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imple indicators of crime by time of day
*
Marcus Felson , Erika Poulsen
School of Criminology, Rutgers University, 123 Washington Street, Newark, NJ 07102, USA
Abstract
Crime varies greatly by hour of day—more than by any other variable. Yet numbers of cases declines greatly when fragmented into hourly counts. Summary indicators are needed to conserve degrees of freedom, while making hourly information available for description and analysis. This paper describes some new indicators that summarize hour-of-day variations. A basic decision is to pick the first hour of the day, after which summary indicators are easily defined. These include the median hour of crime, crime quartile minutes, crime’s daily timespan, and the 5-to-5 share of criminal activity; namely, that occurring between 5:00 AM and 4:59 PM. Each summary indicator conserves cases while offering something suitable to forecast.
2003 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.
Keywords: Hour-of-day periodicity; Crime series data
1
. Introduction 2 . Background
¨
Crime varies more by hour of day than by any Hagerstrand (1973) showed how the individual other predictor we know. Such variation is analyzed traverses a path through space–time in the course of all too seldom. Perhaps one reason for this neglect is a day. The importance of these movements was that hourly data produce too many categories, 168 h explained in social psychological terms by Bandura
per week. The result is too few cases per cell (this (1985), who coined the term, ‘‘the psychology of loss of degrees of freedom impairs statistical analy- chance encounters.’’ Bandura described the intersec-sis) and too many cells (this leads to very large tion of individual paths in the course of a day and tables that are hard to understand). how these chance intersections can change individual
This paper provides some simple indicators that lives and even history.
help gain a solution to these problems. However, a However, human ecology teaches us that many larger problem needs additional work—how to think encounters are not so random as one might think. In about hourly variations in crime. his classic work,Hawley (1950)paid close attention to hourly activity patterns and explained how they are highly interdependent based on sustenance ac-tivities. More generally, Hawley distinguished three features of time organization: tempos, rhythms, and timing. A tempo is the number of events per unit of
*Corresponding author. Tel.: 11-973-353-5237.
time; that includes an annual crime rate or victimiza-E-mail addresses: [email protected](M. Felson),
[email protected](E. Poulsen). tion rate. A rhythm is the periodicity of a time
0169-2070 / 03 / $ – see front matter 2003 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved. doi:10.1016 / S0169-2070(03)00093-1
pattern. The monthly and seasonal cycles of crime majority of those driving cars or taking public transit are examples of periodicities and are widely known in the early hours of the morning might well have among criminologists (Harries, 1980). The hourly high blood-alcohol levels. That makes them likely periodicity of criminal behavior is generally known offenders and targets of crime and ineffective guar-but under-researched. Timing refers to the coordina- dians against it. Hence, it makes no sense at all for a tion or intersection of rhythms. The correspondence criminologist to treat midnight as the transition to a between the rhythm of school activity and the new day.
rhythm of delinquency in the course of a day is an Our first task is to figure out that transition time. important example of timing (Felson, 2002). Crime statistics on hourly crime patterns suggest that Timing is more than description alone; it is best 5:00 AM is probably the best time we have for the understood in light of theories of how crime relates beginning of a new day, at least for a criminologist’s to everyday life. For example, the environmental purposes. By that time, most of the substance abusers criminology of Brantingham and Brantingham and partygoers have either fallen asleep or have at
(1993) helps us understand how the paths of offen- least gone home. The bars are closed. Working ders and victims might cross in space and time. people begin to wake, and a glimmer of light from Geographers of crime also pay close attention to homes or sky sends cues that the window of crime hourly patterns and further assist us in putting this opportunity has largely closed.
information to use theoretically and empirically Hence, a day lasts from 5:00 AM through 4:59
(Harries, 1980; Rengert, 1996).The routine activity AM the next morning. We shall work with this approach pays close attention to hourly activities and assumption for the duration of this paper, but we their link to crime opportunity (Felson, 2002). recognize that not all nations, cities, or epochs will These many theoretical ideas cover both space and fit this pattern precisely. Nor does crime trail away time, but the spatial dimension is far more frequently equally every day of the week. However, such researched. The reason for that might be that geog- variations should not lead one to abandon this useful raphers have devised a variety of tools for mapping convention; it allows criminologists to compare activities in space and for summarizing spatial different places and decades. But first, one needs to processes statistically. Indeed, they have learned to consider the span of data incorporated in formulating conserve degrees of freedom with measures of hourly indicators.
central tendency and dispersion and with statistical analyses linking variables to one another over space.
