Use your assigned readings and research to address the problem of tire slashings. Research tire slashing in a large metropolitan area that may consist of multiple jurisdictions. Search the local news
1306330 – S A GE P ublic a tio ns © e quency a nd P erc e nta g e The m ost b asic fo rm of d ete rm in in g fre q uen cy is u sin g co unt a nd perc en ta ge. H ow ever, i n v a ria ble s th at h ave n um ero us ca te g orie s (e .g ., a ddre sses a nd ty p es o f c a lls fo r s erv ic e), a naly sts so rt th e ca te g orie s in descen din g fre q uen cy b y h ig hest c o unt, a s th is m akes th em ea sie r to exa m in e. T able 1 3.1 s h ow s th e co unt a nd perc en ta ge o f ro bberie s b y b ea t, s o rte d in descen din g co unts . R ath er th an lis t th e b ea ts in ord er, t h is ta ble a llo w s a quic k a ssessm en t o f w hic h bea ts h ave th e m ost s tre et ro bberie s. In sit u atio ns w it h a la rg e n um ber o f v a lu es (in th e T able 1 3.1 b ea ts ), i t m ay n ot b e necessa ry to pro vid e th e en tir e lis t b ut o nly th e to p five, 1 0, o r 2 5 (e .g ., a ddre sses o r c a ll t y p es). T he re st w ould still b e in clu ded in th e ta ble to sh ow th e in cid en t to ta l in aggre g ate f o rm . T able 1 3.2 illu stra te s a lis t o f th e to p five ca lls -f o r-s erv ic e ty p es fo r a n en tir e cit y in d escen din g ord er, w it h th e re st o f th e ca ll t y p es a ggre g ate d . 1306330 – S A GE P ublic a tio ns © A naly sts o fte n pla ce fre q uen cy d ata in bar o r lin e ch arts b eca use th is a llo w s th em to m ake vis u al c o m paris o ns a m ong th e ca te g orie s. F ig ure 1 3.1 is a bar c h art (a ls o ca lle d a his to gra m ) o f th e fre q uen cy o f ro bberie s p er b ea t. B ar c h arts a re ty p ic a lly u sed fo r ca te g oric a l v a ria ble s (e .g ., b ea ts a nd ty p es o f ro bberie s). B eca use th e b ar c h art is a vis u aliz a tio n and th e “fre q uen cy” c a te g ory is o bvio us, i t is n ot a lw ays n ecessa ry to a rra nge th e ca te g orie s in descen din g ord er, b ut in ord er o f th e ca te g oric a l v a ria ble (e .g ., B ea t 1 , B ea t 2 , B ea t 3 ). L in e ch arts a re u sed fo r o rd in al a nd ra tio va ria ble s (e .g ., m onth s and age) a nd are illu stra te d in the n ext s ectio n . S tra te g ic crim e a naly sts u se fre q uen cy o fte n , b ut th ey d o not u se th is sta tis tic a lo ne to u nders ta nd th e p re va le n ce o f a pro ble m fo r th e fo llo w in g re a so ns: J ust b eca use a n addre ss o r a re a has th e “m ost” in cid en ts o f a pro ble m does n ot m ea n it is th e “w ors t” a re a . M any tim es a naly sis is b ased on “re p orte d ” c rim es a nd ca lls fo r s erv ic e, s o le vels o f re p ortin g in fluen ce th e sta tis tic s. B oth “g ood” a nd “b ad” neig hborh oods ca n have lo w fre q uen cie s— th e fo rm er b eca use th ere is lit tle o r n o activ it y to re p ort, a nd th e la tte r b eca use p eo ple a re a fra id to re p ort th e a ctiv it y th at occu rs . In co m paris o ns o f u nit s th at a re d is sim ila r, f re q uen cy m ay d is to rt a pro ble m (e .g ., c o m parin g an are a of 2 00 sq uare m ile s a nd a popula tio n of 3 00,0 00 to one o f 2 0 sq uare m ile s a nd a popula tio n of 1 0,0 00). F ig ure 13.1 B ar C hart: F re q uen cy o f R obberie s b y B ea t 1306330 – S A GE P ublic a tio ns © V aria ble s w it h la rg e n um bers o f c a te g orie s m ay b e d iffi cu lt to illu stra te u sin g sim ple f re q uen cy (e .g ., f re q uen cy o f c rim e a t in div id ual a ddre sses, f re q uen cy o f o ffe n ders b y a ge). T hese lo ng lis ts a re o fte n aggre g ate d in to la rg er c a te g orie s, s u ch as in div id ual a ddre sses a ggre g ate d by stre et s eg m en t o r n eig hborh ood and offe n ders ’ a ges a ggre g ate d in to m ult ip le yea rs (e .g ., 1 7 or y o unger, 1 8 to 24, 2 5 to 34, e tc .) . F re q uen cy o f a va ria ble w it h sm all v a lu es ca n be m ea nin gle ss. F or e xa m ple , c o unts o f h om ic id e fo r 4 yea rs in a sm all c o m munit y m ay b e 0 , 1 , 3 , 0 . C le a rly , t h ese very s m all n um bers d o not te ll u s m uch about w heth er th ere is a hom ic id e p ro ble m . It is im porta nt