Stop and Frisk Practices in New York City




American urbanism is defined by a deep segregation of urban space by race and class (Massey and Denton, 1993; Wilson, 1987; Sampson, 2012).  African-Americans, and people of Hispanic or Latino identity, have long faced explicit bigotry and discrimination in housing markets, as well as in markets for jobs, education, and other aspects of society.  Even after the end of (some but not all) formal mechanisms of discrimination after the victories of the Civil Rights Movement in the 1960s, African Americans and Latinas/Latinos still experience a wide range of implicit discriminatory effects -- and most American cities remain deeply divided spatially.  Communities of color suffer from capital disinvestment -- or the replacement of mainstream financial opportunities with various kinds of predatory practices (pawn shops instead of mainstream banks, for instance) -- and higher rates of crime and poverty.

The role of the state is crucial in this divided, unequal urbanism.  At the national scale, America's political economy has from the beginning been defined by racial inequalities -- and these inequalities have by no means disappeared with the election of Barack Obama to the Presidency.  At the urban scale, communities of color have faced disparate impact from two long-term trends that have been underway for decades:  the withdrawal of the welfare state, and the expansion of "tough-on-crime" policing practices.  The withdrawal of the welfare state involves cutbacks to social insurance and social assistance to poor and working class people and places, and a punitive ideology of "neoliberalism" (Hackworth, 2007) emphasizing that poor people should demonstrate personal responsibility and work to lift themselves out of poverty.  Yet the deep spatial segregation of large cities presents formidable barriers to inner-city workers unable to reach dispersed suburban employment opportunities, and often unable to compete for downtown jobs that require advanced educational credentials of the sort that require major, long-term financial investments.  Since the 1970s, moreover, industrial restructuring has destroyed more and more of the jobs that traditionally offered reasonable pay and prospects for career advancement for workers with limited formal education.  All of these trends have had disproportionate effects on segregated communities of African Americans and Latinas/Latinos.

With an economy unable to provide sufficient mainstream economic opportunities in the inner city, it should come as no surprise that one finds a wide range of "behavioral pathologies" (Wilson, 1987) in these communities.  Landscapes of severe poverty tend also to be places where youth drop out of school, where teenage pregnancy is common, and where "hustling" and other criminal activities often seem to be the only reasonable way for destitute people to survive.  The inner city, therefore, is where we often find the most harsh response by the state through the institution of policing.  The prominent urban sociologist Loic Wacquant (2008, p. 32) puts it best:

"...it is in the segregated Black and Latino areas of the American urban core that relations with the police are the most antagonistic and the most virulent.  Residents of the ghetto are torn between their need for protection from rampant crime and their fear that police intervention will add to the violence, not diminish it, due to their discriminatory and brutal behavior."

This "discriminatory and brutal behavior" has a long history.  Incidents of police brutality have often been the trigger for urban uprisings in American inner cities -- from the wave of rebellions in the late 1960s to the violence in South Central Los Angeles following the 1992 acquittal of five police officers who had been videotaped beating a black motorist, Rodney King, after a traffic stop.  This is not to villainize police as individuals:  individual police offers working in high-crime areas are often presented with impossible situations and risks created by long-term economic and social changes that they simply cannot be expected to correct.  And yet the institutional responses of police forces as social institutions almost invariably make the situation worse, where "the forces of order act as if they were waging a trench war with the residents, treating them as an army of occupation would its enemies."  (Wacquant, 2008, p. 32).  Comparing the police to an army of occupation may seem extreme, but consider the "Rampart Division" scandal of Los Angeles in the late 1990s:  Several dozen members of a special anti-gang unit engaged in systematic beatings and shootings of suspects; they fabricated police reports and lied in court; and they planted drugs and guns on suspects to justify arrests and shootings.

Wacquant (2008), Alexander (2012), and other analysts have theorized the growth of police violence and racism as a systematic feature of American inequality.  A few generations ago, America's inability to integrate a racially marginalized "underclass" was dealt with through a combination of urban spatial segregation and a welfare state that provided just enough social assistance to prevent widespread, sustained rebellion; with the withdrawal of the welfare state, however, urban poverty and disorder have led to a growing reliance on criminal justice practices and policies to deal with systemic inequality.  If the welfare state involved "warehousing" poor communities of color in the segregated inner city, today we are seeing "law-and-order" policies that target not only violent criminals, but also a wide range of nonviolent offenses -- such as the hundreds of thousands of people in America incarcerated for nonviolent offenses like minor drug possession charges.

The other pervasive feature of tough-on-crime policing is the institutionalized suspicion of individuals and communities.  This involves racial and ethnic profiling, as well as the deployment of specialized police squads in high-crime neighborhoods -- where geographical profiling leads to a presumption of suspicion of individuals by virtue of their location.  These processes have been particularly pronounced in New York City, where there has also been a broad coalition of analysts and organizers who have challenged the practice.  As a result of long legal struggles, the New York City Police Department was forced to release parts of their vast internal database on officers' "stop and frisk" activities.

In this project, we will explore these data to see what we can learn about what Wacquant (2001) has called the "deadly symbiosis" of ghetto and prison.  It's a serious issue, with major consequences for innocent individuals arrested by the police -- and who then have an arrest record that shapes how they are treated by police and other institutions.



CopyLeft 2015 Elvin K. Wyly.  Except where otherwise noted, this site is licensed under a Creative Commons Attribution 2.5 License
Litigation, Advocacy, and Public Policy

New York Civil Liberties Union (2012).  Stop-and-Frisk 2011.  New York:  New York Civil Liberties Union.

New York Civil Liberties Union (2012).  Stop and Frisk:  The Facts.  New York:  New York Civil Liberties Union.

Schmitt, John, Kris Warner, and Sarika Gupta (2010). The High Budgetary Cost of Incarceration.  Washington, DC:  Center for Economic and Policy Research.

Terry v. Ohio

U.S. Supreme Court (1968).  Terry v. Ohio.  392 U.S. 1.  Washington, DC:  U.S. Supreme Court. 

Katz, Lewis R. (2004).  "Terry v. Ohio at Thirty-Five:  A Revisionist View."  Mississippi Law Journal 74, 423-486.

President's Task Force on 21st Century Policing (2015). Interim Report of the President's Task Force on 21st Century Policing.  Washington, DC:  Office of Community Oriented Policing Services, U.S. Department of Justice.

The Floyd, Ligon, and Davis Cases

Scheindlin, Shira A. (2013).  Opinion and Order, Floyd v City of New York, 08 Civ. 1034.  New York:  U.S. District Court, Southern District of New York.

Scheindlin, Shira (2013).  Opinion and Order, 12 Civ. 2274, Ligon et al. v. City of New York et al.  New York:  U.S. District Court for the Southern District of New York. 

Zimroth, Peter (2015).  First Report of the Monitor, Floyd et al. v. City of New York, Ligon, et al., v. City of New York, Davis, et al., v. City of New York. New York:  U.S. District Court, Southern District of New York.

NAACP Legal Defense Fund (2010).  Davis et al. v. City of New York, Complaint.  New York:  U.S. District Court, Southern District of New York.

NAACP Legal Defense Fund (2015).  Stipulation of Settlement, Davis et al. v City of New York. New York:  NAACP Legal Defense Fund.

Theory

Fagan, Jeffrey, and Garth Davies (2000).  "Street Stops and Broken Windows:  Terry, Race, and Disorder in New York City." Fordham Urban Law Journal 28(2), 457-506.

Fagan, Jeffrey, and Tracey L. Meares (2008).  "Punishment, Deterrence, and Social Control:  The Paradox of Punishment in Minority Communities."  Ohio State Journal of Criminal Law 6, 173-229.

Gowar, Cheryl (2008).  Globalization and the Transformation of Citizenship.  Ph.D. Dissertation.  New Brunswick, NJ:  Department of Geography, Rutgers University.

Police Perspectives and Mainstream Criminology

Kelling, George L., and James Q. Wilson (1982).  "Broken Windows:  The Police and Neighborhood Safety."  The Atlantic, March 1982.

New York Police Department (1994).  Police Strategy No. 5:  Reclaiming the Public Spaces of New York. New York:  New York City Police Department.

Bratton, William J. (1996).  "Cutting Crime and Restoring Order:  What America Can Learn from New York's Finest."  Washington, DC:  The Heritage Foundation.

Bratton, William J. (2014).  "Bill Bratton:  You Can't Police Without Stop and Frisk."  Boston:  National Public Radio / WBUR, Boston, February 24.

Braga, Anthony A., Andrew V. Papachristos, and David M. Hureau (2012). Crime Prevention Research Review No. 7:  Police Programs to Prevent Crime in Hot Spot Areas.  Washington, DC:  Community Oriented Policing Services, U.S. Department of Justice.

Tierney, John (2013).  "Prison Population Can Shrink When Police Crowd Streets."  New York Times, January 25.

Ridgeway, Greg (2007). Analysis of Racial Disparities in the New York Police Department's Stop, Question, and Frisk Practices.  Santa Monica / Arlington / Pittsburgh:  The RAND Corporation.



City Comptroller John Liu at a protest against the New York City Police Department's "Stop and Frisk" policy, June 2012.  Source:  Photograph by John Good, distributed via Wikimedia Commons and reproduced here under Creative Commons Attribution-Share Alike 3.0 Unported license.
References

Alexander, Michelle (2012).  The New Jim Crow:  Mass Incarceration in the Age of Colorblindness.  New York:  New Press.

Hackworth, Jason (2007).  The Neoliberal City.  Ithaca, NY:  Cornell University Press.

Sampson, Robert J. (2012).  Great American City:  Chicago and the Enduring Neighborhood Effect.  Chicago:  University of Chicago Press.

Wacquant, Loic (2008).  Urban Outcasts:  A Comparative Analysis of Advanced Marginality.  Cambridge, UK:  Polity.

Wacquant, Loic (2001).  "Deadly Symbiosis:  When Ghetto and Prison Meet and Mesh." Punishment & Society 3(1), 95-133.

Wilson, William Julius (1987).  The Truly Disadvantaged:  The Inner City, The Underclass, and Public Policy.  Chicago:  University of Chicago Press.
SAS Code for Preliminary Results
January 11, 2013

libname nypd "g:\nypd";
options linesize=130;

proc contents data=nypd.stop2007; run;
proc contents data=nypd.stop2008; run;
proc contents data=nypd.stop2009; run;
proc contents data=nypd.stop2010; run;


*************************************;
*Data cleaning procedures to reconcile mismatches;
*between character and numeric variables and other;
*technical inconsistencies across years.  NYPD;
*documentation specifies that variable coding is consistent;
*for 2006 to 2010 -- making it impossible to match with 2003;
*2004 and 2005 data.  2006 data, however, have more than a dozen additional;
*inconsistencies beyond those corrected in the code below.  Therefore, we will confine our database to;
*stop-and-frisk activities from 2007 to 2010 inclusive;

data nypd.new2007 (compress=yes);
    set nypd.stop2007;
    length x_stname $ 32;
    x_stname=stname;
    x_htft=0; x_htft=ht_feet;
    x_htin=0; x_htin=ht_inch;
    x_beat=0; x_beat=beat;
    x_post=0; x_post=post;
    x_pct=0; xpct=pct;
    x_timest=0; x_timest=timestop;
    x_datest=0; x_datest=datestop;
    x_repcmd=0; x_repcmd=repcmd;
    x_revcmd=0; x_revcmd=revcmd;
    x_addpct=0; x_addpct=addrpct;
    length x_xcoord 7 x_ycoord 7;
    x_xcoord=0; x_xcoord=xcoord;
    x_ycoord=0; x_ycoord=ycoord;
    drop pct timestop repcmd revcmd addrpct xcoord ycoord ht_feet ht_inch beat post datestop stname;
    run;
data nypd.new2008 (compress=yes);
    set nypd.stop2008;
    length x_stname $ 32;
    x_stname=stname;
    x_htft=0; x_htft=ht_feet;
    x_htin=0; x_htin=ht_inch;
    x_beat=0; x_beat=beat;
    x_post=0; x_post=post;
    x_pct=0; xpct=pct;
    x_timest=0; x_timest=timestop;
    x_datest=0; x_datest=datestop;
    x_repcmd=0; x_repcmd=repcmd;
    x_revcmd=0; x_revcmd=revcmd;
    x_addpct=0; x_addpct=addrpct;
    length x_xcoord 7 x_ycoord 7;
    x_xcoord=0; x_xcoord=xcoord;
    x_ycoord=0; x_ycoord=ycoord;
    drop pct timestop repcmd revcmd addrpct xcoord ycoord ht_feet ht_inch beat post datestop stname;
    run;
data nypd.new2009 (compress=yes);
    set nypd.stop2009;
    length x_stname $ 32;
    x_stname=stname;
    x_htft=0; x_htft=ht_feet;
    x_htin=0; x_htin=ht_inch;
    x_beat=0; x_beat=beat;
    x_post=0; x_post=post;
    x_pct=0; xpct=pct;
    x_timest=0; x_timest=timestop;
    x_datest=0; x_datest=datestop;
    x_repcmd=0; x_repcmd=repcmd;
    x_revcmd=0; x_revcmd=revcmd;
    x_addpct=0; x_addpct=addrpct;
    length x_xcoord 7 x_ycoord 7;
    x_xcoord=0; x_xcoord=xcoord;
    x_ycoord=0; x_ycoord=ycoord;
    drop pct timestop repcmd revcmd addrpct xcoord ycoord ht_feet ht_inch beat post datestop stname;
    run;
data nypd.new2010 (compress=yes);
    set nypd.stop2010;
    length x_stname $ 32;
    x_stname=stname;
    x_htft=0; x_htft=ht_feet;
    x_htin=0; x_htin=ht_inch;
    x_beat=0; x_beat=beat;
    x_post=0; x_post=post;
    x_pct=pct;
    x_timest=timestop;
    x_datest=0; x_datest=datestop;
    x_repcmd=repcmd;
    x_revcmd=revcmd;
    x_addpct=addrpct;
    length x_xcoord 7 x_ycoord 7;
    x_xcoord=xcoord;
    x_ycoord=ycoord;
    drop pct timestop repcmd revcmd addrpct xcoord ycoord ht_feet ht_inch beat post datestop stname;
    run;

data nypd.master(compress=yes);
    set
        nypd.new2007
        nypd.new2008
        nypd.new2009
        nypd.new2010;
run;

proc contents data=nypd.master; run;

proc freq data=nypd.master;
    tables race*frisked
           race*searched
           race*arstmade;
    run;

proc freq data=nypd.master;
    tables race;
    where (arstmade="Y") and (pistol="Y" or riflshot="Y" or asltweap="Y" or machgun="Y");
    run;
Preliminary Results

Between 2007 and 2010, more than 2 million people were stopped and questioned by NYPD officers.  Officers "frisked" about half of the suspects, searched about 200 thousand of those, and made about 135 thousand arrests.  Police officers reported finding guns on 2,684 suspects.

Number of stops per gun found:
817.7
"In the era of colorblindness, it is no longer socially permissible to use race, explicitly, as a justification for discrimination, exclusion, and social contempt.  So we don't.  Rather than rely on race, we use our criminal justice system to label people of color 'criminals' and then engage in all the practices we supposedly left behind. Today it is perfectly legal to discriminate against criminals in nearly all the ways that it was once legal to discriminate against African Americans.  Once you're labeled a felon, the old forms of discrimination -- employment discrimination, housing discrimination, denial of the right to vote, denial of educational opportunity, denial of food stamps and other public benefits, and exclusion from jury service -- are suddenly legal.  As a criminal, you have scarcely more rights, and arguably less respect, than a black man living in Alabama at the height of Jim Crow.  We have not ended racial caste in America; we have merely redesigned it."

Michelle Alexander (2012).  The New Jim Crow:  Mass Incarceration in the Age of Colorblindness.  New York:  New Press, quote from p. 2.







.
Red: significant spatial clusters of older-than-average Black men stopped, frisked, searched and arrested.  Blue:  significant spatial clusters of younger-than-average Black men stopped, frisked, searched, and arrested.
Writing

Here are notes and brainstorms for our evolving collective Barnraising Project.  Look in this directory from time to time for updates...
New!

All stops have been geocoded, along with a limited selection of other variables from the full database.  Download this zip file, unzip to "C:\DATA\NYPD," and begin exploring patterns by race, ethnicity, and arrest/summons/innocent status...
February 25, 2013. 
The latest SAS code for variable definitions and such is here.
Positivist Spatial Science

Geller, Amanda, and Jeffrey Fagan (2010).  "Pot as Pretext:  Marijuana, Race, and the New Disorder in New York City Street Policing."  Journal of Empirical Legal Studies 7(4), 591-633.