The study of temporal patterns, especially by hour of 4 . The second task day, has lagged behind. That lag is probably the
result of inadequate summary statistics for crime In order to study hourly crime patterns, a patterns in time. The purpose of this paper is to criminologist must decide what offenses to summa-provide some summary statistics that are simple and rize and for what broader time period. For example,
easy with which to work. one might wish to describe the hourly patterns for all
armed robberies in the city of Houston from 1990 to 1999, or one might wish to compare New York
3
. The first task City’s hourly aggravated assault patterns for
Sep-tember versus October of 2001.
What is the first hour of the day? From the clock The second task is more complicated than meets viewpoint, one starts with 12:00 to 12:59 AM, but the eye. Many offenses are not readily reported to that would ignore what we know about crime. At the police, so their hourly patterns are not known, or that hour, many people are not yet straggling out of are subject to so much error that the methods urban bars, and parties are for some at a high swing. presented in the current paper are probably unusable. In many places, alcoholic beverage consumption For example, burglaries are generally coded by the accelerates after midnight in anticipation of closing hour the police are notified. Many people discover a hours, and food consumption may well decline. A burglary when they come home after work or a trip.
Thus, hourly burglary data are often missing, unreli- could calculate a standard deviation about the mean able or are coded as ‘‘sometime in the morning.’’ On mentioned above. We think that quartiles offer a the other hand, alarm companies might have accurate simpler and more cogent way to study hourly hourly data on alarms being set off and could even dispersion of crime and are more appropriate to the be able to subtract false alarms to produce realistic problem at hand. We suggest that the most direct and
hourly burglary data files. clearest way to study that dispersion is to find the
The problem with even the best hourly data, quartile minutes. After the median minute of crime is though, is the voluminous number of categories, with known, the first half of the crime day is itself cut in 24 h per day and 168 h per week. That is why half by the same method to give the first quartile summary indicators are essential for hourly analysis minute. The second half of the crime day is then cut
and forecasting. The purpose of this paper is to in half to give the third quartile minute. With the
provide those summary indicators. median minute of crime, these divide up the four
crime quartiles over the course of the day. Thus, if the median minute of crime is 7:00 PM and the first
5
. The median minute of crime quartile minute is 4:30 PM, that means that 25% of
crimes occur from 5:00 AM to 4:30 PM, and another Having selected 5:00 AM as the first moment of 25% from 4:30 PM to 7:00 PM. The third quartile the day, we can now devise several simple indicators minute dissects the latter half of the day. Thus, the for hourly patterns of crime. The first is the median first quartile minute, the median minute of crime, and minute of crime, namely, that minute of the day by the third quartile minute give us a good idea of how which exactly half of the crimes have occurred. For crime disperses over the day.
example, if the median minute of robbery is 6:13 PM, that means that exactly half the daily robberies
occur from 5:00 AM to 6:13 PM, and the rest from 7 . Crime’s daily timespan 6:13 PM to 4:59 AM the next morning. This simple
measure of central tendency tells us a good deal. For Once we know the quartile minutes, it is elemen-example, an entire decade of Houston armed rob- tary to calculate crime’s daily timespan. This is the beries could be summed up with this single indicator, number of minutes between the first and third which in turn gives us an idea of how early or late quartile minute. Where crime is more dispersed over these offenses occur. In Scandinavia, one could test the day, the daily timespan is higher. A narrow daily the hypothesis that summer months have a much timespan will be expected for smaller cities with less later crime pattern than winter months with one extended nightlife. The median minute of crime and number for each. Using unpublished data some years the daily timespan together tell us a lot of in-ago, the senior author noted that the median hour formation, even though they are but two numbers. was much earlier for crimes in Florida cities with High school students appear to have an early median many retired persons than in other cities with more minute of crime (around the time they get out of normal age structures. Hence, the simplicity of the school) and a narrow daily span of crime in-measure does not mean it lacks the power to answer volvement (see Felson, 2002). Entirely different questions. One can also calculate a mean minute as a patterns would be expected for older offenders measure of central tendency by subtracting 5 h from versus young, active offenders versus those who are the time of crime, finding the mean of those times, occasional, entertainment districts versus working
and then adding that time back. versus residential areas.
