James P. Scanlan, Attorney at Law

Ferguson, Missouri Arrest Disparities

(Mar. 23, 2015)

(Draft)

Prefatory note added March 26, 2015: An Addendum to this page addresses certain problems in the calculation of an estimated effect size in circumstances where a population is used as the denominator in the calculation of an outcome rate while the numerator is affected by the time frame chosen (and a like issue). The points made there call into question the illustrations in the tables below.  But, believing that there is nevertheless some illustrative value in the tables, I leave the page itself unchanged, save for this note and the Addendum. 

Prefatory note added April 12, 2016:  Subsequent developments regarding the particular situation of Ferguson, Missouri, involve the filing of a suit against Ferguson by the Department of Justice in February 2016, discussed in my “Things DoJ doesn’t know about racial disparities in Ferguson,” The Hill (Feb. 22, 2016).  A proposed consent decree was submitted by the parties on March 16, 2016.  On April 12, 2016, I filed a submission suggesting that the court not enter the decree until the Department of Justice addressed certain measurement issues.  Also, I the Department of Justice’s actions regarding Ferguson figure significantly into my requests that certain institutions or organizations, among other things, explain to the Department of Justice and other arms of the government that reducing the frequency of an outcome tends to increase, not decrease, relative demographic differences in experiencing the outcome and the proportions groups most susceptible to the outcome make up of persons experiencing the outcome.  See my letters to Chief Data Scientist of White House Office of Science and Technology Policy (Sept. 8, 2015), American Statistical Association (Oct. 8, 2015), Council of Economic Advisers (Mar. 16, 2016), Population Association of America and Association of Population Centers (Mar. 29, 2016), Consortium of Social Science Associations (Apr. 6, 2016).

***

This is a draft of a subpage to the Discipline Disparities page of jpscanlan.com that will address various issues in the Department of Justice’s March 4, 2015 report on racial differences in outcomes in the traffic enforcement and court system in Ferguson, Missouri, and related issues about the measurement of things like racial differences in arrest rates.  This subpage does not fit perfectly as a subpage to the Discipline Disparities page.  But it does involve  the same misunderstanding on the part of the Department of Justice regarding the effects of reducing adverse outcomes rates on relative demographic differences and the proportions disadvantaged groups make up of persons experiencing those outcome found in Department’s actions regarding school discipline issues. 

Certain of those issues are addressed in my March 9, 2015 letter to the Department of Justice and the City of Ferguson, Missouri.  The letter explains that, contrary to the premise of the report that reducing the frequency of adverse outcomes resulting from those practices will tend to reduce the proportion African Americans comprise of persons experiencing those outcomes, reducing the frequency of such outcomes will tend to increase the proportion African Americans comprise of persons experiencing those outcomes.  That is, for example, increasing the number of missed court appearances necessary to trigger issuance of an arrest warrant will tend to increase the proportion African Americans comprise of persons against whom such warrants are issues – just as lowering a test cutoff will tend to increase relative differences in pass rates and, correspondingly, increase the proportion the lower-scoring group comprises of persons failing the test.  See Table 1 of “Race and Mortality Revisited,” Society (July/Aug. 2014), and Table 1 of my amicus curiae brief in Texas Department of Housing and Community Development, et al. v.  The Inclusive Communities Project, Inc., Supreme Court No. 13-1731 (Nov. 17, 2014).  See also note 18 at page 24 of the latter document.

This page will eventually address various measurement issues in the report and other matters relating to the appraisal of differences in the circumstances of blacks and whites in Ferguson.

For the present, I note that apparently the state of Missouri, and certain discussions of perceived arrest disparities in Ferguson, rely on a so-called Disparity Index (DI), which is the ratio of the proportion a disadvantaged group comprises of persons arrested to the proportion the group comprises of the population.  In discussing this issue, I do not mean to suggest that there is any valid measure of difference of the strength of the forces causing outcome rates of advantaged groups and disadvantaged groups to differ other than the EES (which I describe in "Race and Mortality Revisited" and the amicus curiae brief, among many other places).  Nor do I mean to suggest that there is much value trying to make comparisons of the size of gross arrest rate differences between advantaged and disadvantaged groups across jurisdictions (given that the extent of conduct warranting arrest among advantaged groups will vary from jurisdiction to jurisdiction as will the extent  of conduct warranting arrest among disadvantaged groups) or much value in examining gross arrest disparities even with respect to particular jurisdictions (since a very large proportion, and possibly, all of an observed disparity will be explained by differences in conduct).  But it is nevertheless essential to understand the points illustrated here in order to recognize how unsound are standard analyses of such differences (which analyses consume substantial resources and underlie a host of misguided corrective measures).  It is also essential to understand these points in order to conduct sound analyses of demographic differences in outcome rates in any circumstance where such analyses might in fact be useful.

