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BJS says there are 12,501 local police departments. Just eyeballing the numbers but that looks like more than 5%-10% of the 17,000 agencies. So we're getting reporting from about 6% of local police departments if we assume all 750 reportees were local police departments.
The issue isn't % of agencies, but the % of officers covered by what is being reported. Local poice "Agencies" are an ill defined abstraction of widely varying size from 1 person to 40,000. As shown in the BJS report in Tables 15 and 17, about 50% of agencies have less than 10 sworn employees total, including the pencil pushers that don't do any actual arresting. That means a huge % of "agencies" have 1-2 people doing any arresting and serve tiny communities where officer related shooting don't occur, so there is nothing to report.
These 50% of "agencies" employ only 4.5% of the officers and account for only 1.9% of the arrest related homicides being reported. A mere 300 agencies (2.1% of all agencies) employ the majority of police officers and are responsible for 63.4% of the reported arrest related homicides. IOW, the larger agencies are doing most of the reporting of officer inflicted homicides, and these agencies cover the overwhelming majority of officers. Thus, if the 750 agencies reporting were mostly the larger police agencies (and the data suggest it is) then it would cover the vast majority of local police officers, and thus account for the vast majority of deaths by cop. IOW, your 6% of agencies stat is meaningless and tells us nothing relevant to the validity of the numbers in the report.
In addition, the larger agencies doing the vast majority of the reporting of deaths are large precisely because they serve densely populated urban areas, which in turn are disproportionately black and where the majority of shootings of blacks occur. IOW, most of the missing data is coming from small rural areas serving mostly white populations, thus it is most likely that it is deaths of whites that occassionally occur in these areas that are under-reported and thus producing a 3:1 black:white ratio at the national level that is slightly inflated, if anything.
The fact that difference agencies, from bjs, to FBI, to the CDC, employ varied data collection methods and reach highly similar estimates supports the validity of these numbers and that while not exact, are rather close approximations. This is a basic principle of showing measurement validity.
Unless of course they are all getting their data from the same self-reporting information depositories.
Correct, in a fictional world of your invention where the CDC uses self reports by agencies to the FBI. But that is not the real world. The CDC uses official death certificates collected at the State level, and they also collect emergency room records. Each method is independent and all converge upon a ratio of between 2:1 and 4:1 in black:white rates of death or severe injury by police during the period in which the BJS data show a 3:1 ratio.
Larger samples are likely to produce smaller rather than larger differences in rate of deaths. As a matter of basic sampling probability, smaller samples usually inflate the difference in any aggregate stat between two groups. For example, in a room of 100 people, if you want to know the difference in height between males and females, if you only use one randomly picked person of each gender, they are likely to differ in height by more than the true avg difference of all the people.
Cite?
Basic statistical literacy.
In your male/female height ratio example I'd think there'd be a 50/50 chance for the random people to differ by more or less than the avg because isn't that kind of the definition of "avg?"
No, there is not a 50/50 chance or over vs. under estimation. Over estimations of group differences are more likely, with small samples.
Just look at the graph below:
The true difference between the groups is the distance between the 2 vertical line denoting the medians. There are many more random pairs of points (one from under each gender curve) where the distance between them is larger than that true median distance, than there are pairs where the distance is smaller. Only in the purple region in the middle are random pairs equally likely to over or under estimate the median difference. For all males in the blue area, randomly paired females will overwhelmingly tend to over estimate how much taller men are in general. Likewise, for all the women in the pink area, randomly paired males will overwhelmingly likely over-estimate how much shorter women are in general.
3:1 is actually much smaller than the ratio predicted if cops were reacting to legit deadly threats. The OP referred to a 3:1 ratio in overall violent crime,.but includes things like "simple assault" which can be just threat of violence or two guys in a bar fight. Since deadly threat is what cops should be reacting to, it makes more sense to look at rates of committed deadly crime, namely homicides where the ratio is 8:1 in the rates among blacks compared to whites.
IOW, even if the shootings by cops data was extremely biased in underestimating the size of the black:white ratio, and the true ratio was almost 3 times as large as the current data shows, it would still be highly coherent with what is expected by cops reacting non-racistly to deadly threats they encounter.
wat
Pretty simple. Serious criminal violence (such as homicide) is not just 3 times, but 8 times more common among blacks than whites. Thus, if cops were completely ignoring race and just responding to probable violent threat, they could easily be about 8 times more likely to use force, including deadly force, against blacks. The 3:1 ratio of arrest deaths is actually much lower than predicted based upon cops responding non-racistly to assessed violent threats. If anything, the data are more consistent with cops giving blacks more benefit of the doubt in ambiguous situations.
In addition, there is the data I posted in another thread showing that blacks are many many times more likely to shoot at cops, and in fact, the ration of how often blacks are shot relative to how often they shoot at cops is lower than that same ratio for whites. IOW, if you shoot at the cops, you are much more likely to be shot and killed by the cops if you are white than if you are black.
We're talking about Axulus' data in his op not about something you may have posted somewhere else at some other time.
We are talking about an engaging in an honest and rational analysis of the OP data in relation to the larger question of the reasons for the racial disparity in deaths by cops. Such an analysis requires consideration of any relevant data. The much higher rates of shooting at cops by blacks is directly relevant to whom cops are more likely to shoot at and why. The fact that rates of violence against other people and rates of violence against cops both tell the same story and both support that the disparity who cops kill is fully accounted for by cops acting rationally and non-racistly to real threats. Cops may and do sometimes act irrationally to non-real threats, but that is true for across race and it just inflates the total raw numbers of use of force. There is no evidence that any of the racial disparity in question is a product of differential rates of irrational use of force against blacks vs. whites.