6
. Crime quartiles 8 . The 5-to-5 share of offenses
Measures of central tendency of course miss the We have presented so far four summary indicators dispersion over the hours of the day. Of course, one of how crime distributes over the course of a day. To
T able 1
take a different tack, we now ask what share of
Illustration of how to calculate descriptive indicators for hourly
offenses have occurred by a particular time. We pick
robbery patterns, Albany, NY, 2000
5:00 PM as a cutoff time, since that vaguely tells us
Hour of day Number Percent Cumulative Notes
when evening begins. What percent of offenses occur
of of all percent
by that time? We call this the 5-to-5 share of
incidents robberies
offenses. As evening and nighttime crime take over,
5:00–5:59 8 1.97 1.97
this indicator will decline. Technically speaking, this
6:00–6:59 8 1.97 3.94
number represents the percent of offenses that occur 7:00–7:59 1 0.25 4.19 from 5:00 AM to 4:59 PM. An early crime pattern 8:00–8:59 7 1.72 5.91
will push this indicator to higher levels. 9:00–9:59 9 2.22 8.13
10:00–10:59 11 2.71 10.84 11:00–11:59 5 1.23 12.07 12:00–12:59 15 3.69 15.76 9
. Demonstration 1:00–1:59 16 3.94 19.70 afternoon hours
in boldface type
The police departments of 13 middle-sized Ameri- 2:00–2:59 16 3.94 23.65
3:00–3:59 22 5.42 29.06 first quartile
can cities have provided us with robbery data for the
minute 3:00 PM
years 1999–2001 or parts of those periods. These
4:00–4:59 18 4.43 33.50
cities include Akron, OH; Albany, NY; Cincinnati, 5:00–5:59 9 2.22 35.71 5-to-5 share of
OH; Evansville, IN; Fort Wayne, IN; Hartford, CT; robberies 33.5%
Lincoln, NE; and Lowell, MA; Plano, TX; Rockford, 6:00–6:59 18 4.43 40.15
7:00–7:59 20 4.93 45.07
IL; South Bend, IN; Springfield, IL; and Tampa, FL.
8:00–8:59 35 8.62 53.69 median minute
The 2000 Census indicates that the largest of these
8:30 PM
cities is Cincinnati, with a population of 331,285. 9:00–9:59 31 7.64 61.33 The smallest is Albany, with 95,658 inhabitants. 10:00–10:59 14 3.45 64.78
The exact definition of robbery in these data is as 11:00–11:59 28 6.90 71.67
12:00–12:59 22 5.42 77.09 third quartile
follows: We have used all types of robberies for this
minute 12:35 AM
study which includes armed and unarmed robberies
1:00–1:59 29 7.14 84.24
as well as robberies of individuals and robberies of 2:00–2:59 18 4.43 88.67 commercial entities. We have classified these robbery 3:00–3:59 28 6.90 95.57
data by hour of day in order to calculate the 4:00–4:59 18 4.43 100.00
Total 406 100 daily timespan
descriptive statistics discussed in this paper.Table 1
575 minutes
illustrates these calculations for the hourly pattern of
1
robberies in the year 2000 in Albany, NY.
Although the table does not include every minute of the day, its 24 h of data make it easy to see that
one-fourth of the robberies occur by the first quartile or 9.5 h. About a third of the robberies occur by 5:00 minute, 3:00 PM. Another fourth occur by the PM, as indicated by the 5-to-5 share.
median minute of 8:30 PM. Three-fourths occur by These indicators prove quite useful for comparing the third quartile minute 12:35 AM. The rest occur the 13 cities. Although all of these cities have between then and 4:49 AM. The timespan between something in common with regard to hourly robbery the first and third quartile minutes is a full 575 min, patterns, they still differ in noticeable ways.Table 2
presents the descriptive indicators for the 13 cities, all calculated in or around the year 2000. The table orders the cities by the magnitude of their daily
1
This paper neglects standard errors. In future studies, we antici- timespans. For example, Albany’s timespan was 575 pate greater N’s per city and that this would be less an issue. The
min, or 9.5 h. On the other hand, Springfield, IL, had
formula for the standard error of a median can be found in
a daily timespan of only 402 min, or 6.5 h.
