekday, calendar month and force where these vary. Every exclusion step and the final analysed rows can be inspected.

darkness <- sl_veil_of_darkness(records)
knitr::kable(as.data.frame(darkness)[c("odds_ratio", "conf_low", "conf_high",
  "n", "dark_stops", "daylight_stops", "status")], digits = 3)

odds_ratio	conf_low	conf_high	n	dark_stops	daylight_stops	status
593.664	0.295	1195173	648	36	612	estimable

knitr::kable(attr(darkness, "steps"))

stage	remaining
input	4657
reliable force-month time	4657
valid location and instant	4496
known comparison pair	2122
annual intertwilight clock window	747
unambiguous daylight or darkness	648
design window	648

knitr::kable(attr(darkness, "excluded_force_months"))

force_id	month	time_reliable

This short summer sample offers a restricted seasonal comparison and may have few Black records in parts of the design. A finite fitted interval is not evidence that activity patterns, daylight overlap or model controls are adequate. An undefined result reports a limitation of the available design, not no disparity. In this sample, only 36 of 648 retained searches occur in darkness. The extremely wide adjusted interval makes the point estimate unsuitable as a stable substantive finding; more seasonal coverage and an explicit assessment of daylight overlap are needed before interpreting this design.

cat(paste("-", attr(darkness, "assumptions")), sep = "\n")
#> - Darkness reduces visibility of ethnicity before the stop.
#> - Activity, exposure and police deployment are comparable after controls.
#> - Reporting does not vary differentially by darkness and ethnicity.
#> - Times, locations and self-defined ethnicity are measured adequately.
#> - Enough daylight/darkness overlap remains after controls.
#> - Repeated events and unmeasured selection can violate model independence.
#> - A vehicle-stop method needs justification for pedestrian searches.

The optional design = "dst" restricts observations to three weeks on each side of the UK clock changes, adding transition and running-day controls. Clock-change dates come from the Europe/London time-zone rules, not fixed calendar dates. The tests verify 29 March and 25 October 2026 and the one-hour local-clock change. The bundled May-July sample has no observations in these windows, so it cannot support a DST comparison.

dst <- sl_veil_of_darkness(records, design = "dst")
knitr::kable(as.data.frame(dst)[c("odds_ratio", "n", "status")])

odds_ratio	n	status
NA	0	insufficient outcome/predictor variation

knitr::kable(attr(dst, "steps"))

stage	remaining
input	4657
reliable force-month time	4657
valid location and instant	4496
known comparison pair	2122
annual intertwilight clock window	747
unambiguous daylight or darkness	648
design window	0

Grogger and Ridgeway (2006; doi:10.1198/016214506000000168), listed in selected publications by Ridgeway, developed the veil-of-darkness approach for vehicle stops. Its use for pedestrian stop and search requires separate justification: ethnicity may be visible before the decision despite darkness, pedestrian and police activity can vary by light, and selection or reporting can change. These observational diagnostics do not establish a causal effect or, alone, establish discrimination.

Astronomical field names and the time-zone interface were verified against the suncalc package and manual.