Fagan, Jeffrey, Tom Tyler, and Tracey Meares (2011).  Street Stops and Police Legitimacy in New York.  New York:  John Jay School of Criminal Justice.

Giuliani

Mountz, Alison, and Winifred Curran (2009).  "Policing in Drag:  Guiliani Goes Global With the Illusion of Control."  Geoforum 40(6), 1033-1040.

Smith, Neil (1998).  "Giuliani Time:  The Revanchist 1990s."  Social Text 57, 1-20.

Data, Visualizations, and Various Technical Resources

Code for America (2015).  Police Open Data Census.  Indianapolis:  Code for America Indianapolis Fellowship Program.

Civilian Complaint Review Board (2015).  "Complaint Activity Maps, by Police Precinct."  New York:  New York Civilian Complaint Review Board.

Civilian Complaint Review Board (2015).  "What To Do if a Police Officer Stops You."  New York:  New York Civilian Complaint Review Board.

Retrospect and Prospect

Bellin, Jeffrey (2014).  "The Inverse Relationship Between the Constitutionality and Effectiveness of New York City 'Stop and Frisk.'"  Boston University Law Review 94, 1495-1550.

Assorted Critical Perspectives on Race, Policing, Inequality, and Injustice

Taylor, Flint (2015).  "How Activists Won Reparations for the Survivors of Chicago Police Department Torture."  In These Times, June 26.

Essif, Amien (2015).  "How Black Lives Matter Has Spread Into a Global Movement to End Racist Policing."  In These Times, June 29.

Ford, Glen (2015).  "Black Self-Determination Matters."  Black Agenda Report, July 8.

Katz, Cindi, and Neil Smith (1992).  "L.A. Intifada:  Interview with Mike Davis."  Social Text 33, 19-33.

Cheney-Rice, Zak (2015).  "15 Things Your City Can Do Right Now to End Police Brutality."  Portside.  New York:  Committees of Correspondence for Democracy and Socialism, July 1.

Balko, Radley (2013).  "'Why Did You Shoot Me?  I Was Reading a Book':  The New Warrior Cop is Out of Control."  Salon, July 7.

Goodman, J. David (2015).  "Eric Garner Case is Settled by NewYork City for $5.9 Million."  New York Times, July 13.

Hamid, Eba, and Benjamin Mueller (2015).  "Fatal Police Encounters in New York City."  New York Times, July 13.

Rabin, Roni Caryn (2015).  "'Illegal Activity' Fine Print Leaves Some Insured, but Uncovered."  New York Times, July 20.

Day, Elizabeth (2015).  "#BlackLivesMatter:  The Birth of a New Civil Rights Movement."  The Guardian, July 19.

Amsden, David (2015).  "Who Runs the Streets of New Orleans?"  New York Times, July 30.

Amadou Diallo

Cooper, Michael (1999).  "Officers in Bronx Fire 41 Shots, and an Unarmed Man is Killed."  New York Times, February 5.

Iverson, Kristin (2015).  "The NYPD Has Been Updating the Wikipedia Pages of Eric Garner, Amadou Diallo, and Sean Bell."  Brooklyn Magazine, March 13.



Odds ratio for the likelihood that a stop-and-frisk encounter with a police officer will result in an episode of physical force, after controlling for all justifications cited by officers for their decision to detain an individual.

In police precincts shaded dark red, physical force is more than twice as likely as the citywide average, after controlling for all justifications cited by police officers.
Percentage of stops yielding gun and arrest, 2007-2013
Percentage of stops in which an officer used physical force, and where there was no arrest or summons.
"The white polity痴 response to Black demands for a more just society was to create a mass incarceration regime so pervasive that one out of every eight prison inmates in the world is an African American."  Ford, Glen (2015).  "Black Self-Determination Matters."  Black Agenda Report, July 8.


Percentage of Stops where No Arrest was Made, and No Summons Issued (i.e., innocent).
Non-Hispanic Blacks as Share of All Stop-and-Frisks, 2007-2013
Hispanic Blacks as Share of All Stop-and-Frisks, 2007-2013
Asians and Pacific Islanders as Share of All Stop-and-Frisks, 2007-2013
White Hispanics as Share of All Stop-and-Frisks, 2007-2013
Odds that a stop-and-frisk will result in an encounter with pepper spray, baton, or handcuffs
Percentage of stop-and-frisks that result in suspect being pushed against wall/car/ground
Classifying Neighborhoods of New York City by
Stop-and-Frisk Activity from 2007 to 2013

1.  SAS Code to Aggregate the individual UF-250s to Census Tract Summaries

proc summary data=nypd.master_y;
    class newfips;
    var rx_asn rx_nhw rx_nhb rx_ntv rx_bhs rx_whs rx_unk rx_oth sx_f sx_z
    csxbulge csxcasng csxcloth csxdescr csxdrgtr csxfurtv csxlkout csxobjcs csxvcrim csxnumbr o_pers
    xa_rept xa_inves xa_proxm xa_evasv xa_assoc xa_cgdir xa_incid xa_time xa_stsnd xa_other notunif
    ifc xforce w_ars w_smm w_gun w_wep w_tol w_wgn w_frs w_src w_ag1 w_ag2 innocent;
    output out=nypd.classtmp
    sum=rx_asn rx_nhw rx_nhb rx_ntv rx_bhs rx_whs rx_unk rx_oth sx_f sx_z
    csxbulge csxcasng csxcloth csxdescr csxdrgtr csxfurtv csxlkout csxobjcs csxvcrim csxnumbr o_pers
    xa_rept xa_inves xa_proxm xa_evasv xa_assoc xa_cgdir xa_incid xa_time xa_stsnd xa_other notunif
    ifc xforce w_ars w_smm w_gun w_wep w_tol w_wgn w_frs w_src w_ag1 w_ag2 innocent;
    id newfips;
run;
data nypd.catclass(compress=yes);
    set nypd.classtmp;
    cz_asn=(rx_asn/_FREQ_)*100; label cz_asn="Percentage of stops Asian";
    cz_nhw=(rx_nhw/_FREQ_)*100; label cz_nhw="Percentage of stops Non Hispanic White";
    cz_nhb=(rx_nhb/_FREQ_)*100; label cz_nhb="Percentage of stops Non Hispanic Black";
    cz_ntv=(rx_ntv/_FREQ_)*100; label cz_ntv="Percentage of stops Native American";
    cz_bhs=(rx_bhs/_FREQ_)*100; label cz_bhs="Percentage of stops Black Hispanic";
    cz_whs=(rx_whs/_FREQ_)*100; label cz_whs="Percentage of stops White Hispanic";
    cz_fem=(sx_f/_FREQ_)*100; label cz_fem="Percentage of stops Female";

    cz_blg=(csxbulge/_FREQ_)*100; label cz_blg="Percentage of stops Suspicious Bulge";
    cz_csn=(csxcasng/_FREQ_)*100; label cz_csn="Percentage of stops Casing Victim or Scene";
    cz_clt=(csxcloth/_FREQ_)*100; label cz_clt="Percentage of stops Clothes/Disguises";
    cz_des=(csxdescr/_FREQ_)*100; label cz_des="Percentage of stops Fits Description";
    cz_drg=(csxdrgtr/_FREQ_)*100; label cz_drg="Percentage of stops Drug Transaction";
    cz_fur=(csxfurtv/_FREQ_)*100; label cz_fur="Percentage of stops Furtive Movements";

    cz_rep=(xa_rept/_FREQ_)*100; label cz_rep="Percentage of stops Add circ: Report";
    cz_inv=(xa_inves/_FREQ_)*100; label cz_inv="Percentage of stops Add circ: Investigation";
    cz_pxm=(xa_proxm/_FREQ_)*100; label cz_pxm="Percentage of stops Add circ:  Proximity";
    cz_eva=(xa_evasv/_FREQ_)*100; label cz_eva="Percentage of stops Add circ:  Evasive";
    cz_ass=(xa_assoc/_FREQ_)*100; label cz_ass="Percentage of stops Add circ:  Association";
    cz_cgd=(xa_cgdir/_FREQ_)*100; label cz_cgd="Percentage of stops Add circ:  Change Direction";
    cz_inc=(xa_incid/_FREQ_)*100; label cz_inc="Percentage of stops Add circ:  Incident";
    cz_tim=(xa_time/_FREQ_)*100; label cz_tim="Percentage of stops Add circ:  Time";
    cz_sts=(xa_stsnd/_FREQ_)*100; label cz_sts="Percentage of stops Add circ:  Sights/Sounds";
    cz_oth=(xa_other/_FREQ_)*100; label cz_oth="Percentage of stops Add circ:  Other";
    cz_nun=(notunif/_FREQ_)*100; label cz_nun="Percentage of stops Plainclothes Officer";

    cz_ars=(w_ars/_FREQ_)*100; label cz_ars="Percentage of stops yielding arrest";
    cz_smm=(w_smm/_FREQ_)*100; label cz_smm="Percentage of stops yielding summons";
    cz_gun=(w_gun/_FREQ_)*100; label cz_gun="Percentage of stops with gun/arrest";
    cz_wep=(w_wep/_FREQ_)*100; label cz_wep="Percentage of stops with Force:  Weapon";
    cz_tol=(w_tol/_FREQ_)*100; label cz_tol="Percentage of stops with Force:  Baton/Peps";
    cz_wgn=(w_wgn/_FREQ_)*100; label cz_wgn="Percentage of stops with Force:  Wall/Ground";
    cz_frs=(w_frs/_FREQ_)*100; label cz_frs="Percentage of stops with frisk";
    cz_src=(w_src/_FREQ_)*100; label cz_src="Percentage of stops with search";
    cz_ag1=(w_ag1/_FREQ_)*100; label cz_ag1="Percentage of stops Age up to 18";
    cz_ag2=(w_ag2/_FREQ_)*100; label cz_ag2="Percentage of stops Age 19-21";
    cz_ifc=(ifc/_FREQ_)*100; label cz_ifc="Percentage of stops innocent/force";
   
run;

2a.  SAS Code for Hierarchical Cluster Analysis

*Classify all census tracts according to the characteristics of stop-and-frisk;
*activity over this eight-year period;
*Exclusing twenty tracts with fewer than 50 stops in the eight-year period;
proc cluster data=nypd.catclass method=average rsq;
    where _FREQ_ > 49;
    var cz_asn cz_nhw cz_nhb cz_ntv cz_bhs cz_whs
    cz_ars cz_gun cz_wep cz_tol cz_wgn cz_frs cz_ifc;
    run;

2b.  Results

                                                         The SAS System                        18:52 Saturday, July 11, 2015 283

                                                     The CLUSTER Procedure
                                                Average Linkage Cluster Analysis

                                              Eigenvalues of the Covariance Matrix

                                          Eigenvalue    Difference    Proportion    Cumulative

                                     1    525.919449    361.003752        0.6542        0.6542
                                     2    164.915697    106.579941        0.2051        0.8593
                                     3     58.335756     37.186315        0.0726        0.9319
                                     4     21.149442      4.719057        0.0263        0.9582
                                     5     16.430384      5.001500        0.0204        0.9786
                                     6     11.428884      6.885746        0.0142        0.9928
                                     7      4.543137      3.783936        0.0057        0.9985
                                     8      0.759201      0.515159        0.0009        0.9994
                                     9      0.244042      0.131100        0.0003        0.9997
                                    10      0.112942      0.034810        0.0001        0.9999
                                    11      0.078132      0.053050        0.0001        1.0000
                                    12      0.025082      0.013986        0.0000        1.0000
                                    13      0.011095                      0.0000        1.0000

                                  Root-Mean-Square Total-Sample Standard Deviation    7.864004

                                   Root-Mean-Square Distance Between Observations    40.09871


                                                        Cluster History
                Number
                    of                                                 Semipartial                Norm RMS
              Clusters    ------Clusters Joined-------         Freq       R-Square    R-Square    Distance    Tie

                  2123    OB1499          OB1577               3553         0.0000        1.00      0.0312
                  2122    OB1960          OB2100              12023         0.0000        1.00      0.0319
                  2121    OB1679          OB2047               8297         0.0000        1.00       0.032
                  2120    OB1258          OB1288               2355         0.0000        1.00      0.0332
                  2119    OB1804          OB1862               6094         0.0000        1.00       0.035
                  2118    OB1237          OB1512               2850         0.0000        1.00      0.0375
                  2117    OB615           OB758                1081         0.0000        1.00      0.0394
                  2116    OB1345          OB1363               2662         0.0000        1.00      0.0394
                  2115    OB1813          OB2068               9450         0.0000        1.00      0.0398
                  2114    OB1939          CL2122              15990         0.0000        1.00      0.0418
                  2113    OB1143          OB1656               3189         0.0000        1.00      0.0425
                  2112    OB1806          OB1969               7157         0.0000        1.00      0.0433
                  2111    OB2107          OB2119              18514         0.0000        1.00      0.0454
                  2110    OB964           OB1659               3001         0.0000        1.00      0.0457
                  2109    OB1599          CL2119               8047         0.0000        1.00      0.0461
                  2108    OB493           OB1493               2061         0.0000        1.00      0.0474
     
        [results omitted for about two thousand steps to avoid cognitive overload...]    
               
                    75    CL108           CL121              4.03E6         0.0018        .917      0.5148
                    74    CL113           OB2034              70471         0.0003        .916      0.5159
                    73    OB120           CL696               13125         0.0000        .916      0.5161
                    72    CL102           CL302              227293         0.0002        .916      0.5199
                    71    CL85            CL111               87517         0.0004        .916      0.5208
                    70    CL389           CL171                4555         0.0000        .916       0.521
                    69    CL103           CL311              126081         0.0013        .914      0.5228
                    68    CL194           CL79                18495         0.0002        .914      0.5241
                    67    CL83            OB935                2678         0.0000        .914      0.5248
                    66    CL223           CL129                7395         0.0000        .914      0.5312
                    65    CL91            CL84                39483         0.0004        .914      0.5387
                    64    CL80            CL225               20558         0.0002        .914      0.5412
                    63    CL128           CL89                40959         0.0003        .913      0.5447
                    62    CL75            CL117              4.05E6         0.0014        .912      0.5466
                    61    CL142           CL105              546116         0.0023        .910      0.5474
                    60    CL146           CL86                21696         0.0003        .909      0.5477
                    59    OB137           CL179                9958         0.0000        .909      0.5479
                    58    CL104           CL152               51189         0.0006        .909      0.5486
                    57    CL72            CL59               237251         0.0005        .908      0.5497
                    56    OB219           CL406               71572         0.0000        .908      0.5532
                    55    CL92            CL154               41310         0.0004        .908      0.5532
                    54    CL62            CL148              4.27E6         0.0132        .895      0.5554
                    53    CL131           CL114               58417         0.0006        .894      0.5556
                    52    OB163           CL183                 598         0.0000        .894      0.5617
                    51    CL74            OB307               70754         0.0000        .894      0.5652
                    50    CL107           CL87                32500         0.0004        .894      0.5671
                    49    CL127           CL101               89374         0.0012        .892      0.5733
                    48    CL76            CL657               14660         0.0000        .892      0.5736
                    47    CL61            CL56               617688         0.0041        .888      0.5805
                    46    CL98            CL48                53170         0.0005        .888      0.5821
                    45    CL68            CL65                57978         0.0005        .887      0.5891
                    44    CL78            CL53               130509         0.0014        .886       0.598
                    43    CL55            CL176               48582         0.0004        .885      0.6014
                    42    CL64            CL100               38637         0.0006        .885      0.6135
                    41    CL71            CL57               324768         0.0037        .881      0.6201
                    40    CL96            CL81               221988         0.0031        .878      0.6315
                    39    CL49            CL58               140563         0.0017        .876       0.633
                    38    CL54            CL70               4.28E6         0.0004        .876      0.6345
                    37    CL50            OB360               32819         0.0000        .876      0.6381
                    36    CL262           CL115                2643         0.0001        .876      0.6434
                    35    CL141           CL38               4.28E6         0.0000        .876      0.6467
                    34    CL47            CL124              1.11E6         0.0200        .856      0.6515
                    33    CL63            CL110               45348         0.0003        .856      0.6555
                    32    CL44            CL66               137904         0.0005        .855      0.6678
                    31    CL125           CL658               25510         0.0003        .855      0.6702
                    30    CL95            CL82               129150         0.0020        .853      0.6764
                    29    CL88            CL77                 7265         0.0000        .853      0.6787
                    28    CL37            CL40               254807         0.0019        .851      0.6976
                    27    CL39            CL31               166073         0.0014        .849      0.7002
                    26    CL46            CL52                53768         0.0001        .849      0.7103
                    25    CL33            CL134               56627         0.0008        .849      0.7132
                    24    CL35            CL45               4.34E6         0.0056        .843      0.7164
                    23    CL29            CL26                61033         0.0006        .842      0.7206
                    22    CL90            CL36                47254         0.0002        .842      0.7298
                    21    CL60            CL23                82729         0.0013        .841      0.7351
                    20    CL25            CL43               105209         0.0020        .839      0.7437
                    19    CL34            CL123              1.14E6         0.0030        .836       0.746
                    18    CL24            CL41               4.66E6         0.0338        .802      0.7502
                    17    OB26            OB804                 692         0.0000        .802      0.7517
                    16    CL32            CL99               138893         0.0001        .802      0.7607
                    15    CL67            CL28               257485         0.0003        .802      0.7846
                    14    CL15            CL18               4.92E6         0.0274        .774       0.793
                    13    CL27            CL51               236827         0.0065        .768      0.8314
                    12    CL14            CL204              4.93E6         0.0011        .767      0.8333
                    11    CL12            CL17               4.93E6         0.0001        .767      0.8424
                    10    CL22            CL42                85891         0.0029        .764      0.8457
                     9    CL21            CL20               187938         0.0042        .759      0.8473
                     8    CL16            CL73               152018         0.0021        .757      0.8831
                     7    CL11            CL30               5.06E6         0.0309        .726      1.0447
                     6    CL13            CL69               362908         0.0186        .708      1.0539
                     5    CL7             CL19                6.2E6         0.2416        .466      1.0877
                     4    CL9             CL10               273829         0.0125        .454      1.1209
                     3    CL4             CL6                636737         0.0444        .410       1.335
                     2    CL5             CL3                6.83E6         0.2793        .130      1.6082
                     1    CL8             CL2                6.99E6         0.1302        .000      1.9197

***

Note:  With 28 clusters we can preserve 85 percent of the total variance.
Once we've decided how many clusters to identify, we can use the iterative, non-hierarchical partitioning method of the FASTCLUS procedures, which provides several diagnostic indicators that are particularly helpful in subsantive interpretation.

3a.  SAS Code for Non-Hierarchical Partitioning Cluster Analysis

proc fastclus data=nypd.catclass out=nypd.clust maxclusters=28 maxiter=5000;
    where _FREQ_ > 49;
    var cz_asn cz_nhw cz_nhb cz_ntv cz_bhs cz_whs
    cz_ars cz_gun cz_wep cz_tol cz_wgn cz_frs cz_ifc;
    run;

3b.  Results

                                                         The SAS System                        18:52 Saturday, July 11, 2015 292

                                                     The FASTCLUS Procedure
                               Replace=FULL  Radius=0  Maxclusters=28 Maxiter=5000  Converge=0.02

                                                         Initial Seeds

Cluster           cz_asn           cz_nhw           cz_nhb           cz_ntv           cz_bhs           cz_whs           cz_ars
ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ
     1         0.39215686      88.03921569       2.54901961       0.78431373       0.78431373       5.49019608       5.68627451
     2         5.78186597      22.73324573      40.47306176       0.26281209       4.99342970      20.49934297      38.50197109
     3         5.46875000      59.37500000      18.75000000       1.17187500       3.51562500       8.98437500       4.68750000
     4        15.93045113       6.90789474      15.93045113       3.05451128       5.26315789      50.75187970       2.86654135
     5         1.46370023      20.08196721       5.50351288       0.23419204      10.18735363      60.83138173       7.49414520
     6         3.57142857      25.00000000      64.28571429       0.00000000       0.00000000       3.57142857       5.35714286
     7         4.23728814      45.76271186       6.77966102       0.00000000       5.08474576      33.05084746      16.10169492
     8         0.48939641       0.95548823      54.60265672       0.18643673       9.83453740      27.42950361       4.59100443
     9        15.51724138      32.75862069      22.41379310       1.72413793       5.17241379      20.68965517       3.44827586
    10         3.27868852      42.62295082      44.26229508       0.00000000       1.63934426       8.19672131       9.83606557
    11        10.05434783      40.48913043       5.43478261       0.54347826       4.07608696      37.50000000       2.44565217
    12         1.99282583      14.94619370      43.20446393       0.19928258       4.46392985      29.89238741       7.97130331
    13         1.48331273       1.35970334      92.45982695       0.12360939       1.35970334       2.71940667       3.21384425
    14         0.90567705       1.50209852       3.07046609       0.11044842       9.05677049      82.81422576       3.31345262
    15         0.42602634       1.04570101      33.50116189       0.07745933      15.56932610      42.33152595       5.26723470
    16        42.07650273       9.01639344       4.78142077       0.27322404       7.78688525      32.65027322      14.48087432
    17         5.00000000       4.28571429       7.85714286       0.71428571       9.28571429      70.71428571       7.85714286
    18         0.00000000       8.33333333      30.95238095       0.00000000       7.14285714      52.38095238      20.23809524
    19        48.90016920       2.53807107      30.28764805       0.67681895       2.70727580      10.65989848       9.13705584
    20         0.45454545       1.47727273      85.00000000       0.00000000       2.61363636       8.63636364      12.04545455
    21        25.16243355      29.17897224      16.95215594       1.35853514       3.83933845      19.07855877       4.13467218
    22         0.23948909       1.86269292      74.05534859       0.06652475       4.27088877      17.38956892       7.77009047
    23         9.03954802      11.86440678      25.98870056       0.56497175       5.08474576      42.37288136      13.55932203
    24         1.63398693      58.82352941       7.84313725       0.00000000       2.28758170      28.10457516       8.82352941
    25         6.55737705      36.61202186      10.38251366       0.54644809       6.55737705      35.51912568      27.86885246
    26         0.86206897      79.31034483       6.03448276       0.86206897       0.86206897       8.33333333       1.43678161
    27         0.36016949       2.54237288       8.47457627       0.12711864      35.74152542      45.14830508       8.34745763
    28         9.49720670      31.84357542      29.60893855       0.00000000       6.14525140      21.22905028       8.37988827

                                                         Initial Seeds

       Cluster           cz_gun            cz_wep            cz_tol            cz_wgn            cz_frs            cz_ifc
       ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ
           1         0.00000000        0.19607843        0.58823529        0.39215686       25.09803922        2.54901961
           2         0.13140604        0.00000000        1.44546649        1.83968463       48.09461235        8.93561104
           3         0.00000000        0.00000000        0.00000000        0.00000000       36.32812500        3.12500000
           4         0.00000000        0.04699248        1.45676692        1.92669173       59.11654135       29.13533835
           5         0.11709602        0.11709602        0.23419204        0.81967213       68.38407494        9.66042155
           6         0.00000000        0.00000000        0.00000000        0.00000000       25.00000000        5.35714286
           7         0.00000000        0.00000000        0.00000000        0.84745763       29.66101695        3.38983051
           8         0.06991377        0.39617805        0.74574691        5.26683757       64.53041249       26.63714752
           9         0.00000000        0.00000000        3.44827586        1.72413793       13.79310345       10.34482759
          10         0.00000000        0.00000000        1.63934426        3.27868852       44.26229508        6.55737705
          11         0.00000000        0.00000000        0.81521739        4.34782609       52.44565217       23.36956522
          12         0.31885213        0.63770426        1.55440415        2.63053009       28.89597449        8.88800319
          13         0.00000000        0.24721879        0.74165637        1.23609394       37.82447466       27.81211372
          14         0.02208968        0.28716589        1.76717473        4.30748840       79.92047714       41.88204109
          15         0.03872967        0.00000000        1.31680868       12.23857475       80.86754454       57.31990705
          16         0.13661202        0.40983607        2.18579235        2.86885246       51.22950820       19.39890710
          17         0.00000000        0.00000000        1.42857143        5.00000000       40.71428571       19.28571429
          18         0.00000000        0.00000000        2.38095238        2.38095238       47.61904762       11.90476190
          19         0.16920474        0.00000000        0.50761421        1.18443316       57.69881557        6.09137056
          20         0.90909091        0.45454545        2.61363636        6.25000000       81.02272727       40.00000000
          21         0.00000000        0.00000000        0.17720024        0.64973420       61.13408151        3.60307147
          22         0.07982970        0.19957424        0.53219798        1.01117616       45.70250133        5.98722725
          23         1.12994350        0.00000000        1.12994350        1.69491525       79.66101695       10.73446328
          24         0.00000000        0.00000000        0.32679739        0.32679739       65.68627451        7.51633987
          25         0.00000000        0.00000000        0.54644809        2.18579235       62.84153005       10.38251366
          26         0.00000000        0.00000000        0.00000000        2.58620690       55.17241379       15.80459770
          27         0.31779661        0.33898305        0.72033898        5.33898305       57.62711864       20.25423729
          28         0.55865922        5.58659218        5.58659218       13.96648045       43.01675978       24.58100559


                                       Minimum Distance Between Initial Seeds = 31.30624

                                                        Iteration History

                                                           Relative Change in Cluster Seeds
    Iteration  Criterion         1         2         3         4         5         6         7         8         9        10
    ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ
            1     5.6231    0.2722    0.4840    0.4076    0.3359    0.3473    0.4231    0.4645    0.2489    0.4410    0.4214
            2     3.9760    0.0254    0.0938    0.0317    0.1010    0.1040    0.2807    0.0946    0.1122    0.1094    0.0824
            3     3.7930         0    0.0526    0.0165    0.0404    0.0656    0.1550    0.0465    0.0806    0.1227    0.0653
            4     3.7115    0.0199         0    0.0260    0.0313    0.0258    0.1022    0.0406    0.0355    0.0642    0.0965
            5     3.6748    0.0171         0    0.0267    0.0498    0.0427    0.0555    0.0352    0.0208    0.0360    0.0553
            6     3.6535    0.0189         0    0.0190    0.0277         0    0.0407    0.0314    0.0251    0.0273    0.0759
            7     3.6386         0         0    0.0216   0.00719         0    0.0288    0.0342    0.0227    0.0253    0.0486
            8     3.6286         0         0    0.0238   0.00911         0    0.0449    0.0259    0.0346    0.0246    0.0307
            9     3.6199         0    0.0685    0.0220   0.00773         0    0.0397    0.0131    0.0249    0.0227    0.0565
           10     3.6113    0.0206    0.0660    0.0318   0.00788    0.0143    0.0224   0.00848    0.0252    0.0181    0.0294
           11     3.6054         0    0.0542    0.0198   0.00820         0    0.0242    0.0134   0.00901    0.0134    0.0324
           12     3.6024         0    0.0487   0.00592         0         0    0.0225    0.0104    0.0219    0.0165    0.0156
           13     3.6001         0    0.0692   0.00673         0         0    0.0127         0    0.0283    0.0103   0.00989
           14     3.5976         0    0.1067         0   0.00887         0    0.0148         0    0.0219   0.00976   0.00814
           15     3.5931         0    0.0741   0.00641         0         0    0.0130         0    0.0210    0.0184   0.00900
           16     3.5900         0    0.0470   0.00616   0.00708         0    0.0147         0    0.0202   0.00834   0.00846
           17     3.5883         0    0.0200         0         0         0   0.00780         0    0.0121         0    0.0135
           18     3.5872         0   0.00922         0         0         0   0.00899         0   0.00532   0.00667    0.0116

                                                       Iteration History

                                                     Relative Change in Cluster Seeds
    Iteration        11        12        13        14        15        16        17        18        19        20        21
    ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ
            1    0.3948    0.3833    0.6196    0.4343    0.5103    0.4841    0.4237    0.5626    0.3603    0.6201    0.3687
            2    0.0746    0.1056    0.0925    0.0711    0.2223    0.1754    0.1029    0.0968    0.0600    0.0732    0.0465
            3    0.1238    0.0440    0.0457    0.0392    0.0777    0.0849    0.1192    0.0550    0.0427    0.0444    0.0456
            4    0.1054    0.0318    0.0303         0    0.0394    0.0231    0.0365    0.0382    0.0219    0.0346    0.0265
            5    0.0868    0.0397    0.0260         0   0.00845    0.0533    0.0174    0.0218    0.0192    0.0396    0.0176
            6    0.0610    0.0313    0.0172         0    0.0152    0.0260         0    0.0169    0.0209    0.0373    0.0332
            7    0.0320   0.00684   0.00720         0   0.00935    0.0198         0    0.0211    0.0217    0.0234    0.0232
            8    0.0375    0.0149   0.00590         0         0    0.0119         0    0.0137         0    0.0193    0.0236
            9    0.0209    0.0318   0.00541         0         0         0    0.0156    0.0195         0    0.0145    0.0138
           10    0.0203    0.0360   0.00331         0    0.0140    0.0123    0.0175    0.0265         0   0.00334         0
           11   0.00881    0.0278         0         0         0         0    0.0150   0.00581         0         0    0.0189
           12         0   0.00849         0         0         0         0         0    0.0161         0         0         0
           13         0    0.0118         0         0         0         0         0    0.0225         0         0    0.0197
           14         0    0.0103         0         0   0.00970         0         0    0.0147         0   0.00475         0
           15         0    0.0140   0.00165         0    0.0152    0.0134         0    0.0122         0   0.00842         0
           16         0   0.00677         0         0         0   0.00962         0    0.0130         0         0         0
           17         0    0.0115   0.00151         0         0         0         0    0.0248         0   0.00304         0
           18         0   0.00719         0         0         0         0         0    0.0103         0         0         0

                                                       Iteration History

                                                     Relative Change in Cluster Seeds
                  Iteration        22          23          24          25          26          27          28
                  ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ
                          1    0.4020      0.5128      0.3617      0.4636      0.4154      0.3342      0.4691
                          2    0.0697      0.1912      0.0364      0.2022      0.0730      0.0392      0.0501
                          3    0.0164      0.1456      0.0244      0.1247      0.0341      0.0392      0.0665
                          4    0.0146      0.0922      0.0211      0.0524      0.0259           0      0.0633
                          5    0.0124      0.0385      0.0133      0.0295      0.0390      0.0204      0.0544
                          6    0.0143      0.0150      0.0274      0.0419      0.0228           0      0.0487
                          7    0.0164     0.00881      0.0247      0.0190      0.0191           0      0.0640
                          8    0.0278           0      0.0150      0.0173      0.0107           0      0.0546
                          9    0.0112     0.00284      0.0157      0.0120     0.00484           0      0.0594
                         10   0.00597           0      0.0177           0      0.0155           0      0.0441
                         11         0     0.00533     0.00499           0     0.00528           0      0.0218
                         12   0.00730           0     0.00632           0           0           0      0.0126
                         13         0     0.00345           0           0           0           0      0.0123
                         14   0.00730      0.0106     0.00552     0.00658           0           0      0.0116
                         15   0.00675     0.00940           0           0           0           0      0.0171
                         16   0.00959      0.0102           0           0           0           0     0.00999
                         17   0.00914      0.0114     0.00595           0     0.00627           0      0.0164
                         18   0.00514     0.00321           0           0           0           0     0.00434


                                Convergence criterion is satisfied.


                                           Criterion Based on Final Seeds =   3.5868


                                                        Cluster Summary

                                                     Maximum Distance
                                          RMS Std           from Seed     Radius     Nearest     Distance Between
               Cluster     Frequency    Deviation      to Observation    Exceeded    Cluster    Cluster Centroids
               ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ
                   1              23       2.5172             20.2292                     26              21.6532
                   2              46       4.3984             28.3383                     12              16.6060
                   3              77       3.2579             25.5908                     26              14.2717
                   4              67       4.1912             23.0362                      5              17.7421
                   5              39       3.8857             21.2551                      4              17.7421
                   6             111       3.8352             27.0188                     12              20.8593
                   7              68       4.0595             27.2352                     24              17.7063
                   8             102       3.8009             29.1344                      6              20.8955
                   9             103       4.0415             26.5106                      2              20.1950
                  10              57       3.8945             27.2975                      7              22.2343
                  11              57       3.9768             20.5445                      7              18.6154
                  12              88       3.7535             27.6149                      2              16.6060
                  13             212       2.7112             26.9549                     22              15.5653
                  14              59       3.4285             21.5653                      4              31.6400
                  15              55       3.8331             25.0483                     23              23.4782
                  16              49       4.0332             23.8154                      4              22.2599
                  17              36       3.6554             22.5428                      5              17.9420
                  18              99       3.4357             23.1994                     23              16.1084
                  19              27       4.2949             30.7784                     16              28.4299
                  20             138       3.5110             22.7642                     13              16.1132
                  21              34       3.2914             21.0145                     25              19.7757
                  22             139       3.4273             24.6881                     13              15.5653
                  23              94       3.3282             19.6888                     18              16.1084
                  24              79       3.4423             22.7552                      7              17.7063
                  25              87       3.6669             21.5062                     21              19.7757
                  26              80       3.1274             18.1496                      3              14.2717
                  27              29       3.4399             21.2298                     17              26.0521
                  28              69       4.1418             23.0388                      2              17.7911


                                                    Statistics for Variables

                               Variable     Total STD    Within STD      R-Square     RSQ/(1-RSQ)
                               ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ
                               cz_asn         7.16377       3.66810      0.741154        2.863300
                               cz_nhw        20.81273       4.37872      0.956300       21.883493
                               cz_nhb        28.90710       5.36766      0.965959       28.376317
                               cz_ntv         0.77407       0.68830      0.219372        0.281019
                               cz_bhs         4.90828       2.27236      0.788390        3.725664
                               cz_whs        16.75970       4.72257      0.921609       11.756605
                               cz_ars         3.55969       3.32296      0.139667        0.162341
                               cz_gun         0.26638       0.25802      0.073697        0.079560
                               cz_wep         0.44596       0.43973      0.040105        0.041780
                               cz_tol         0.78318       0.73658      0.126689        0.145067
                               cz_wgn         2.02715       1.70991      0.297550        0.423589
                               cz_frs        12.59452       6.24750      0.757064        3.116319
                               cz_ifc         8.60155       5.12351      0.649714        1.854811
                               OVER-ALL      12.01269       3.61013      0.910832       10.214815


                                                 Pseudo F Statistic =   792.97


                                      Approximate Expected Over-All R-Squared =   0.77303


                                             Cubic Clustering Criterion =   92.584

                              WARNING: The two values above are invalid for correlated variables.


                                                         Cluster Means

Cluster           cz_asn           cz_nhw           cz_nhb           cz_ntv           cz_bhs           cz_whs           cz_ars
ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ
     1         1.79759512      81.57497587       4.81117497       0.14333385       1.20348393       8.04541232       4.32132480
     2         9.32776807      15.12673535      39.71996334       1.50756658       6.42204119      23.59365704      11.23850992
     3         5.00554158      59.20180562       9.55327105       0.67451288       2.62235325      20.61109771       5.00813204
     4        10.48630626      12.36368550      16.65185440       0.91293813       6.79167950      49.87485297       7.39838238
     5         8.86946042      17.91568275       8.26329725       0.40369925       7.94162628      55.35234428       5.81536842
     6         4.48899883       7.36472986      58.52296418       0.78196531       5.12690354      20.73745074       7.05684776
     7         6.43614063      40.50096138      14.08618772       0.77408578       5.45950041      29.17699357       8.33932486
     8         1.42699190       4.47530169      58.24515880       0.35218524       7.57742468      24.00810264       6.43052289
     9         5.49605236      27.85361416      29.64325949       0.69548753       6.01483235      25.89869686       8.06477387
    10         2.96390378      49.12153857      27.02267772       0.58568737       2.82831681      14.73680032       5.09419665
    11         8.80129356      26.22514155      14.45717173       0.83106110       7.09519854      39.67703170       8.37369052
    12         3.36748845      21.34233981      48.23051992       0.40889726       4.39835178      18.68077210       8.16572242
    13         1.10798956       1.78978143      88.76833637       0.19842299       1.39906063       4.35641260       5.76181382
    14         3.75236468       4.23612614       6.26807106       0.41258040       7.75690843      75.59046465       5.23795483
    15         0.52356981       1.26536678      46.16697275       0.17406938      13.94184724      32.48902858       6.51684890
    16        24.65981792      11.27775586      18.15533491       1.02060486       6.02416069      35.67622126       9.79889647
    17         2.69437112       9.82319313      12.84207237       0.41398091      10.80073861      59.75282972       5.65201187
    18         1.80707600       5.31016753      39.36928785       0.55291211      10.52772289      38.42386870       7.39669309
    19        42.63546681       5.87006179      24.33673437       1.98902004       3.52513905      17.99780288       8.12859659
    20         1.18921234       1.92527966      86.07746143       0.22551004       1.97624757       6.20570275       6.00564206
    21        17.81936772      33.38958009      14.71068821       1.23290968       2.94135559      26.03893471       5.60294830
    22         1.77892290       4.81234343      75.62665902       0.36141882       3.08237814      11.30694275       6.09970247
    23         1.37335471       3.50326924      35.18324963       0.41878672      13.14905492      41.00095388       7.22189187
    24         4.52846243      52.62034333       8.71764499       0.59946569       3.67025229      27.43004324       7.03211396
    25         6.12251211      36.38711052      13.63014262       1.05419802       4.41653114      34.03301697       8.11491009
    26         3.15182859      67.49818208       9.29353978       0.45517522       1.94342627      14.58119109       5.00262002


                                                         The SAS System                        18:52 Saturday, July 11, 2015 293

                                                     The FASTCLUS Procedure
                               Replace=FULL  Radius=0  Maxclusters=28 Maxiter=5000  Converge=0.02

                                                         Cluster Means

Cluster           cz_asn           cz_nhw           cz_nhb           cz_ntv           cz_bhs           cz_whs           cz_ars
ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ
    27         0.47875928       4.76976632      14.32684213       0.26185624      29.50456559      44.92358232       6.66414000
    28         6.82210836      21.73869972      34.92974152       1.29755307       4.93693457      27.55982261       6.84358831

                                                         Cluster Means

       Cluster           cz_gun            cz_wep            cz_tol            cz_wgn            cz_frs            cz_ifc
       ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ
           1         0.09282449        0.14554253        0.41860258        0.88460894       32.72775908        4.89889097
           2         0.20266047        0.36313303        1.19493824        2.45549446       45.50228305       12.05302245
           3         0.06700229        0.18223957        0.67533805        1.27438527       37.10248163        6.63825963
           4         0.13328924        0.27768601        1.11308374        2.71026019       65.60935024       22.74791830
           5         0.06438557        0.22173923        0.59878603        1.40292836       60.88706459       10.39462149
           6         0.11596138        0.27973615        0.95911871        1.95596229       47.35825522       12.71020666
           7         0.11925359        0.31877476        1.06224914        2.41968550       43.06390452       12.73153693
           8         0.16918163        0.35434145        1.16771168        3.02358931       65.50960490       21.12903741
           9         0.09889521        0.47643120        1.47408339        2.75891407       34.89031304       11.26322487
          10         0.05602821        0.38785720        0.92048040        2.40327904       46.29086805       14.77824141
          11         0.11490963        0.27254419        0.91818245        2.32861003       47.92802667       12.11562008
          12         0.06188482        0.43345733        1.89904030        3.89415827       36.48230998       14.57086738
          13         0.24768176        0.39016425        1.08155489        1.69974523       56.27213387       14.59655842
          14         0.06904598        0.31996262        1.10256364        4.20707475       72.67999969       30.65251949
          15         0.23394715        0.39032713        1.21314632        6.27577555       77.68780276       40.29733296
          16         0.17549556        0.22264726        0.91859653        2.26426991       57.35338050       18.89956270
          17         0.09925945        0.52713974        1.02502399        3.65121736       49.55621814       16.39837652
          18         0.14704249        0.33241445        1.11457491        2.60967863       56.18776396       15.54352390
          19         0.12154177        0.23401323        0.80953433        1.38083866       51.30577621       11.29616460
          20         0.27033090        0.45886277        1.22161373        2.93137332       65.27458791       27.47954522
          21         0.05959550        0.10807045        0.33284689        0.85435938       58.97078441        6.06485167
          22         0.19742764        0.40852250        1.19204104        1.84101374       53.33881976       14.34020423
          23         0.19730979        0.38453225        1.42991708        4.40955235       68.31326800       24.17899574
          24         0.02838982        0.32989738        1.01320009        1.56223135       54.05027701       10.55593441
          25         0.07439667        0.35191664        1.02639220        2.29907173       65.87610462       17.08180158
          26         0.04384103        0.30365450        0.84229501        2.31674966       44.68762682       12.62275114
          27         0.08408784        0.56067751        1.02424855        5.09183263       57.12623025       20.38496379
          28         0.12697424        0.47553944        1.44914774        4.19699741       56.23756998       21.42976468