introductory textbooks. That same formula could be applied to
T able 2
Descriptive indicators for hourly robbery patterns in 13 cities, 1999–2001
City* Year First Median Third Daily The 5-to-5 Base
quartile minute quartile timespan share of number of
minute minute (min) robberies (%) robberies
Albany, NY 2000 3:00 PM 8:30 PM 12:35 AM 575 33.5 406 Evansville, IN 2000 3:30 PM 9:14 PM 12:58 AM 568 29.3 133 Tampa, FL 2000 3:14 PM 9:00 PM 12:25 AM 550 30.4 2199 Cincinnati, OH 2000 2:45 PM 8:12 PM 11:45 PM 540 34.2 1533 South Bend, IN 1999–2000 2:31 PM 8:00 PM 11:23 PM 532 33.6 801 Akron, OH 1999–2000 3:18 PM 9:00 PM 12:00 AM 521 31.9 1418 Fort Wayne, IN 2000 2:54 PM 8:32 PM 11:33 PM 519 32.2 367 Rockford, IL 2000 3:44 PM 8:30 PM 11:59 PM 494 27.5 298 Hartford, CT 2000 3:20 PM 8:16 PM 11:30 PM 489 30.2 872 Plano, TX 1999–2000 3:00 PM 7:52 PM 10:55 PM 475 32.6 218 Lowell, MA 2000–2001** 3:00 PM 7:00 PM 10:48 PM 468 30.1 246 Lincoln, NE 2000 5:08 PM 9:50 PM 12:22 AM 433 24.7 150 Springfield, IL 2000 4:21 PM 8:30 PM 11:03 PM 402 27.9 269
Note that the 5-to-5 share of robberies refers to those occurring from 5:00 AM to 4:59 PM. * Cities are ordered by magnitude of their daily timespans.
** Lowell, MA, robberies include April 2000 through September 2001.
information not measured by the timespans. For crime and making comparisons. We only considered example, one-fourth of South Bend’s robberies one crime and a limited range of mid-sized cities, but occurred by 2:31 PM, while in Lincoln, Nebraska, we believe that these indicators can in the future the same share was not achieved until 5:08 PM. The assist researchers in describing and predicting how third quartiles varied rather less, but still were not crime distributes over time.
equal across cities. Lowell, MA, saw three-fourths of
its robberies occurring by 10:48 PM, while Evansvil- 1 0.1. How crime timing distributes within cities le, IN, did not reach that mark until nearly 1:00 AM.
As Column 4 indicates, these same cities had the One might predict that entertainment districts of earliest and latest median minutes of robbery: 7:00 cities will tend to have both later median minutes PM for Lowell and 9:14 PM for Evansville. On the and a wider timespan of crime on weekends, but a other hand, the latest median minute was for Lincoln, narrower timespan Monday through Thursday. Busi-NE—9:50 PM. That was despite its being second ness districts might have earlier median minutes, a
lowest in daily timespan. very early third quartile point, and narrower
times-The 5-to-5 share of robberies provides a somewhat pans. Residential areas would probably vary by different summary of robbery time patterns. The proximity to central and shopping areas and by highest value on this indicator is calculated for commuting patterns. Areas near high schools will Cincinnati, with 34.2% of robberies occurring by tend to have earlier median minutes and narrower 5:00 PM. Although Rockford, IL, is in the middle of timespans. However, crimes carried out specifically the distribution on the other indicators, it had one of by more active young offenders might have an the lowest percentages on the 5-to-5 indicator. earlier median minute but wider timespan.
1
0.2. How crime timing distributes among cities
1
0. General implications
Cities with an older age structure will probably We believe that these descriptive indicators serve have earlier median minutes and narrower timespans. as useful tools for describing hourly patterns of Cities with greater variance in age will probably
have wider timespans for crime. Earlier bar closing forecasting directly. In recent decades, substantially laws when enforced may produce earlier crime more data on crime by hour of day has become medians. Cities with more liquor consumption in available. Such data can suitably be aggregated cars and outdoors will tend to have later medians and according to the rules presented in the current paper. perhaps wider timespans, too. Cities with earlier As a result, we suggest that crime forecasting store closing hours will tend to constrain their crime strategy shift and make use of what we now know
patterns in time as well. about shifting activity patterns in the course of daily
life. 1
0.3. How crime distributes among nations The central purpose of this paper is to argue that forecasting strategies based on monthly, quarterly, or Nations in the northern part of the Earth would annual crime totals miss the essential dynamic in probably have, during the summer, later median crime rate trends. Such breakdowns might be suit-minutes and wider timespans for both property and able for studying labor markets, housing starts, and violent offenses. However, crimes of violence during other economic shifts and cycles, but are less than their winter months might well depend upon liquor ideal for studying and forecasting changes in crime. policies and enforcement. Nations with indoor gar- The econometric roots of crime forecasting, includ-ages will tend to constrain later car thefts, while ing that carried out by the senior author, can hinder those lacking indoor parking will tend to have later more than they help. The time is to move beyond hours and wider timespans of auto theft. Gun availa- these roots and to recognize that crime has its own bility will probably tend to widen the daily timespan dynamics, driven by the daily course of activities, of robbery by making it easier for an offender to shifting by the hour.