As discussed in Section I.B of the above amicus brief (at 23-27), analyses of demographic differences based on the proportion a group comprises of the pool and the proportion it comprises of persons experiencing and outcome are never sound, and, in fact, one cannot make a sound judgment of the strength of the forces causing differences between outcome rates on such basis (since one needs actual outcome rates in order to make such judgments).  But the Ferguson situation highlights a particular problem of any analysis that in some manner evaluates the situation of the disadvantaged group compared with the entire population (of which the disadvantaged group is a part and sometimes very large part) rather than compared with the advantaged group (an issue discussed on both the IDEA Data Center Disproportionality Guide and the Keep Kids in School Act subpages of the Discipline Disparities page). 

The tables below are based is on data made available by a November 19, 2014 USA Today article titled “Racial gap in U.S arrest rates: ‘Staggering disparity.’”  The article provided information on black and non-black arrest rate rates, and black and non-black persons in the relevant populations, for 3358 police (or sheriff’s) departments.   The information enables one to calculate the ratio of the arrest rate of black persons to the arrest rates of other persons (Rate Ratio or RR) and the ratio of the proportion blacks comprise of persons arrested to the proportion blacks comprise of the population (Disparity Index or DI), as well as the EES (for estimated effect size), which is the measure that, in the amicus curiae brief, "Race and Mortality Revisited" and elsewhere, I maintain is the only sound measure of the strength of the forces causing outcomes rates of advantaged groups and disadvantaged groups to differ. 

Initially, I note that analyses based on comparisons of the disadvantaged group’s rate with the rate of all other persons, rather than the rate of the advantaged group, is a problem for all measures, including the Rate Ratio and the EES.  But in the case of the Disparity Index (as well as the measures identified as (c) (essentially the DI – 1) and (d) on the IDEA Data Center Disproportionality Guide subpage, there also exists a problem in fact that the rate against which the disadvantaged group rate is compared is importantly influenced by the disadvantaged group’s own rate and the proportion the disadvantaged group comprises of the entire population.   Ferguson itself highlights the problem.  For, inasmuch as blacks comprise 67% of the population, the Disparity Index can never exceed 1.49.  By contrast, where a disadvantaged group comprises only 10% of the population, the Disparity Index can reach 10.0.

In the USA Today database, 3365 police (or sheriff’s) department have some black arrests and a black arrest rate that is greater than the non-black arrest rate.  In terms of EES, which is the only sound measure of the size of the disparity, Ferguson (EES = .62 standard deviations) was the 1435^th highest.  An EES of .62 reflects a situation where approximately 27% of the disadvantaged group is above the mean for the advantaged group (that is, with respect to avoidance of the adverse outcome).  The figure is the same as that shown for the black and white male rates of suspension or greater punishment in Table 1 of the Discipline Disparities page.

See Table 12 (at 69) of the January 2015 University of California Methods Workshop “The Mismeasure of Discrimination”  for examples of the meaning of various EES values in similar terms. 

In terms of the Rate Ratio, Ferguson (RR= 2.82) was 1585^th highest.  That RR, a function of the frequency of arrests and the EES, will tend to increase if, in compliance with recommendations in the DOJ report, arrests in Ferguson are generally reduced.  In terms of Disparity Index, Ferguson (DI = 1.27) was the 3043th highest.  The low ranking is a function of Ferguson’s RR and the high proportion blacks comprise of the population of Ferguson.  Like the RR, the DI will tend to increase if in compliance with the DOJ recommendations, arrests are generally reduced. 

The first and second table below show the way that that police departments that have essentially the same racial arrest rate disparity as the Ferguson Police Department according to a valid measure (the EES) vary widely according the Rate Ratio and the Disparity Index by which disparities are commonly appraised.  The third and fourth tables show the way that police departments that have essentially the same racial arrest rate disparity as the Ferguson Police Department according to the Rate Ratio or the Disparity Index vary widely according to the EES.  The first two tables can be compared to Tables 1 and 2 of the IDEA Data Center Disproportionality Guide subpage (versions of which appear as Table 23 and 24 (at 98-108) of the October 2014 Maryland Population Research workshop), save that the latter tables are based on hypothetical data and the tables below are based on actual data).  The IDEA Data Center Disproportionality Guide subpage tables may be reproduced using same database used in the Keep Kids in School Act subpage of the Discipline Disparities page.