to note th at b efo re n arro w in g th e sco pe o f a pro ble m , f re q uen cy ca n be m is le a din g beca use d if fe re n t ty p es o f a ctiv it y a re re p re sen te d in th e m ore g en era l ca te g ory . A n im porta nt e xa m ple o f th is is a ggra va te d assa ult s . T here is a very im porta nt d if fe re n ce b etw een aggra va te d assa ult s b etw een in tim ate s (i.e ., d om estic v io le n ce) a nd assa ult s b etw een stra ngers o r e ven acq uain ta nces (i.e ., fi ghts a t b ars , d riv e-b y sh ootin gs). A fre q uen cy o f a ll a ggra va te d assa ult s w ill h id e th e co unts o f th ese tw o dis tin ct ty p es o f a ctiv it y a nd m ay le a d to erro neo us co nclu sio ns a bout pote n tia l r e sp onses. In clu din g perc en ta ges in fre q uen cy ta ble s a nd ch arts a llo w s a co m paris o n of c a te g orie s a nd help s to in dic a te th e p re va le n ce o f a pro ble m . T his is p artic u la rly re le va nt w hen co m parin g acro ss d if fe re n t d ata sets . F or e xa m ple , T able 1 3.3 is a co m paris o n of d ata sets f o r 2 yea rs a nd sh ow s 2 10 stre et ro bberie s in Yea r 1 and 200 in Yea r 2 . T hese co unts a ppea r s im ila r w hen co nsid erin g th em alo ne. H ow ever, i f w e lo ok a t w hat p erc en ta ge stre et ro bberie s a re o f th e to ta l f o r th e yea r, Y ea r 1 has 8 5% , a nd Yea r 2 has 5 0% . T hese p erc en ta ges a re m uch dif fe re n t, e ven th ough th e fre q uen cie s fo r Y ea rs 1 and 2 are sim ila r. T his is b eca use th e n um ber o f o vera ll r o bberie s in cre a sed fro m 247 in Yea r 1 to 400 in Y ea r 2 , m akin g stre et ro bberie s a m uch sm alle r p ortio n of a ll r o bberie s in Yea r 2 . P erc en ta ge va lu es co uld pro vid e m ea nin gfu l in fo rm atio n fo r a n assessm en t o f a re sp onse to stre et ro bberie s in th is exa m ple . T hat is , e ven th ough th e a ctu al n um ber o f s tre et ro bberie s o nly d ecre a sed by 1 0, t h e p erc en ta ge o f th e to ta l r o bberie s d ecre a sed by 3 5, sh ow in g th at s tre et ro bberie s a re m uch le ss fre q uen t in Yea r 2 th an in Yea r 1 re la tiv e to th e to ta l. L ik e fre q uen cie s, p erc en ta ges ca n als o be d ep ic te d in ch arts . T he ty p e o f c h art m ost co m monly u sed fo r th is p urp ose is a pie ch art. W hen cre a tin g pie ch arts , c rim e a naly sts ty p ic a lly in clu de n o m ore th an five to seven ca te g orie s so th at th e slic es o f th e p ie d o not beco m e to o sm all t o see a nd la bel. J ust a s w it h ta ble s, c h arts ca n be u sed to co m pare a cro ss d is trib utio ns. F ig ure 1 3.2 a nd Fig ure 1 3.3 illu stra te th e re la tiv e p erc en ta ge o f s tre et ro bbery in both yea rs a nd allo w fo r a n ea sy vis u al c o m paris o n of th e d if fe re n ces sh ow n in T able 1 3.3 . N ote th at th e fi gure ca ptio n of e a ch ch art in clu des th e to ta l n um ber o f ro bberie s (i.e ., N m ea ns n um ber o f c a ses); t h is is im porta nt b eca use it p ro vid es co nte xt f o r th e p erc en ta ge va lu es illu stra te d in th e ch art. 1306330 – S A GE P ublic a tio ns © R ate In addit io n to usin g perc en ta ge, c o m putin g a ra te is a ls o an im pro vem en t o ver f re q uen cy to unders ta nd th e p re va le n ce o f a pro ble m . R ate s a llo w th e a naly st to co m pare fre q uen cy o f in cid en ts fo r d is sim ila r a re a s a nd lo ca tio ns. T he exa m ple g iv en fo r ra te s in th e p re vio us ch apte r u sed popula tio n as th e d en om in ato r. H ow ever, w hen an analy st is exa m in in g a pro ble m , u sin g popula tio n to co m pute a ra te m ay n ot a lw ays p ro vid e re le va nt in fo rm atio n fo r c o m paris o n. F or in sta nce, i t w ould not b e a ppro pria te to use p opula tio n to co m pare f re q uen cy o f c o m merc ia l b urg la rie s o ver s evera l a re a s b eca use p eo ple d o not liv e a t co m merc ia l b usin esses. A co m merc ia l b urg la ry ra te u sin g popula tio n w ould sh ow hig h ra te s in co m merc ia lly zo ned are a s b eca use th e p opula tio n co unts w ould be lo w . In c o ntra st, a ra te o f c o m merc ia l b urg la rie s b y n um ber o f c o m merc ia l b usin esses w ould s h ow th e re la tiv e n um ber o f b urg la rie s in dif fe re n t a re a s a cco rd in g to th e n um ber o f re le va nt ta rg ets . T able 1 3.4 d ep ic ts co m merc ia l b urg la rie s b y 1 00 ta rg ets (c o m merc ia l pla ces) p er b ea t. F ig ure 13.2 P ie C hart: P erc en ta ge o f S tre et R obbery (N = 247), Y ea r 1 F ig ure 13.3 P ie C hart: P erc en ta ge o f S tre et R obbery (N = 400), Y ea r 2 1306330 – S A GE P ublic a tio ns © A naly sts co m pute ra te s fo r p ro ble m s b y u sin g th e a ppro pria te d en om in ato r, d ep en din g on th e co m paris o ns th ey w ant to m ake. H ere a re so m e exa m ple s: P er d w ellin g or a partm en t u nit (e .g ., t o co m pare th e n um ber o f re sid en tia l b urg la rie s b eca use th e ta rg e t is th e re sid en tia l u nit , n ot th e n um ber o f p eo ple liv in g in it ) P er ro om (e .g ., t o co m pare h ote ls a nd m ote ls o f d if fe re n t s iz es) P er b uild in g (e .g ., t o co m pare co m merc ia l d is tric ts b y th eir re la tiv e siz e) P er s q uare fo ot (e .g ., t o co m pare co m merc ia l b uild in gs co nta in m ult ip le fl oors o f co m merc ia l s p ace) P er o ccu pancy ra te (e .g ., t o co m pare b ars , n ig htc lu bs, o r o th er s erv ic e esta blis h m en ts , g iv en th at th e a ctu al n um ber o f p atro ns is d iffi cu lt to m ea su re ; n ote 1306330 – S A GE P ublic a tio ns © t h at o ccu pancy ra te a nd sq uare fo ota ge a re co rre la te d and th us essen tia lly m ea su re th e sa m e th in g) P er p ark in g sp ace (e .g ., t o co m pare p ark in g lo ts , g iv en th at th e n um ber o f s p aces in a lo t d ete rm in es h ow m any ca rs it c a n hold ) P er a cre (e .g ., t o co m pare p ark s o r o th er la nd m asses) P er b uild in g perm it (e .g ., t o co m pare n um ber o f b urg la rie s a t c o nstru ctio n sit e s b y how m any h ouses a re u nder c o nstru ctio n) H ow ever, u sin g su ch alt e rn ativ es to dete rm in e ra te s d oes n ot a lw ays so lv e th e co m paris o n pro ble m . F or e xa m ple , u sin g park in g spaces to dete rm in e th e re la tiv e siz e o f a park in g lo t does n ot a cco unt f o r h ow m any sp aces in th e p ark in g lo t a re a ctu ally u sed or h ow m uch tim e ea ch ca r s p en ds in th e lo t. Ot her in fo rm atio n, s u ch as th e le n gth of tim e p er d ay th e park in g lo t is o pen and th e a m ount o f tim e th at c a rs ty p ic a lly sp en d in th e p ark in g lo t, a ls o w ould be u sefu l f o r c o m paris o n purp oses. H ow ever, s o m e kin ds o f in fo rm atio n ca n be diffi cu lt to obta in and update re g ula rly , s o analy sts m ay h ave to re ly o n th e m ost re le va nt and accessib le in fo rm atio n fo r th e p ro ble m at h and. W hen co m munic a tin g th eir re su lt s , th ey sh ould be cle a r a bout w hat is b ein g used fo r c o m paris o n. Case S tu dy, C hula V is ta , C alif o rn ia : I n a stu dy o f th eft f ro m ve hic le in C hula V is ta , r e searc hers and analy s ts fo und th e fo llo w in g: “ O ur R is k R ate S ubcom mit te e m ade som e in te re stin g findin gs. T he ta rg et lo ts w it h th e hig hest v o lu m e of th efts w ere not n ecessarily th ose w it h th e hig hest ris k ra te . O ne of o ur ta rg et lo ts , t h e S w ap M eet, o pen only 2 days a w eek, e xp erie nced 42 auto th efts in 2001 and tw o auto burg la rie s. W e suspecte d th at th e S w ap M eet w ould have th e hig hest lo t ris k ra te . T his t u rn ed out to be untru e, a s som e of th e sm alle r lo ts , o pen 7 days a w eek, e ve n w it h lo w er v o lu m es of th eft w ere m uch ris kie r. W hen th e S ubcom mit te e to ok in to account th e vo lu m e of c ars ente rin g and exit in g th ese lo ts , t h e num ber o f p ark in g spaces in th ese lo ts , t h e ave ra ge le ngth of tim e park ed fo r th ese lo ts , a nd th e num ber o f d ays th ese lo ts w ere open to park in g, t h ey fo und th at C hula V is ta ’s t ro lle y c om mute r lo ts had ris k ra te s of u p to te n tim es hig her th an th e ave ra ge of th e oth er lo ts c om bin ed. P erh aps w e should not h ave been so surp ris ed as th e tro lle y lo ts (a m ongst a ll t h e ta rg et lo ts ) h ad th e m ost f a vo ra ble condit io ns fo r a uto th eft (a w id e ra nge of o ld er v e hic le s, n o re gula r securit y p atro ls , u nfe tte re d access, m ult ip le exit s , v e hic le ow ners park ed fo r v e ry lo ng perio ds of tim e, and pro xim it y to th e fre ew ay— tw o m in ute s or le ss by c ar) .” (S am pson, 2 004, p . 1 3) In th e sca nnin g and analy sis ste p s, c rim e a naly sts u se th re e ra te s re g ula rly to co m pare lo ca l c rim e p ro ble m s w it h natio nal c rim e p ro ble m s, a s w ell a s to describ e p artic u la r gen era l p ro ble m s: c rim e ra te , c le ara nce ra te , a nd re co ve ry ra te . A crim e ra te is ty p ic a lly t h e n um ber o f re p orte d crim es in an are a div id ed by th e n um ber o f p eo ple liv in g in th e are a . N atio nal a nd sta te crim e ra te s a re ty p ic a lly re p orte d as th e n um ber o f P art I c rim es p er 1 00,0 00 pers o ns (n um ber o f c rim es d iv id ed by p opula tio n and th e re su lt m ult ip lie d by 100,0 00). A t th e lo ca l le vel, h ow ever, r e p ortin g crim e ra te b y 1 00,0 00 pers o ns m ay n ot b e appro pria te , e sp ecia lly in co m munit ie s w it h popula tio ns sm alle r th an 100,0 00 (i.e ., r e p ortin g crim e ra te p er 1 00,0 00 w ould giv e th e im pre ssio n th at m ore crim es a re o ccu rrin g th an actu ally a re ). If a to w n of 5 0,0 00 re sid en ts h as 3 ,0 00 P art I c rim es, t h is co m pute s to a P art I c rim e ra te o f 6 ,0 00 crim es p er 1 00,0 00 pers o ns. A lt h ough it is im porta nt th at analy sts u se “p er 1 00,0 00” ra te s w hen co m parin g crim e le ve ls in th eir ju ris d ic tio ns w it h n atio nal o r s ta te le vels , t h ose w ork in g in sm alle r ju ris d ic tio ns ca n exa m in e ra te s p er 1 0,0 00 or 1 ,0 00 pers o ns, d ep en din g on w hic h is m ore re le va nt f o r c o m parin g crim e ra te s o f s m alle r a re a s w it h in a partic u la r ju ris d ic tio n (e .g ., c en su s tra cts , b ea ts , p re cin cts ). A noth er is su e th at c rim e a naly sts n eed to co nsid er w hen usin g crim e ra te s a t th e lo ca l le vel is th e d is tin ctio n betw een pro perty crim e a nd pers o ns crim e. M ost p eo ple th in k th at vio le n t c rim e is m ore co m mon th an pro perty crim e, e ven th ough th e re vers e is tru e. F or exa m ple , i n 2014 la w en fo rc em en t a gen cie s a cro ss th e U nit e d S ta te s re p orte d a to ta l o f 1,1 65,3 83 vio le n t c rim es to th e F B I; i n th e sa m e yea r, t h ey re p orte d 8,2 77,8 29 pro perty c rim es (F B I, 2 016), a bout a 1:7 ra tio . C rim e a naly sts n eed to be ca re fu l t o sep ara te th e tw o ty p es o f c rim e in to tw o dif fe re n t ra te s to avo id m is in te rp re ta tio n. A noth er ra te o fte n used in pro ble m analy sis is th e cle a ra nce ra te . T he U nif o rm Crim e Rep ort p ro gra m ackn ow le d ges tw o w ays in w hic h crim es a re cle a re d : ( a ) b y a rre st a nd (b ) by excep tio nal m ea ns. A crim e is cle a re d by a rre st if a t le a st o ne p ers o n is a rre ste d fo r th e crim e, c h arg ed w it h th e co m mis sio n of th e crim e, a nd tu rn ed over to th e co urt f o r pro secu tio n. T he U CR co unts th e n um ber o f c rim es cle a re d , n ot th e n um ber o f in div id uals a rre ste d ; t h e a rre st o f o ne in div id ual m ay cle a r s evera l c rim es, a nd th e a rre st o f m any in div id uals m ay cle a r o nly o ne crim e. A crim e is cle a re d by excep tio nal m ea ns if c ir c u m sta nces b eyo nd polic e co ntro l p re ven t th e cle a rin g of th e crim e b y a rre st. F or th e U CR pro gra m to co unt a crim e a s cle a re d by excep tio nal m ea ns, t h e p olic e a gen cy m ust h ave th e fo llo w in g: k n ow le d ge o f th e o ffe n der’s id en tit y ; e n ough evid en ce to su pport a rre stin g, c h arg in g, a nd tu rn in g over th e o ffe n der to th e co urt f o r p ro secu tio n; a nd kn ow le d ge o f th e o ffe n der’s exa ct lo ca tio n so th at la w en fo rc em en t c a n m ake a n arre st (F B I, 2 016). E xa m ple s o f e xcep tio nal c le a ra nce in clu de d ea th of th e o ffe n der, v ic tim ’s r e fu sa l t o pro secu te , a nd den ia l o f e xtra dit io n. C le a ra nce ra te s a re ty p ic a lly re p orte d as p erc en ta ges. F or e xa m ple , i f 2 00 ro bberie s w ere re p orte d in th e p ast y ea r a nd 90 of th em were cle a re d , t h e cle a ra nce ra te w ould be 4 5 per 1306330 – S A GE P ublic a tio ns © 1 00 ro bberie s, o r 4 5% (in ste a d of .4 5). A s w it h natio nal c rim e ra te s, n atio nal c le a ra nce ra te s a re b ased on P art I c rim es o nly . W hen analy zin g pro ble m s, c rim e a naly sts u se cle a ra nce ra te s to dete rm in e th e n um bers o f c rim es fo r w hic h arre sts h ave b een m ade a nd to co m pare lo ca l t o natio nal r a te s (e .g ., t o see if th e lo ca l c le a ra nce ra te is lo w er th an th e natio nal r a te ). F in ally , t h e th ir d ra te ty p ic a lly u sed in pro ble m analy sis is re co very ra te , w hic h is th e perc en ta ge o f v eh ic le s th at h ave b een sto le n in a ju ris d ic tio n and su bseq uen tly re co vere d (i.e ., f o und) a nyw here . It is a ls o re p orte d as a perc en ta ge. A naly sts u se th is ra te to help u nders ta nd th e n atu re o f a n auto th eft p ro ble m . F or in sta nce, i f th e re co very ra te in a cit y is 9 0% (i.e ., 9 out o f 1 0 sto le n ca rs a re la te r f o und), i t is cle a r th at th e cit y ’s a uto th eft p ro ble m does n ot p rim arily in vo lv e o ffe n ders w ho dis m antle ca rs fo r re sa le o f p arts o r exp ort th em out o f th e co untry . M ean and S ta ndard D evia tio n Lastly , a s n ote d in C hapte r 1 2 , m ea n and sta ndard devia tio n are n ot h elp fu l t o describ e dis trib utio ns o f d ata beca use crim e a naly sis d ata te n d to have sig nifi ca nt o utlie rs . H ow ever, t h ese sta tis tic s a re very h elp fu l in pro vid in g yet a noth er w ay to co m pare a re a s, lo ca tio ns, a nd oth er a sp ects o f a pro ble m to dete rm in e h ow wid esp re a d or f o cu sed a pro ble m mig ht b e. B eca use m ea n and sta ndard devia tio n help estim ate th e cen tra l te n den cy o f th e va lu es, t h ey ca n be u sed to dete rm in e w heth er a partic u la r c o unt o r ra te is n orm al o r u nusu al. F or e xa m ple , i f a crim e a naly st is exa m in in g a pro ble m of th efts fro m veh ic le s a t re ta il e sta blis h m en ts , t h e a naly s t m ig ht c o m pute th e ra te fo r th e n um ber o f th efts p er p ark in g sp ace fo r e a ch re ta il lo ca tio n in th e cit y . W hen th ese lo ca tio ns a re so rte d in descen din g ord er, t h e lo ca tio n w it h th e h ig hest ra te is a t th e to p. H ow ever, i s th e ra te o f crim e a t th is lo ca tio n pro ble m atic o r th at m uch dif fe re n t f ro m th e o th ers ? M ea n and sta ndard devia tio n help to dete rm in e th is . T able 1 3.5 s h ow s a lis t o f 1 0 su ch lo ca tio ns lo okin g at d ata fo r 1 2 m onth s. T he R eta il P la za 1 has th e h ig hest ra te o f th eft, b ut if th e m ea n and sta ndard devia tio n fo r th e en tir e c it y (n ot a ll lo ca tio ns a re sh ow n fo r s im plic it y ) a re 2 .6 7 and 0.8 6, r e sp ectiv ely , w e see th at R eta il P la za 1 is w it h in 1 sta ndard devia tio n of th e m ea n (2 .6 7 +.8 6 = 3.5 3), w hic h in dic a te s th e to p lo ca tio n is n ot th at m uch dif fe re n t th an th e o th er lo ca tio ns. 1306330 – S A GE P ublic a tio ns © T able 1 3.6 s h ow s a dif fe re n t e xa m ple co m parin g assa ult s p er 1 00 pers o ns (i.e ., o ccu pancy o f th e b ar) a t th e to p five b ars o ver 1 2 m onth s. If th e m ea n of a l l 1 00 bars in t h e cit y is 9 .2 3 and th e sta ndard devia tio n is 4 .0 1, 3 sta ndard devia tio ns (4 .0 1 × 3 = 12.0 3) fro m th e m ea n is a va lu e o f 2 1.2 6 assa ult s p er p ers o n (1 2.0 3 + 9.2 3). W it h va lu es o f 25.3 0, 2 5.2 3, a nd 24.0 2, r e sp ectiv ely , t h e to p th re e b ars h ave co nsid era bly m ore a ssa ult s th an are ty p ic a l in all t h e b ars in th e cit y a nd in dic a te th at th e a ssa ult p ro ble m and th e ta ilo re d re sp onse m ig ht b e fo cu sed on th ese th re e lo ca tio ns. L ik e fre q uen cy a nd perc en ta ge, i t c a n be h elp fu l f o r th e a naly st to illu stra te th e re su lt s o f m ea n and sta ndard devia tio n in a ch art. F ig ure 1 3.4 s h ow s th e ra te s o f a ssa ult f o r th e fi ve b ars fro m Table 1 3.5 a lo ng w it h lin es th at re p re sen t th e m ea n and firs t, s eco nd, a nd th ir d s ta ndard devia tio ns a bove th e m ea n. T hose b elo w th e m ea n are n ot s h ow n sin ce o ur purp ose is to id en tif y b ars w it h th e h ig hest ra te s. T he ch art illu stra te s th e re su lt s a nd m akes it e a sy to dete rm in e w hic h bars a re sig nifi ca ntly h ig her th an th e o vera ll m ea n. N ote th at th is is ju st a sim ple exa m ple , a nd m ore lo ca tio ns ca n be in clu ded on su ch a ch art. F ig ure 13.4 R ate s o f A ssa ult s p er 1 00 P ers o ns a t B ars , M ea n and S ta ndard D evia tio ns 1306330 – S A GE P ublic a tio ns © I t is im porta nt to note th at m ea n and sta ndard devia tio n are le ss re lia ble a nd not a lw ays n ecessa ry w hen w ork in g w it h data sets w it h fe w er th an 10 ca ses b eca use o ne o r tw o unusu al c a ses ca n sig nifi ca ntly in fluen ce th e sta tis tic s. H ow ever, t h is is n ot a hard and fa st ru le , a nd th e re su lt s o f th ese a naly ses sh ould be clo sely scru tin iz ed w hen w ork in g w it h sm all n um bers o f c a ses. Case S tu dy, C hula V is ta , C alif o rn ia : M edia n can als o be used to dete rm in e th e dif fe re nce of o ne lo catio n fro m th e oth ers because it in dic ate s th at 5 0% of th e lo catio ns are above and belo w a partic ula r v a lu e. F ig ure 13.5 is fro m a pro ble m analy s is of b udget m ote ls in C hula V is ta in w hic h th e hote ls are show n by th eir c alls fo r s erv ic e per ro om (ra te ) in com paris on to th e m edia n fo r a ll t h e hote ls . T he re port s ta te s, “ T he pro ble m analy s is conducte d up to th is poin t in th e pro je ct w as ve ry h elp fu l in id entif y in g basic pro ble m s th at n eeded atte ntio n at th e m ote ls (s uch as ro om securit y ) a nd fa cto rs associa te d w it h hig h C FS (re ntin g to lo cal a nd lo ng-te rm guests ), b ut th ese analy tic al fi ndin gs did not f u lly e xp la in th e extre m e va ria tio n in C FS per ro om ra tio s fo und at C hula V is ta m ote ls (f ro m a hig h of 2 .7 7 C FS per ro om to a lo w of 0 .1 1 C FS per ro om . . . . W hile m any m ote ls th at c ate re d to a lo cal clie nte le had hig h C FS per ro om ra tio s, s om e did not.” (C hula V is ta (C alif o rn ia ) P olic e D epartm ent, 2 009, A ppendix I) F ig ure 13.5 C alls fo r S erv ic e p er R oom per Y ea r S ourc e: C hula V is ta (C alif o rn ia ) P olic e D ep artm en t (2 009). H as th e P ro ble m In cre ase d or D ecre ase d ? In addit io n to unders ta ndin g how fre q uen t a pro ble m is , i t is im porta nt to unders ta nd th e lo ng-t e rm tre n ds o f th e p ro ble m both befo re a nd afte r a re sp onse is im ple m en te d . T hat is , h as th e p ro ble m in cre a sed , d ecre a sed , o r s ta yed th e sa m e o ver tim e? D urin g th e sca nnin g ste p , a naly sts lo ok fo r in cre a sin g tre n ds to help prio rit iz e a nd sele ct p ro ble m s fo r f u rth er exa m in atio n. D urin g th e a ssessm en t s te p , a naly sts lo ok fo r d ecre a sin g tre n ds th at h elp to in dic a te th at re sp onses h ave w ork ed . F re q uen cie s, p erc en ta ges, r a te s, a nd avera ges ca n be co m pute d and dis p la yed acco rd in g to te m pora l v a ria ble s su ch as yea r, m onth , a nd w eek in ord er to dete rm in e w heth er th e p ro ble m has ch anged over tim e. A naly sis o f te m pora l v a ria ble s is n orm ally d is p la yed in lin e ch arts b eca use th is is a cle a r w ay to sh ow co ntin uit y a nd ch ro nolo gic a l o rd er. T he p erc en ta ge o f c h ange is a ls o used to dete rm in e w heth er a pro ble m has in cre a sed or d ecre a sed . 1306330 – S A GE P ublic a tio ns © B y Y ear A yea r is th e la rg est tim e u nit u sed in stra te g ic crim e a naly sis to unders ta nd in cre a ses a nd decre a ses o f a pro ble m . M ost c rim e sta tis tic s co lle cte d on a natio nal le vel a nd by lo ca l polic e a gen cie s a re ta bula te d by yea r, a llo w in g analy sts to m ake co m paris o ns to pre vio us yea rs a nd acro ss ju ris d ic tio ns. F ig ure 1 3.6 is a n illu stra tio n of a lin e ch art s h ow in g th e fre q uen cy o f ro bbery fo r 5 yea rs . A noth er c o m paris o n by yea r m ig ht in clu de ro bbery ra te s p er p opula tio n th at a llo w co m paris o n acro ss d if fe re n t le vels (e .g ., c it y vs. n eig hborin g cit y , c it y vs. s ta te , c it y vs. co untry ). T able 1 3.7 p ro vid es th e in fo rm atio n necessa ry to m ake a ch art c o m parin g a cit y ’s ro bbery ra te p er 1 00,0 00 pers o ns to th e sta te ’s ra te . T he ta ble sh ow s th at th e cit y ’s r o bbery ra te is m uch hig her th an th e sta te ’s , e ven th ough th e a ctu al n um bers o f ro bberie s a re m uch lo w er. A lt h ough th is ta ble p ro vid es su ffi cie n t in fo rm atio n about ro bbery ra te s, d is p la yin g th e d ata in th e fo rm of a lin e g ra ph, a s in Fig ure 1 3.7 , a llo w s a re a der to m ake co m paris o ns m ore ea sily . F ig ure 13.6 L in e C hart o f N um ber o f R obberie s b y Y ea r 1306330 – S A GE P ublic a tio ns © F ig ure 13.7 C hart C om parin g C it y a nd S ta te R obbery R ate s B y M onth or Q uarte r Crim e a naly sts re p ort s ta tis tic s a s w ell a s stu dy p ro ble m s b y m onth prim arily , a s d o m ost b usin esses a nd oth er o rg aniz a tio ns. A m onth is a sm all e n ough unit o f tim e to allo w th e analy sis o f v a ria tio n over a yea r, a nd at th e sa m e tim e, i t is la rg e en ough to pro duce a su ffi cie n t a m ount o f d ata to exa m in e. C rim e a naly sts a ls o stu dy sta tis tic s b y q uarte r (i.e ., a perio d of 3 m onth s) w hen th e va lu es b y m onth are to o sm all t o m ake m ea nin gfu l co nclu sio ns. A naly sts u se th e te ch niq ues d escrib ed here w hen exa m in in g data fo r b oth m onth and quarte r. F ig ure 1 3.8 illu stra te s th e n um ber o f lo ud party ca lls fo r s erv ic e a t a partm en t c o m ple xes in a cit y b y m onth fo r th e p ast 3 yea rs . N otic e th at th is fi gure co nta in s m any m ore d ata p oin ts th an th e p re vio us yea r c h arts , w hic h re su lt s in pea ks a nd va lle ys w it h in ea ch yea r. T his ty p e o f a naly sis a llo w s th e a naly st to see in cre m en ta l ( m onth ly ) c h anges in th e d ata . T he stra ig ht lin e o n th e ch art re p re sen ts th e lin ea r tre n d lin e a nd help s th e a naly st d ete r m in e th e o vera ll lin ea r tre n d of th e fre q uen cy. 1306330 – S A GE P ublic a tio ns © F ig ure 13.8 C hart o f L oud P arty C alls a t A partm en t C om ple xes, 3 Yea rs T re n d lin es a re u sed to help dete rm in e th e d ir e ctio n of a pro ble m when th e in cre m en ta l in cre a ses a nd decre a ses in th e d ata are n ot c le a r. T he lin ear tr e nd lin e is cre a te d by a sta tis tic a l e q uatio n (lin ea r re g re ssio n), w hic h pro duces a lin e th at b est e stim ate s th e dir e ctio n of th e m onth -t o -m onth figure s a nd is m ost o fte n used in crim e a naly sis . Ot her ty p es o f tre n d lin es a ls o ca n be p ro duced sin ce n ot a ll d is trib utio ns a re lin ea r, s u ch as exp onen tia l o r m ovin g avera ge. H ow ever, t h e a naly st s h ould be su re to unders ta nd th e sta tis tic s b eh in d th ese tre n d lin es b efo re u sin g th em . Im porta ntly , t h e d ir e ctio n of th e tre n ds in dic a te d by th e lin es ca n be d if fe re n t f o r th e sa m e p ro ble m , b ased on th e ty p e o f sta tis tic u sed in th e a naly sis (e .g ., f re q uen cy, r a te , m ea n). On e p ro ble m wit h usin g m onth s to id en tif y va ria tio ns in pro ble m activ it y is th at m onth s are n ot e q ual u nit s — th ey va ry in le n gth fro m 28 to 31 days. A 3-d ay p erio d ca n m ake a big d if fe re n ce in m onth ly co unts o f c rim e a nd oth er a ctiv it y . On e w ay in w hic h crim e a naly sts c o rre ct th is p ro ble m is b y co m putin g th e m ea n num ber o f o ccu rre n ces o f th e a ctiv it y o f in te re st p er d ay fo r e a ch m onth . S o fo r e xa m ple , i n ste a d of J anuary a nd Feb ru ary h avin g lo ud party fre q uen cie s o f 1 23 and 164, r e sp ectiv ely , t h ey h ave a vera ges o f 3 .9 7 and 5.8 6 (i.e ., 1 23 div id ed by 3 1 and 164 div id ed by 2 8) p er d ay. B y W eek Anoth er p ro ble m wit h usin g m onth as th e tim e u nit f o r a naly sis is th at m onth s va ry in th e num bers o f in div id ual w eekd ays th ey co nta in ; t h at is , o ne m onth m ay co nta in five F rid ays, a nd th e n ext m onth m ay h ave o nly fo ur. T hese va ria tio ns ca n affe ct th e co unts o f c erta in t y p es o f a ctiv it y th at a re p artic u la rly h ea vy o n w eeken ds a s o pposed to w eekd ays— lo ud partie s a t a partm en t c o m ple xes, f o r e xa m ple . A naly sts a ddre ss th is p ro ble m by co m parin g tim e p erio ds u sin g in te rv a ls o f s et n um bers o f w eeks (e .g ., 4 -w eek, 2 -w eek, o r 1 -w eek in te rv a ls ). W it h in su ch in te rv a ls , e a ch unit o f tim e h as th e sa m e n um ber o f d ays a nd th e sa m e ty p es o f d ays (e .g ., f o ur F rid ays, f o ur S atu rd ays). In co nductin g te m pora l a naly sis , crim e a naly sts ca n use lin e ch arts to dep ic t a ll o f th ese ty p es o f a naly sis , b ut th ey n eed to b e ca re fu l t o sele ct a ppro pria te tim e u nit s — th at is , u nit s th at w ill p ro vid e en ough data in e a ch unit to allo w th em to dra w su bsta ntiv e co nclu sio ns. H ow ever, o ne w arn in g is th at w eekly co unts o f c rim e a nd dis o rd er a re n ot a lw ays h elp fu l t o dete rm in e th e tre n ds o r eva lu ate a pro ble m . S even days is a very sh ort tim e fra m e a nd co unts fl uctu ate g re a tly f ro m week to w eek, e sp ecia lly w hen th e co unts a re lo w . S om eth in g as sim ple a s a hea vy ra in sto rm ca n in fluen ce th e a m ount o f a ctiv it y in a cit y d urin g one w eek, s o it is r e co m men ded to use lo nger tim e p erio ds a nd/o r c a utio n w hen exa m in in g w eekly co unts . P erc e nta g e of C hang e To answ er th is q uestio n, t h e p erc e nta ge of c h ange c a n als o be u sed to exa m in e th e am ount o f re la tiv e in cre a se o r d ecre a se in a pro ble m betw een tw o tim e p erio ds. T his ca n be p artic u la rly h elp fu l in th e a ssessm en t s te p w hen exa m in in g th e le vel o f a pro ble m b efo re a nd afte r a re sp onse. T he p erc en ta ge o f c h ange exp re sses th e a m ount o f c h ange as a pro portio n of th e va lu e a t th e fi rs t tim e p erio d (T im e 1 ), o r th e d if fe re n ce b etw een a m ea su re m en t a t T im e 1 and a m ea su re m en t a t T im e 2 , d iv id ed by th e m ea su re m en t a t 1306330 – S A GE P ublic a tio ns © T im e 1 , a nd th en m ult ip lie d by 1 00 (to arriv e a t a perc en ta ge). T he fo rm ula fo r a rriv in g at th e p erc en ta ge o f c h ange is a s fo llo w s: T im e 2−Tim e 1Tim e 1×100 =% of ch ange For e xa m ple , f ro m July to D ecem ber 2 016 (b efo re th e re sp onse), 3 20 co m merc ia l burg la rie s w ere co m mit te d in a partic u la r b usin ess d is tric t in S m allt o w n, a nd fro m July to D ecem ber 2 017 (a fte r th e re sp o nse th at to ok p la ce fro m January to June 2 016), 2 56 burg la rie s w ere co m mit te d . T he p erc en ta ge o f c h ange o f b urg la rie s in th is a re a is c o m pute d as fo llo w s: 2 56 (T im e 2)−320 (T im e 1)320 (T im e 1)×100 ,or −64 320 ×100 =20 % of ch ange T he b usin ess d is tric t e xp erie n ced a 20% decre a se in burg la rie s in th e 6 m onth s a fte r th e re sp onse w as im ple m en te d . T he p erc en ta ge o f c h ange ca n als o be u sed m ore g en era lly in t h e sca nnin g pro cess fo r y ea rly , q uarte rly , o r m onth ly co m paris o ns. T able 1 3.8 c o nta in s data on th e ch ange in fre q uen cy a nd th e p erc en ta ge o f c h ange o f s tra nger ra pes b y b ea t fo r 2 016 and 2017. It s h ow s th at e ven th ough th e o vera ll n um ber o f ra pes h as in cre a sed b y 7 0% , t h e n um bers w it h in in div id ual b ea ts h ave fl uctu ate d dif fe re n tly a nd th at B ea t 6 h as h ad th e m ost s ig nifi ca nt in cre a se. 1306330 – S A GE P ublic a tio ns © T here a re so m e co nsid era tio ns to re m em ber w hen co m putin g perc en ta ge o f c h ange. N ote th at T able 1 3.8 s h ow s n o stra nger ra pes in B ea t 5 in 2016, 1 2 in 2017, a nd N C ( f o r “ n ot ca lc u la ble ”) in th e la st c o lu m n in ste a d of a perc en ta ge o f c h ange va lu e. T his is b eca use it is a m ath em atic a l r u le th at a num ber c a nnot b e d iv id ed by zero ; t h