                                                  Cluster Standard Deviations

Cluster           cz_asn           cz_nhw           cz_nhb           cz_ntv           cz_bhs           cz_whs           cz_ars
ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ
     1        1.961329790      4.344866701      2.192033054      0.217083330      0.543020639      1.990729200      1.092867974
     2        7.470427708      5.596975699      5.667452567      1.751362267      2.833685292      5.048890921      6.561107552
     3        2.802311291      4.585399949      5.338740827      0.614489610      1.136605703      4.304536561      2.382066174
     4        5.590988547      5.222995863      6.055865341      0.645851568      2.596150215      5.753261455      2.860370737
     5        6.739399197      5.356433856      2.753884359      0.340558901      2.032737738      6.127253657      2.149615726
     6        5.982645679      4.654681649      5.597896816      1.087828582      2.342822469      5.477139567      3.005598093
     7        4.853900284      5.140451815      5.542581811      0.710442674      2.930520867      5.102340121      5.121342832
     8        2.068196632      5.144778685      6.604092242      0.447307841      3.274500898      5.814189559      2.615135203
     9        4.678705056      5.501877398      5.228929658      0.841843408      2.653822454      5.678869761      4.712351458
    10        2.124982414      5.906154832      7.490069843      0.783001238      1.677883764      4.611976927      2.728793458
    11        6.052251681      4.705825429      5.272240961      0.957680864      2.894634186      4.729932308      4.124175081
    12        1.532699022      5.650212782      5.744876490      0.267923355      1.844610707      4.341078590      3.851720035
    13        0.760016948      1.209592048      3.616936205      0.238582259      0.638838728      1.952329170      2.422691910
    14        2.684366834      2.098570331      3.267062188      0.300364898      2.122727936      5.662671761      1.610599329
    15        0.369772351      0.731892150      7.721316303      0.113304145      3.052027806      6.468964139      2.870775817
    16        6.637294980      4.727743549      6.377145739      0.530968913      1.620538513      4.727000736      4.321247520
    17        2.651397051      3.540430768      4.780485675      0.339209335      3.712040167      5.888712204      2.167766544
    18        1.777734241      3.858618744      6.745243588      0.572489546      3.320426069      4.528204769      3.392158832
    19        7.683324579      4.010599262      7.703887518      2.124367848      1.599932101      4.717874184      3.523864668
    20        0.754579239      1.659415510      5.033579428      0.249722282      0.960638453      3.291762571      3.351166501
    21        5.052640209      5.404711233      4.577338071      0.617690269      0.833904633      4.561368834      1.888723215
    22        2.469270301      4.002083151      4.647841678      0.375124579      1.162868659      3.236060320      2.890996126
    23        1.414278740      2.826388998      6.297268931      0.521477966      3.663560404      4.543007704      2.996190480
    24        3.355304990      4.853121608      3.589013249      0.573291704      1.817230986      5.435046044      3.706371850
    25        2.733951407      6.055533001      4.451006991      0.734590180      1.901811547      5.451030820      3.470601083
    26        1.968879442      5.084869732      4.551910029      0.430605434      1.099494386      3.935311465      2.498282871
    27        0.237268318      2.820809419      6.296117101      0.163281043      4.361137700      4.589551527      2.746787887
    28        5.425628531      6.008757995      5.497594664      1.252352338      2.614977895      6.247988732      3.567500465

                                                  Cluster Standard Deviations

       Cluster           cz_gun            cz_wep            cz_tol            cz_wgn            cz_frs            cz_ifc
       ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ
           1        0.249983187       0.169069888       0.288489484       0.767408583       6.387498195       2.789616838
           2        0.581486159       0.311977822       0.629715110       1.652845092       5.390844226       4.469764013
           3        0.186333231       0.293600674       0.544810264       1.073365493       6.398844282       3.494521717
           4        0.235492838       0.321777072       0.709523942       1.897045405       7.082896137       5.502424509
           5        0.171998071       0.209868253       0.319595670       0.761321949       6.484651747       5.036818728
           6        0.169432362       0.226666111       0.494914042       0.890773735       6.132080535       4.241629325
           7        0.407654254       0.480454584       1.077785625       2.290082335       5.899302602       5.528665961
           8        0.182133587       0.557042735       0.657551293       1.265656344       5.589554892       5.315867353
           9        0.260396980       0.838740782       1.345041387       2.135889981       6.548381036       4.539452264
          10        0.139181572       0.644512287       0.943045188       1.874525823       6.404902682       4.864720076
          11        0.291700041       0.306100311       0.597292546       1.993915714       5.978364820       5.485643863
          12        0.176542257       0.475185566       1.080731808       2.179738427       6.812773835       5.112173503
          13        0.299555423       0.344588240       0.556629764       0.937817255       6.720968360       4.870453490
          14        0.094021053       0.384333189       0.625106958       3.684043563       6.712881972       5.664512427
          15        0.255406737       0.330673664       0.449400286       2.762843737       3.260122842       7.256720356
          16        0.316889800       0.237158325       0.435673503       1.095257673       5.870666092       4.945715955
          17        0.133652851       0.514169170       0.605343603       2.718989388       6.361312526       5.431864536
          18        0.195888875       0.386125480       0.614037606       1.482269805       5.414366477       3.803199785
          19        0.173694355       0.214711051       0.409859960       0.754754570       5.772167869       5.427257390
          20        0.323761835       0.318641850       0.548544001       1.645352036       7.174319478       7.338595024
          21        0.217055421       0.155050414       0.398085296       1.059299437       5.343837940       3.127257435
          22        0.288887246       0.455345242       0.808263841       1.304971533       7.368611733       5.631993571
          23        0.357043166       0.475245063       0.911845658       1.954150768       5.011198755       4.574995891
          24        0.088495139       0.485488164       0.750518888       1.095420272       6.507792247       3.884364054
          25        0.172698484       0.502443261       0.664763403       1.480170040       6.030550289       5.064708600
          26        0.149286172       0.442055503       0.655918456       1.370001707       5.032493824       5.072088234
          27        0.110756953       0.629556759       0.542001709       1.508846191       6.435339934       3.758064703
          28        0.267979105       0.463591195       0.884537999       2.180054182       5.824756879       5.226676060



4.  Map the Clusters

The final step is to map the results of the statistical cluster analysis -- essentially transposing the purely mathematical space of the cluster analysis into the more familiar space of neighborhoods across the metropolis.  The cluster analysis shown above captures about 85 percent of the cross-neighborhood variance in the entire dataset; the variables on racial and ethnic composition dominate the analysis, however, as shown in the R2/1-R2 measures above.

In this map, we only shade a few of the clusters -- the ones that stand out on key variables of interest.  Each cluster may be regarded as a set of neighborhoods that are statistically distinctive on the basis of the measures used in the analysis.

The most severe "neighborhood spaces of violence" between the police and innocent civilians are in Clusters 15, 14, and 20.  In Cluster 15, 40 percent of all stops result in a case of physical force used by the officer, with no subsequent arrest or summons.  This share is 30 percent in Cluster 14, and slightly lower (27 percent) in Cluster 20. 


 
An interactive version of a sample of the stop-and-frisk data is available as a Google Fusion Tables file.  First, read the facts of the case of Leroy Downs, on pages 119-122 of this.  Then explore the 9,142 stop-and-frisk encounters during the same week Leroy was told by the officers to "get the [fuck] against the fence" for the offense of talking to a friend on his cell phone as an unmarked police car drove by his house.

This Google Fusion table is limited to a single week, August 17-23, 2008, to keep the numbers down.  The entire database between 2007 and 2013 is some 3.6 million stops, but the translation tool developed by Josh Livni to upload geographic data -- Shape Escape -- is limited to only 100,000 records; indeed, repeated tries with a database of about 36 thousand records fails to make the transfer.  So we reduce the number of observations by focusing on a shorter interval of time, and the translation is a success.  Now it's possible to explore the fine-grained geographies of stop-and-frisk encounters across the city for one summer week in 2008.