Table 1A below is an abbreviated version of a larger Table 1 found on the Large Ferguson Tables document, where the 108 departments with approximately the same EES as Ferguson (EES = .61 to .63) are ranked by RR (with values that range from 1.86 to 7.98).  The abbreviated table shows only the departments with the two lowest and two highest RR values, along with Ferguson and one other department.  I include the Montgomery County, MD Police Department (MCPD) because the department has essentially the same EES (and involves the same jurisdiction) as the Montgomery County, MD Sheriff’s Department (MCSD) (which has the second highest RR for a department with an EES essentially equivalent to that of the Ferguson Police Department).  As would be expected, the MCSD, with far few arrests, has a much higher RR than the MCPD. Though the pattern is not present in Table 1A, one will observe in Table A that lower the black arrest rates tend to be associated with higher RRs.

Table 1A.  Police departments with essentially the same EES value for differences between black and white arrest rates as the Ferguson Police Department, ranked by black to non-black arrest rate ratio (RR), with disparity index (DI) shown (abbreviated)

 

police department	state	Pop	Blk Perc Pop	Blk Perc Arr	Blk Arr Rt	NonBl Arr Rt	B/NB Ratio	Disparity Index	EES
Eureka Police Department	CA	27,191	1.89%	3.45%	513.62	276.76	1.86	1.83	0.63
Byhalia Police Department	MS	1,302	44.85%	61.80%	457.19	229.81	1.99	1.38	0.63
Ferguson Police Department	MO	21,203	67.43%	85.37%	186.12	66.03	2.82	1.27	0.62
Montgomery County Police Department	MD	971,777	17.22%	44.74%	65.2	16.75	3.89	2.60	0.62
Montgomery County Sheriff's Office	MD	971,777	17.22%	58.55%	7.81	1.15	6.78	3.40	0.63
Muscogee County Marshal Office	GA	189,885	45.50%	86.90%	2.78	0.35	7.98	1.91	0.62

 

Table 2A is an abbreviated version of Table 2 on the Large Ferguson Tables document, which is based on the same EES values as Table 1, but with the jurisdictions ranked by DI (with values that range from 1.07 to 4.06).  In this case the abbreviated table is limited in same manner as Table 1A, but without the additional jurisdiction.  Notice that Seat Pleasant Maryland Police Department reflects an extreme example of the manner in which the high proportion blacks comprises of the population limits the DI.  In this case, the maximum DI for Seat Pleasant would be 1.10.

Table 2A.  Police departments with essentially the same EES value for differences between black and white arrest rates as the Ferguson Police Department, ranked by disparity index (DI), with black to non-black arrest rate ratio (RR) shown (abbreviated)

 

police department	state	Pop	Blk Perc Pop	Blk Perc Arr	Blk Arr Rt	NonBl Arr Rt	B/NB Ratio	Disparity Index	EES
Seat Pleasant Police Department	MD	4,542	91.04%	97.49%	75.21	19.66	3.83	1.07	0.62
Lithonia Police Department	GA	1,924	85.19%	94.63%	139.72	45.61	3.06	1.11	0.61
Ferguson Police Department	MO	21,203	67.43%	85.37%	186.12	66.03	2.82	1.27	0.62
Tuscola County Sheriff's Office	MI	55,729	1.14%	4.29%	61.51	15.81	3.89	3.77	0.61
Phelps County Sheriff's Department	MO	45,156	2.23%	9.07%	47.62	10.90	4.37	4.06	0.62

 

Table 3A below is an abbreviated version of a larger Table 3 found on the Large Ferguson Tables document, where the 27 departments with approximately the same RR value as Ferguson (RR = 2.81 to 2.83) are ranked by EES (with values that range from .27 to .91 standard deviations).  The former EES would reflect a situation where approximately 39% of the disadvantaged group is above the mean for the advantaged group; the latter EES would reflect a situation where approximately18% of the disadvantaged group is above the mean for the advantaged group.  Again, the abbreviated table shows the departments with the two lowest and two highest EES values, along with Ferguson.   

Table 3A.  Police departments with essentially the same black to non-black arrest rate ratio (RR) as the Ferguson Police Department, ranked by EES, with disparity index (DI) shown (abbreviated)

 

police department	state	Pop	Blk Perc Pop	Blk Perc Arr	Blk Arr Rt	NonBl Arr Rt	B/NB Ratio	Disparity Index	EES
Tarrant County Hospital District Police Department	TX	1,809,034	14.87%	32.92%	0.59	0.21	2.83	2.21	0.27
Stuttgart Police Department	AR	9,326	36.54%	61.99%	62.21	21.97	2.83	1.70	0.47
Ferguson Police Department	MO	21,203	67.43%	85.37%	186.12	66.03	2.82	1.27	0.62
City Of West Columbia Police Department	SC	14,988	18.47%	38.99%	369.09	130.86	2.82	2.11	0.79
Hammond Police Department	LA	20,019	47.52%	71.96%	479.61	169.25	2.83	1.51	0.91

 

Table 4A below is an abbreviated version of a larger Table 3 found on the Larger  Ferguson Table Page, where the 33 departments with approximately the same DI value as Ferguson (DI = 1.26 to 1.28) are ranked by EES (with values that range from .13 to 1.0 standard deviations).  The former EES would reflect a situation where approximately 45% of the disadvantaged group is above the mean for the advantaged group; the latter EES would reflect a situation where approximately 16% of the disadvantaged group is above the mean for the advantaged group. 