accost someone and quickly succeed, even in light or That is not to say that monthly, quarterly, and
dusk. annual crime statistics should be dropped in
forecast-ing. Indeed, summing hourly data to these larger 1
0.4. Significance for policy levels provides a way to have your small statistics
and aggregate them, too. Thus, an annual summary
Knutsson (1994) has shown a major discrepancy of median hour of burglary can be calculated and between the hourly patterns of crime and the hourly then put into a time series for a statistical analysis levels of police assignment. That point offers us over a longer timespan, taking into account the small strong evidence that ignoring these ‘‘details’’ leads to features of daily crime that drive crime rate trends serious waste of resources. Not only does demand and cycles, even over the years.
for service vary greatly over the day, but the types of A secondary purpose of this paper is to argue that service demanded also vary. Earlier in the day, truant we no longer need to rely solely on spectral analysis officers and school crime officers might be needed. as a means for studying crime over detailed time. Later, drug control expertise might be most relevant. This is not to deny its benefits when one lacks Still later, alcohol management personnel are central. hypotheses and a priori knowledge about the various trends and cycles, nor is this to deprecate its beauty in pulling out various cycles statistically, ones that fit
1
1. Implications for forecasting roughly what we know about daily activity patterns over the calendar. However, we know much more Some years ago, the senior author discovered that today about how the specifics of daily crime congeal forecasting crime from 1963 to 1975 depended on and disperse over time and, hence, how to build both studying trends in crime settings and crime timing independent and dependent variables explicitly into
(Cohen & Felson, 1979).The dispersion of activities forecasting models.
away from family and household settings produced a The third purpose of this paper, by no means major crime wave. That paper pointed towards a small, is to help relieve the central frustration of forecasting strategy that emphasized time patterns of many forecasters who, perhaps, are tired of being activity in spirit, but lacked the data to carry out such ignored by larger policy makers and substantive
H
arries, K. D. (1980). Crime and the environment. Springfield, IL:
scholars. These groups are not oriented towards the
Charles C. Thomas.
more advanced methods and more difficult
in-H
awley, A. (1950). Human ecology: A theory of community
dicators. The simple ones presented here can help structure. New York: Ronald Press.
sophisticated forecasters communicate beyond their K nutsson, J. (1994). More crimes while police resources remain
own ranks, while at the same time making good use constant—what will happen with the clearance rate in the future? Studies on Crime and Crime Prevention,3, 132–145.
of forecasting methodologies.
R
engert, G. (1996). The geography of illegal drugs. Boulder, CO: Westview.
R
eferences
Biographies: Marcus FELSON is author of Crime and Everyday Life, (Sage Publications), now in its third edition, and has
B
andura, A. (1985). The psychology of chance encounters and life developed the ‘‘routine activity approach’’ to crime analysis. He is patterns. American Psychologist,37, 747–755. also co-author (with Ronald V. Clarke) of Opportunity Makes The B
rantingham, P. L., & Brantingham, P. J. (1993). Nodes, paths and Thief, published by the British Home Office. Professor Felson edges: Considerations on the complexity of crime and the graduated from University of Chicago and received his graduate physical environment. Journal of Environmental Psychology, degrees from the University of Michigan. He is Professor of
13, 28–53. Criminal Justice at Rutgers University.
C
ohen, L. E., & Felson, M. (1979). Social change and crime rate trends: A routine activity approach. American Sociological
Erika POULSEN is a PhD candidate in the Geography
Depart-Review,44, 588–608.
ment at Rutgers University, and is the research director for the F
elson, M. (2002). Crime and everyday life. 3rd ed.. Thousand
Crime Mapping Research Lab in the School of Criminal Justice, Oaks, CA: Pine Forge Press.
Rutgers University. Her research involves applying geographic ¨
H
agerstrand, T. (1973). The domain of human geography. In
techniques and methodologies for the spatial analysis of crime. Chorley, R. J. (Ed.), Directions in geography. London:
