contemporary statistical maps evidence of spatial and graphic ignorance

8/3/2019 Contemporary Statistical Maps Evidence of Spatial and Graphic Ignorance

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CONTEMPORARY STATISTICAL MAPSEVIDENCEOF SPATIAL AN D GRAPHICIGNORANCE

G e o rg e F . J e n k sUnive r s i t y o f K a n s a s

INTRODUCTION

Maps a r e windows i n t o th e minds o f t h e i r c r ea t o r s a nd , i f o n e peeks i n t o th e s ein ne r r e c e s s e s , ev id e n c e s o f spa t i a l a n d g r a p h i c i g n o r a n c e become r ead i ly a ppa ren t .An i n s p e c t i o n o f a j umb le of s t a t i s t i c a l maps t aken f ro m magaz i ne s , newspape r s ,p r o f e s s i o n a l j o u r n a l s a n d gove rnmen ta l r e p o r t s g ive s r i s e t o t h e fo l l owin g s eman t i cr a n g e o f con t empora ry ma p qua l i t i e s : I /

c o m m u n ica t i ve / s ec re t i ve s imp l i s t i c / complex c l ea r / i nd i s t i nc t p l e a s i n g / u g l y d i r e c t e d / h a p h a z a r d a c c u r a t e / e r ro n e o u sdeco ra t i ve /u se fu l

Wha t d o t h e s e p o l a r ad j ec t i ve s imp l y abou t modern s t a t i s t i c a l m aps? 2 / Fi r s t ,t he r e i s a c o n f u s i o n i n t h e minds o f m a n y c a r t o g r a p h e r s a s t o t h e func t ion o f as t a t i s t i c a l m a p . S e c o n d , t h e gr a p h i c l a n g u a g e , o r th e c o n ve n t i o n a l symbo logy o ft h ema t i c mapping , w h i c h ha s been deve lop e d th rough c e n t u r i e s o f c a r t o g r a p h i c e xp e r i e n c e , i s no t pa r t o f t h e vo c a b u l a r y of many m a p make r s . T h i r d , s o m e s t a t i s t i c a lm ap m aker s d o n o t s eem t o s ense t h e r e l a t i onsh ip be tween d a t a p r o c e s s i n g a nd thef i d e l i t y w i t h w h i c h t h e i r map po r t r ays th e i n fo rma t ion th e y w i s h t o c on v e y . L a s t ,to o many m a p maker s a r e e i t h e r no t t r a i n ed i n , o r ap p rec i a t i ve o f , t h e s u b t l e t i e so f g r a p h i c c o mmun ica t i on . I n t h i s p a p e r t h e se de f i c i en c i e s o f con tempora ry s t at i s t i c a l m a p making a r e e xa mined , co r r e c t i ve p r o c e d u r e s a r e s u g g e s t e d , an d s o m e o ppor tun i t i e s f o r i mpr ov ing s t a t i s t i c a l maps a r e p ropo sed .

WHY MAKESTATISTICAL MAPS?

I f o ne r a i s e s t h e q u e s t i o n , Why make s t a t i s t i c a l m a p s ? , h e p oses th e q u e r y b e

ca u s e h e a s sum es t h a t t he r e i s a l o g i c a l n e e d beh ind each c a r t o g r a ph i c d i sp l ay. Add i t i on a l l y, s i nce s t a t i s t i c a l maps a r e o f t e n inc luded i n a l a rg e r w o r k, o n e can a l soa s s u m e t h a t t he r e i s s ome th ing a b o u t a map w h i c h m a k e s i t more u se fu l t h a n w o rd s ,t ab l e s o r g r a p h s i n t h e t r ans f e r o f c e r t a i n t ypes o f i n fo rma t ion . T h e e n o r m o u s u -t i l i t y o f a s t a t i s t i c a l map can e a s i l y b e d emons t r a t ed i f th e r e a de r wi l l r e f e r t oTa b l e 1 , a t yp i ca l c e n s u a l m a p o f e n u m e r at e d d at a . 3 / At tempt t o desc r ibe t h e s p at i a l i n fo rma t ion c o n t a i n e d i n t h e se t a b l e s . M o s t r e a de r s , e v e n i f p r o v i d e d w i t h abas e ma p ( F i g u r e 1 ) a r e u n a b le t o i n t eg r a t e a r e a l l y t h e twen ty -n ine c r o p l a n d a c r e a g ev a l u e s g i v e n i n t h e t a b l e . F u r t h e r m o r e , i f t h e r e ade r i s prov ided w i th a n "a r ea l



t a b l e " ( F i g u r e 2 ) , h e w i l l s t i l l f i n d i t d i f f i c u l t t o p e r c e i v e " i n h i s m i n d ' s e y e "t h e d i s t r i b u t i o n a l c h a r a c t e r i s t i c s o f c r o p l a n d a c r e a g e i n U t a h .