The abbreviated table shows the departments with the two lowest and two highest EES values.  The latter includes Ferguson.  

Table 4A.  Police departments with essentially the same disparity index (DI) as the Ferguson Police Department, ranked by EES, with black to non-black arrest rate ratio (RR) shown

police department	state	Pop	Blk Perc Pop	Blk Perc Arr	Blk Arr Rt	NonBl Arr Rt	B/NB Ratio	Disparity Index	EES
Allegany County Sheriff's Office	MD	75,087	8.03%	10.20%	52.42	40.27	1.30	1.27	0.13
Azusa Police Department	CA	46,361	3.23%	4.09%	73.38	57.53	1.28	1.26	0.13
Ferguson Police Department	MO	21,203	67.43%	85.37%	186.12	66.03	2.82	1.27	0.62
Belzoni Police Department	MS	2,235	75.39%	95.47%	162.61	23.64	6.88	1.27	1.00

 

The above examples should make clear that both the RR and DI are essentially nonsensical means of appraising demographic differences in arrest rates.

Addendum: Two shortcomings of the EES for quantifying an effect in certain circumstances (added March 26, 2015)

Discussed below are two shortcomings of the EES for quantifying the strength the forces causing outcome rates to differ that may exist in particular circumstances.    

Calculation of the EES requires outcome rates for the groups being compared.  The outcome rates are the proportions of a population experiencing (or failing to experience an outcome).  In many contexts, identifying the numerators and denominators for these rates is fairly straightforward (putting aside nuances such as discussed on the Cohort Considerations subpage of the Measuring Health Disparities and Truncation Issues and the Irreducible Minimums subpages of the Scanlan’s Rule page) – as in the case of infant survival/mortality, mortgage approval/rejection, graduation/non-graduation from school, and even surviving/failing to survive to particular ages.

One problem involves the use of a population as the denominator in circumstances where the figures in the numerator are based on a particular time frame.  The arrest rates for blacks and non-blacks underlying the tables on this page are based on a single year.  (They almost certainly include instances where certain individuals were arrested more than once.  But while that is a complicating factor, it involves a problem that is different from the more fundamental problem addressed here.)   But for statistical purposes a year is meaningless, as is any other arbitrarily chosen time frame.  Thus, suppose we observe that two groups have arrest rates of 20% and 10% for one year.  Such figures would yield an EES of .44.  But if we were to instead look at arrests over a two-year period, we would (presumably) tend to find rates of 40% and 20%, which would yield an EES of .59.  On the other hand, if we examined a six-month period, we would (again, presumably) tend to find arrest rates of 10% and 5%, which would yield an EES of .36.  But the strength of the forces causing the rates to differ is the same in each period. 

The problem can be illustrated with some of the figures from Table 1A.  Doubling the time period examined, hence, doubling black and non-black arrest rates, would change the Ferguson Police Department EES from .62 to .8, while it would change the Byhalia Police Department EES from .63 to 1.47, the Montgomery County Police Department EES from .62 to .715, and the Montgomery County Sheriff’s Office EES from .63 to .69.  Yet Table 1A is based on the premise the strength of the forces causing the rates to differ is the same for each department.

Similarly, in the school discipline context, if for the school year the suspension rate is 18% for black students compared with 6% for white students, that typically would mean rates of 9% and 3% for a semester, and 2% and 0.7% for a month.  These rates would yield different EES values even though the strength of the forces causing rates to differ remains the same through the year.

A second matter involves certain specificity issues.  Certain age groups get arrested more often than others.  When the age makeup differs for the groups being compared, the arrest rates should be adjusted accordingly.  But even when there is no such difference in the age makeup of the groups, the concentration of arrests among certain age groups can affect the EES calculation and do so in different ways for different pairs of underlying rates.  Suppose, for example, that all arrests are concentrated in a particular age group such that the arrest rates for that age group is double that of the overall rate for each race. That would mean that, as in a case where rates of 20% and 10% become 40% and 20% noted above, the EES would change substantially.[i]

Possibly there exists a solution in the calculation of a figure like the EES based on person days/month/years.  But I do not know how that calculation would work.

These issues do not affect the calculation of the Rate Ratio and Disparity Index (though they would affect calculation of the absolute difference between rates and the odds ratio).  But that does not mean that the Rate Ratio or Disparity Index is a sound measure.  That they are unsound can be demonstrated in the circumstances where the numerator and denominator identification is straightforward, as, for example, in Tables 5 of "Race and Mortality Revisited."