Crop land Acrea ge, by Count ies , Utah , 196 9

BeaverBox ElderCacheCar b o nDagge t tDavisDuche s neEmeryGar f i e ldGrandIronJuabKaneMil la rdMorgan

29 ,91 7360 ,571176 ,926

1 4 , 6 9 28 ,106

4 0 , 9 4 696 ,0354 8 , 3 4 42 3 , 7 1 4

3 , 1 3 26 5 , 9 737 7 , 2 7 51 1 , 2 1 5

1 5 1 , 3 1 91 6 , 5 2 7

P i u t eR i c hS a l t LakeSan Ju anS a n p e t eSevierS u m m itT ooe l eUint ahUtahWasa tchWash ing tonWayneWeber

15,3 0266,5 5069,41591,29998,0 2952,32038 ,21839,61*393 ,023

139,98720,11633,65017,61*2

W hat then is the function of a m ap and particu larly a statistical map? Simply,it is to prov ide the r eader with a graphic display of information in such formatthat it promotes a conceptual re lationship with spatial arrange ments on the surfaceof the earth. The information communica tedby a m ap m ay be the distanc e or directional relat ionships among thing s, the pattern o f objects in space, or the shapeand location of a region such as the Corn Belt. Very fe w reade rs of the informa tion presented in Table 1 are able to per ceive the geographical patterns and spa-

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t i a l r e l a t i o n s h i p s of c r o p l a n d ac reages w h i c h a r e s o c l e a r l y s e t f o r t h o n t h e m api n F i g u r e 3 .

C o n t e mpo r a r y map make r s o f t en con fu s e t h e p r i m a r y p u r p o s e o f a s t a t i s t i c a l mapwi th t h a t o f a t a b l e . A s a r e su l t t hey a t t emp t t o prov id e t h e r ea de r wi th sp ec i f i cf ac t s abou t spec i f i c p l ace s . U s u a l l y t h e se a t t emp t s a r e n o more succes s f u l t hanthose ac h i eved b y i nven to r s who hav e t r ied t o c r ea t e a hybr id b e t w e e n t h e au tomob i l e and t h e a i r c r af t . There a r e t w o dominan t r ea sons w h y a u tho r s ough t no t t o co nfu se ca r tog raph ic and t abu l a r u t i l i t y. The f i r s t , a n d mo st o b v i o u s , i s t h a t s t at i s t i c a l maps a r e symbol i zed g e n e r a l i z a t i ons o f t h e i n fo rma t ion co n t a ined i n at a b l e . S ta t i s t i c a l maps t e n d , th e r e fo r e , t o be i ne ff i c i en t a n d i naccu ra t e s o u r c e so f d a t a . F o r e x am p l e , i t i s no t ea sy t o c o u n t t h e do t s o n F i g u r e 3 . Fur the rmore ,e a c h d o t o n F i g u r e 3 r e p r e sen t s f i ve thousand a cr e s , a nd i n p r o c e s s i n g t h e da t a i nt o sy mb o l s t h e map m a k e r was ob l iged t o rou nd o f f th e speci f ic va lues g ive n i n t h et a b l e . T h i s p r o c e d u r e m ay c rea te e r ro r s o f a s m u c h a s t w o t h o u s a nd a n d fo r ty -n i neac re s i n s o m e pa r t s o f t h e m a p .

A s e c o n d , a nd g e o g r a p h i c a l l y m o r e s in i s t e r e r ro r i s invo lved i n a t t e m p t i n g t oprov id e t h e d u a l f u n c t i o n i n a s t a t i s t i c a l map a nd i s i l l u s t r a t ed i n F i g u r e * f . M o s t

r eade r s a r e t h o u g h t t o be u n f a m i l i a r w i th t h e g e o g r a p h i c base i n fo rma t ion o f an a -r ea a n d t h u s t h e ca r to g r a p h e r f ee l s t h a t h e m u s t p rov ide bounda r i e s a n d names t oas s i s t h is r eade r i n ob ta in ing da t a f rom t h e m ap . T h u s , a p o r t i o n o f t h e m ap s u rf a ce i s occup ied w i t h l i ne s and word s p r i o r t o symbol iz a t ion . Th i s g e n e r a l l y r es u l t s i n spa t i a l p a t t e r n s o f symbo l s wh ich a r e no t p r o p e r l y r e l a t ed t o ea r th pos it i o n . What you r e a l l y s e e o n the map i n F i g u r e i s a combina t ion o f th e pa t t e r n sc rea t e d b y p a s t h i s t o r i c a l - p o l i t i c a l dec i s i o ns a nd a spa t i a l l y e r ron eous d i s p l a y o fc rop l and ac r ea g e .

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tn the. State, ofi Utah .

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on



Sta t i s t i c a l map s have a l s o b e e n u s e d fo r p u r p o s e s o t h e r t h a n t h o s e j u s t d es c r i b e d . I f one r e a d s the te x tua l ma te r i a l a s soc i a t e d wi th s t a t i s t i c a l m a p s , i tb ec omes appa ren t t h a t s o m e a u t h o r s u s e m a p s on ly f o r deco ra t i ve pu rposes s i n c e no r e f e r e n c e i s made t o t h e s i gn i f i c a n c e o f t h e m a p m e s s a g e e i t he r i n th e c ap t i on o rt h e expo s i t i on . O t h e r a u t h o r s s e e m t o u s e maps a s b a d g e s o f m e m b e r s h i p i n t h e f r at e rn i t y o f s c i en t i s t s and t h e s e ind iv i dua l s a l so i gno re the map a s a c o m m u n i c a t i v e

dev i ce . I f a n a u th o r o r a m a p m a k e r i s no t p r i m a r i l y c o n c e r n e d wi th t h o s e u n i q u es p a t i a l r e l a t i o n s h i p s w h i c h c a n b es t b e i l l u s t r a t e d i n ma p f o r m a t , s o m e dev i ceo t h e r t h a n a ma p o ugh t t o b e u t i l i z e d t o c ommu n i c a t e h i s c once rns t o h i s r e a de r .

T H E SY M BOLIC LANGU AGEO F MA PP I N G

The s t a t i s t i c a l m a p s f o u n d i n c o n t e m p o r a r y l i t e r a t u r e a r e th e p r o d u c t s o f ahe t e roge neou s l o t o f i nd i v idua l s wh o a r e grouped toge the r be c a u s e o f t h e func t iont h a t th e y p e r f o r m r a t he r t han be c a u s e o f t h e t r a i n ing tha t t hey have r ece i ved . I no n e w a y , t h i s d iv e r s i t y o f a c a d e mic e x p e r i e n c e and methodo log i c a l o u t l o o k i s advant a g e o u s b e c a u s e n e w i n f o r m a t i o n a l conce p t s a nd ty pe s o f s t a t i s t i c a l m a p s a r e p r od u c e d . I n ano t h e r w a y i t i s d i s adva n t a g e o u s , h o w ev e r, s i n c e m a n y o f t h e se c ar tog r aph e r s d o not know t h e symbol ic l anguage o f t h e i r t r a d e . A r e v i e w o f th e a c c e p te d prac t i ce s i n t h e u s e o f ma p symbo l s and a c o m m o n e r r o r i n p r e s e n t a t i o n a r e d i sc us sed i n t h e f o l l o w i n g p a r a g r a ph s .

I n g e n e r a l , t h e r e a r e f i v e types o f s ymbo l s w h i c h a r e u s e d t o p r e s e n t i n fo rmat i on o n s t a t i s t i c a l m aps and each s ymbol ic f o r m has been a s s i g n e d a p a r t i c u l a r f unct i on i n t h ema t i c co nven t i on . Po in t s y m b o l s , e . g . do t s , a r e u s ed t o r ep re sen t phen o m e n a wh ic h o c c u r s i n g l y a t po in t s o n t h e su r f ace o f t h e e a r t h . Typica l l y o n ef i n ds popu l a t i on , e i t he r hu m a n o r a n i m a l , and c r o p a c r e a g e s r ep re sen t ed by po in t s y m bo l s . Pr opor t i ona l s y m b o l s , e . g . c i r c l e s , a r e u s e d t o p r e s e n t c l u s t e r s o f t h in g sw h i c h o c c u r i n ve r y l im i t ed a r e a s . T h e p o p u l a t i on o f c i t i e s o r t h e v a l u e a dded b y

ma n u f a c t u r i n g m ay b e sym bo l i zed i n t h i s w a y . Are a symbo l s a r e u s e d t o r e p r e s e n tsp a t i a l p h e n o m e n a w h i c h m ay be cons ide r e d t o b e e v e n l y d i s t r i bu t ed o v e r the a r e a .D u e t o t h i s a s sumpt i o n , i t i s c ommon prac t i ce t o r e p r e s e n t r a t i o s wi th shad in g pa tt e r n s . L a s t l y , we f i n d ce r t a i n p h e n o m e n on w h i c h o c c u r u b i q u i t u o u s l y o n , a b o v e , o rb e l o w th e su r f ac e o f t h e e a r t h . Air pre s su re o r e l e v a t i o n a re d i s t r i bu t ions o ft h i s t yp e and t h e i r c o n f i g u r a t i o n s a r e r ep re sen t e d by i s a r i t hms o f w h i c h t h e cont o u r i s m os t c o m m o n . Each o f t h e se symbo l i c t ype s c a n b e v a r i e d i n c o l o r , s i z e ,sh ape and t ex tu r e s o t h a t a ve r y d i v e r s i f i e d a r r a y o f m a r k s i s a v a i l a b l e t o th e c a rt og r a phe r. £ /

W h i l e t he r e a r e n o a b s o l u t e ru l e s f o r sy mbo l i c con ven t i ons , t he s t a t i s t i c a lc a r t o g r a ph e r i s we l l a d v i s e d t o p r a c t i c e r e c o m m e n d e d u s a g e . Eac h m a p p a b l e p h e n o men o n ha s d i s t i nc t i ve geog raph ic a l c h a r a c t e r i s t i c s an d an u n d e r s t and ing o f t he se i sth e bas i s u p o n w h i c h sym bo l i c con ven t i ons wer e e s t ab l i she d . I t i s a l s o c l ea r t ha t

m an y m a p u s e r s e x pe c t c e r t a i n typ es o f p h e n o m e n o n t o be de p ic t ed i n a c e r t a i n m ann e r a n d i f the s y mbo l i c l angu a g e o f t h e map co inc ide s w i t h t h e e x p e c t a t i o n s o f th er e a d e r t h e i mpac t o f t h e map m e s s a g e oc cu r s more r a p i d l y and wi th f e w e r abe r r a t i onst h a n w o u l d be t he c a s e othe rw i se .

T h e t w o c o n t r a s t i n g maps shown i n F i g u r e 5 i l l u s t r a t e t h e s i g n i f i c a n c e o f f a i lu r e t o fo l l ow symb o l i c c o n v e n t ion . T h e t w o ma ps c o m m u n i c a t e v e r y d i f f e r e n t s pa t i a lm e s s a g e s bu t bo th we re d e r i v e d f r o m t h e s a m e c ro p l and da t a u s e d fo r t he do t maps o f



F i g u r e s 3 a nd A t l e a s t p a r t o f w h a t i s s e e n o n map A r e s u l t s f r om t h e s i m p l ef a c t t h a t l a rg e e n u m e r a t i o n d i s t r i c t s t e n d t o h a v e l a rg e n u m b e r s o f t h i n g s a n ds m a l l d i s t r i c t s t e n d t o h a v e s m a l l n u m b e r s o f t h i n g s . I f on e f l e w o v e r t h e S t a t eo f U t a h a nd o b s e r v e d c r o p l a nd p a t t e r n s h e w o u l d p e r c e i v e r e g i o n s w i t h a l a r g e pr op o r t i o n o f c r o p l a n d a s d i s t i n c t f r o m r e g i o n s w i t h w i d e l y d i s p e r s e d f i e l d p a t t e r n s .H i s i m p r e s s i o n o f t h e d i s t r i b u t i o n o f c r o p l a n d wo u l d , t h e r e f o r e , b e m o r e l i k e t h a t

s h o w n o n m ap B t h an o n m ap A o f F i g u r e5 »

I t t h e n f o l l o w s t h a t a c r e a g e a n d s i m i l a rt y p e s o f d a t a s h o u l d b e a r e a l l y s t a n d a r d i z e d b y t h e c a r t o g r a p h e r i n o r d e r t o p r es e n t a t r u t h f u l v i s u a l s t a t e m e n t o n h i s c h o r , o p l e t h m ap a b o u t t h o s e d i s t r i b u t i o n s ,t h e e n u m e r a t i o n s o f w h i c h ar e d i r e c t l y r e l a t e d t o t h e s i z e o f t h e e n u m e r a t i o n

u n i t s . 2 /

B

5 : Tt e eA ^cve -c&m

b e c a u s e4 ^ z e , B

b e en A . e u e A 4 ed . B

A .

M A P A C C U R AC Y A N D D ATAP R O C E S S I N G

C a r t o g r a p h e r s i n s u r v e y ma p p i n g e s t a b l i s h m e n t s t a k e g r e a t p r i d e i n t h e h i g hl e v e l o f a c c u r a c y t h a t t h e y i n c o r p o r a t e i n t o t h e i r m a p s . A n y o n e w h o h a s vi s i t e da t o p o g r a p h i c m a p p i n g o r g a n i z a t i o n h as n o d o u b t b e e n m a d e a w a r e o f t h e c a r e w i t hw h i c h t h e c o n t o u r a n d c u l t u r a l d a t a w e r e m e a s u r e d , s y mb o l i z e d an d p l o t t e d o n t h et o p o g r a p h i c s h e e t s . T h i s i s a s i t s h o u l d b e , bu t t h i s c o n c e r n fo r p o s i t i o n a l a n de l e v a t i o n al a c c u r a c y h as c a u s e d s o m e t h e m a t i c m a p m a k e r s ( a s w el l a s t h e g e n e r a lp u b l i c ) t o b e l i e v e t h a t t h e i r m a p s a r e e q u a l l y a c c ur a t e . T h i s i s a n u n f o r t u n a t ec i r c u m s t a n c e b e c a u s e s o me s t a t i s t i c a l m ap m a k e r s , h a v i n g t a k e n g r e a t c a r e i n t h ea r i t h m e t i c m a n i p u l a t i o n o f t h e i r d a t a , fa i l t o r e a l i z e t h a t o t h e r t y p e s o f s i g n if i c a n t e r r o r m ay c r e e p i n t o t h e i r m a p p r o d u c t s .

5 5



I n 1 97 1 J oe l M or r i s on i n t r oduce d t h e t e r m , " me t hod p ro du c e d e r r o r " . 8 / Th i s

t e rm wa s u s e d t o d i s t i ngu i sh de c i s i o n-ma k in g e r r o r s f r o m a r i t h me t i c e r r o r s i n t h e

c a r t o g r a p h i c pr oce ss . The t wo ma ps pr e s e n t e d i n Figu re 6, a l t h o ugh b o t h a r i t h me

t i c a l l y a c c u r a t e a nd s ymbo l i c a l l y c o r re c t a r e qui t e d if f e re n t i n a p pe a r a nc e . Th i s

d i f f e re nc e i n m ap m ess a g e i s not re l a t e d t o t h e numbe r , or i en t a t i o n o r v a l u e s

( t o n es ) o f t h e s ymbol s on t h e ma p no r i s i t r e l a t ed t o t h e sc a l e a t w hic h t h e ma p s

wer e pr e pa r e d . I n s t e a d , t h e d i f f e r e nc e i n me s s a g e i s t he d i r e c t r e s u l t o f t h e me t ho d use d t o s ubd i v i de t h e t w en t y- n i n e va l u e s ( pe rc en t o f l a nd i n cr op l an d) i n t o

f ou r c l a s s e s . Qua r t i l e c l a s s e s w er e use d on m ap A w hi l e t h e c l a s s e s on ma p B we r e

de r i ve d by a n op t imiz in g te ch n i que . Ho w c a n t wo a r i t h me t i c a l l y a nd c o m put a t i o na l l y

a c c u ra t e m aps pro d uce s uc h d i f f e r e n t d i s t r i bu t i o na l pa t t e r ns ?

Ca r t o g ra phe r s o f t en f a c e a ch o i c e l i ke t ha t pos e d b y t h e t wo ma p s i n Fi gure 6,

a n d o f nec e s s i t y , t h e y mus t s e l e c t o n e t o p l a c e be fo re t he i r r ea de r s. T o o of t en

t he s e l e c t io n i s ma de in t ui t i ve ly , bu t i f one t u r ns t o t r a d i t i o na l s ta t i st i cs , t h e

p r o b l e m c a n be r e so l v e d mo r e r a t io na l l y . I de a l l y , t h e c a r to g r a p he r sh ou l d se le c t

t h e r e p r e s e n t a t i on w hic h m inimiz es t h e d i f f e r e n c e s w i t h i n c l a s s e s a nd ma x imiz e s

t h e ^ d i f f e re nc es be t w ee n c l a s s e s o n h i s m ap , a nd t h i s c an be me a su re d by a na l ys i s o f

va ri a n c e . Appl i c a t io n o f th is me a s u r e t o t h e m aps i n q ue s t i o n re ve a l s t ha t t h e

wit h in -c l a s s v a r i a n c e o f ma p A i s 2 , 5 2 ^ wh i l e t h a t o f

m ap B i s 9^ 0 . Thes e va l ue s,

whe n c ompa r e d wi t h t h e t o t a l va r i a n c e o f t h e d a t a s e t , i n d i c a t e t ha t ma p B i s

n i ne t y - f o ur pe r c e n t a c c ura t e wh i l e ma p A i s on l y e i g h t y- t h r e e p e r c e nt a cc u r a t e .

Wi t h t h i s i n f o r ma t io n t he r e i s n o pr ob l e m i n de c id in g w hic h ma p s hou l d be u s e d.

St a t i s t i c a l ma p s a r e c o ns i de re d t o be poor d a t a r e t r i e va l s our c e s b u t ma n y

c en s us m ap m ake r s be l i e v e t h a t t h e a v e r a ge ma p r e a de r wi l l us e a m ap a s a d a t a

b a nk . I f t he i r as su mpt io n i s c o r r e c t , a nd i t ha s no t be e n pr ove n ot h e rwi s e , t h e

c ho i c e o f c l a s s i f i c a t i on pr o c e d u r e be c o me s c r i t i c a l . The s t a nda rd e r r o r of t h e

e s t i m ate s f o r t h e ma p s i n Fi g u r e 6 i nd i c a t e t h a t on t he a v e r a g e a va l u e ob t a i ne d

f r om ma p A w il l be i n e rr o r 9 . 3 pe r c e n t whi l e a va lu e o bt a in e d f r o m ma p B wi l l b e

i n e r ro r 5 . 7 pe r ce nt .

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6: Two ma p-6 O AC . diM&L&nt v/e /L6 -to n6 o& one d is t r ib u t io n , tke. p&ic< int o fa an.ua

i n cAopland -w U tah.. " Hie c£ at> A<n > ^O /L Ma p A (Via quaAtiZeA w hU -2 . tk ob< L faof i Ma p B

cA eated by an o p tim iza ti o n te.cnniqu.e.. Eigh ty-thSL&e. p&id&nt o& the. t ot al , v a l a n c e

ac.c.ounte.d ^ on. by th<L C£O AA &> A JI Ma p A and ninety-&OUA. p&io .<ivit by thoA e. -in M ap B .Thai, M ap B ^4 the, mot ie . aa c.uAate map.



A ES T H E T I C S A N D M A P C O M MU N I C ATI O N

T h e me ss a g e o f a ma p i s c o mm u n i c a t e d t o t h e r e a d e r b y a p r o c e s s o f v i s u a l i nt e g r a t i o n i n whi c h t h e c h a r a c t e r i s t i c s of i n d i v i d u a l symbols a r e s u b j u g a t e d t o th ep e r c e i v e d p a t t e r n s o f s e t s o f s y m b o l s . Re c o g n i t i o n o f t h i s map r e a d i n g p r o c e d u r ei s e s s e n t i a l i n c a r t o g r a p h i c d e s i g n b e c a u s e s i z e , c o l o r , t e x t u r e o f symbols m u st bec o n s i d e r e d o n t w o b as e s . I n t h e f i r s t i n s t a n c e e a c h symbol m u st b e i d e n t i f i a b l e .I n a dd i t ion , e a c h symbo l must b e c o m p a t i b l e wi t h a l l o t h e r s y m b o ls s ince t h e y m u s tw o r k t o g e t h e r t o c r e a t e a v i s u a l w h o l e. Fa i l u r e t o r e c o g n i z e symbol i c i d e n t i f i a -b i l i t y a nd c o m p a t i b i l i t y r e s u l t s i n m a p mess a g e s w h i c h a r e c o m p l e x an d " n o i s y " r at h e r t h a n s i m p le a nd c l e a r .

S e v e r a l g r a p h i c p r i n c i p l e s a r e o f c o n c e r n t o t h e c a r t o g r a p h i c d es i g n e r. F i g u r e a n d g r o u n d m u s t be s e p a r a t e d c l e a r l y s o t h a t t h e m a j o r symbo ls wh i c h p r e s e n t t h e d i s t r i b u t i o n c a n b e s ee n a s d i s t i n c t l y d i f f e r e n t f r o m t h o s e l e s s e r s ymbolsw h i c h m a y be n e c e s s a r y t o t h e p u r p o s e o f t h e m a p . P o o r f i g u r e - g r o u n d r e l a t i o n s h i p s ar e d e m o n s t r a t ed o n th e map p r e s e n t e d i n F i g u r e w h e r e , i n a d d i t i o n t o a r e a l mi sp l a c e m e n t , t h e d o t s b e c o m e v i s u a l l y c o n f u s e d w i t h t h e b o u n d a r y l i n e s a n d t h e c o u n t y n a me s . A seco nd a s p e c t o f f i g u r e - g r o u n d r e l a t i o n s h i p s i s s h o wn i n F i g u r e 7 w h e r el a c k o f c o n t r a s t o n map A su bd ue s t h e ma p mes s a g e w h i c h b e c o m e s c lea r a n d d i s t i n c to n ma p B .

Many o f t h e mo s t c o n f u s i n g an d d i s p l ea s i n g m a p s t o be f o u n d i n c o n t e m p o r a r y l i t e r a t u r e a r e t h o s e wh i c h a r e s y m b o l i z e d w i t h s e l f - a d h e s i v e sh ad ing p a t t e r n s . T h e s e p a t t e r n s a r e a v a i l a b l e i n a v a r i e t y o f s t y l e s , t e x t u r e s a n d v a l u e s and t h e yc a n be a p p l i ed i n a l l o f th e o r i e n t a t i o n s o f t h e c o m p a s s . T h e p a t t e r n s u s e d o n mapA o f Fi gu r e 8 a r e s o c o a r s e l y t e x t u r e d th a t t h e y ar e v i s u a l l y u n s tab le . C om p a r et h i s m a p w i t h t h o s e s h o w n i n F i g u r e 6 a n d t h e r e i s l i t t l e d o u b t a s t o w h i c h a r e e a s i e r t o r e a d an d mo r e p l e a s a n t t o l o ok a t .

7 : Mivwmal ( M a pA ) and maxAjnal(M ap B ) dowtnaAt b & t i o e . &nMa p B ^4 a c^ ea^e A and m o n o, fiolc&fiul vi sual Atate.m&nt than M a p A

and gio iwd.



A t f i r s t g l a n c e , t h e r eade r o f map B i n F i g u r e 8 m i g h t conc lude tha t he i sl o o k i n g a t a two-c l a s s map bu t i n r e a l i t y i t i s a f o u r - c l a s s m a p . A s ing l e p a t t e r ni s u s e d for c l a s se s o n e and t w o and ano the r fo r c l a s se s th r ee and fou r a nd the o n l yv i s u a l d i f f e r e n c e b e t w e e n t he se p a i r s o f c l a s se s r e s u l t s f r o m p a t t e r n or i en t a t i on .Th i s makes t he t a sk o f t he m ap r ead e r more d i f f i c u l t t h a n w o u l d be the case w e r et he p a t t e r n s a l so sepa ra t ed b y v i s u a l d i f f e r e n c e s i n va l ue . The i n t e r s e c t i o n o f

t h e l i n e s i n t he se r a the r c o a r s e p a t t e r n s w i t h the b o u n d a r y l i n e s o f t h e r eg ionscauses a degree o f n o i s e on th i s map tha t cou ld b e r e d u c e d b y d e c r e a s i n g tex ture .

B

T w o m a p *. T h e" d a n c e "

T o p a r a p h r a s e a cu r r en t t e l ev i s ion commerc i a l , s t a t i s t i ca l ca r tog raphe r sshould p r e p a r e m a p s w h i c h are i n " g o o d t a s t e . " Grea t works o f a r t l i ke t h e M o n a

L i s a o r Venus d e Milo a r e apprec i a t ed because t he i r c rea to r s p r e s e n t e d t he i r s u bj e c t m a t t e r w i t h s imp le and c l ea r g raph ic s t a t emen t s . S t a t i s t i c a l m ap make r sw o u l d d o wel l t o r emember and emula t e these a r t i s t s w h e n t h e y d e s i g n t he i r m a p s .

A L O O KINTO TH E FUTURE

R u d o l p h A r nh e i m i n hi s b o o k , Ar t and Vi s u a l Percep t ion , s t a t e s t ha t g e s t a l tp s y c h o l o g i s t s b e l i e v e t ha t " a ny s t imulus p a t t e r n t ends t o b e s e e n i n suc h a w a yt ha t t he r e s u l t i n g s t ruc tu re i s a s s i m p l e a s t he g iven cond i t i o ns pe rmi t . " 2/ ^

t h i s concep t i s a p p l i e d t o the p e r c e p t i o n o f m a p s , o n e can as sume tha t c o m p l e x p a tt e r n s o f symbols a re p e r c e i v e d a s s imp l i f i ed o r gene ra l i zed pa t t e rn s . Ca r r y i n g theidea f u r t h e r , t h e s imp l i f i ed p a t t e r n s tha t a r e p e r c e i v e d m u s t b e t hose t ha t a r e r em e m b e r e d and l a t e r u t i l i z e d w h e n t he r eade r wishes t o r e c a l l the i n f o r m a t i o n a l conten t o f t he m a p . These n o t i o n s r a i s e a v e r y impor t an t qu e s t i o n ab ou t map communic a t i o n . D o al l ( o r a m a j o r i t y o f ) map r eade r s v i s u a l l y s i m p l i f y a p a t t e r n o f s y mb o l s i n t he s a m e w a y and thus o b t a i n and r e m e m b e r t h e s a m e m a p m essage?

C u r r e n t r e s e a r c h i n m a p c o m m u n i c a t i o n seems t o i n d i c a t e tha t m e s s a g e s o b t a i n e df r o m m a p s m a y have an ind iv idua l i s t i c and h i g h l y p e r s o n a l i z e d i n f o r m a t i o n a l c o nt e n t ,



A s a c a se i n p o i n t , s t u d y the t h r ee m a ps p r e s e n t e d i n Figure 9« 10 / The cen t e r ma p( B ) w a s s hown t o a group o f i nd iv i d u a l s wh o a s h or t t ime la t e r r e c o n s t r u c t e d w h a tt h e y ha d s e e n and r emembered . T h e r e s p o ns e m ap s o n th e l e f t and r i gh t ( A an d C )i nd i c a t e t h a t , t he r e a d e r s o b t a i n e d b o t h a n a b e r r a nt a nd a d i f f e r en t spa t i a l messa ge . R e s e a r c h c a r t o g r a p h e r s a r e u n a b l e t o e xp la in w h y t h e se r e s p o n s e ma ps a r e d i f f e r en t ,no r a r e t h e y s u r e w h e t h e r t h e s e r e s p o n s e s r e p r e s e nt e x t r eme ca s e s o f ma p r e a d e r d ive r s i t y. Th i s e x a m ple m ak e s o n e wonde r w h e t h e r r e s e a r c h c a r t o g raphe r s c an d e p e n du p o n m ap r e a d e r g ene ra l i z a t i on . P e rh a ps th e map d e s igne r s ho u ld t a k e t h e in i t iat i ve a n d c r e a t e t h e s i mp l i f i c a t i o ns h e wish e s t o co mmu n ica t e .

T r a d i t i o n a l ma p m a k e r s m a y t h ink t h a t s u c h ma n i p u l a t i o n o f t h e map m e s s age i sa n a b h or r en t mi s us e o f c a r t o g rap h ic p r e r o g a t i v e s and ak in t o p re p a r ing p ropagand a .U p o n fu r t h e r c on t empla t i on , how eve r, w e r e a l i ze t h a t s p e a ke r s a nd a u tho r s s e l e c twords , c r ea t e phra s e s , and s t ruc tu re p a ra g r a p h s t o s u i t th e m e s sa ge t ha t t h e y a r ea t t e m pt ing t o co mmun i cat e . Sh o u l d c a r t o g rap h e r s b e d e n ied t h e s a m e pr iv i l e g e ?

B w m

c A e 0 4 f ee d Ma p - 6A

O f)( Ma p B ) e a c A i a / a e 6

RESUME

A nu m b er o f r a t h e r p e r n i c i o u s i m p res s ions a bo ut s t a t i s t i c a l ma ps and the c a rt o g r a p h e r s who c r e a t e t h e m h a v e c r e p t i n t o t h e mi nds o f t h e pub l i c . I t ha s b e e n t h e o b j ec t i ve o f t h i s p a p e r t o h e l p d i spe l t h e s e no t ions an d t o p ro v id e a l t e r nat iv e w a y s o f l o o k i ng a t m a p s an d the i r c r e a t o r s . The f o l l o w i ng s t a t e ment s summar

i z e t he s e a t t emp t s . Sta t i s t i c a l m a p s a r e no t good s o u rce s o f spec i f i c i n f o r ma t i o n

abou t spec i f ic p l ace s . M a p s a r e c re a t e d t o p r o v ide i n f o r ma t ion abo u t spa t i a l r e l a t io n

s h i p s . N o o the r m e d i u m c o mmunicat e s d i s t ance , d i r e c t i o n a l a n da r e a l p a t t e r n r e l a t i o n s h i p s a s w e ll .

The r e i s a s ymbo l i c l a nguage o f m a p ping a nd good maps c a n bec rea t ed o nl y b y t ho s e who u n d e r s t a n d i t .

A c cu r a c y i n c a r t o g r a p h y invo l ve s c o n c e p t u a l a s w e l l a s a r i t h me t i c

5 9



p r e c i s i o n i n d a t a h a n d l i ng . Ma p s ar e g r a p h i c c o m mu n i c a t o r s a n d c l e a r an d co n c i s e ma p m es

s ages r e s u l t f r o m e a s i l y r e a d , c l e a r r a t h e r t h a n n o i s y m a p s. C o m mu n i c a t i o n v ia t h e map i s n o t p e r f e c t l y u nd e r s t o o d a nd th e re

i s n e e d f o r co n t i n u e d r es e a rc h i f w e a re t o c r e a t e m o r e e ff e c t i v e m a p s .

R E F EREN C E S

1 . Pe t c h e n i k , Ba r b a r a B ., " A Ve r b a l Ap p r o a ch t o Ch a r a c t e r i z i n g t h e L o o k o f Ma ps , "T he A me r i c a n Ca r t o g r a p h e r, v o l 1 , N o . 1 ( l 9 7 iO » 63 - 7 1 .

2 . S t a t i s t i c a l m a ps a r e n o t n e c e s s a r i l y p r o d u c t s o f s t a t i s t i c a l i n fe r e nc e ; r a t h e rma n y s t a t i s t i c a l m a p s are t w o - d i m e n s i o n a l g r a p h i c r e p r e s e n t a t ions o f e n u m e r a te d d a t a o b t a i n e d b y c e n s u a l p r o c e d u r e s .

T h i s p a p e r i s an a b b r e v i a t e d v e r s i o n o f a n o r a l p a p e r p r e se n t e d a t t h e I n t e rn a t i o n a l S y m po s i u m o n C o m p ut e r - A s s i s t e d C ar t o g r a p h y ( A ut o- C a r t o I I ) , s p o n s o r e db y t h e A m er i c a n C o n g r e s s o n S u r v e y i n g a nd Map p i n g i n coope r a t i o n wi t h th eB u r e a u o f t h e C e n s us .

3 . T h e d a t a p r e s e n t e d i n T a b l e 1 a n d th a t u s e d f o r o t h e r m a ps o f U t a h w e r e t a k e nf r o m Ut a h A g r i c u l t u r a l S t a t i s t i c s 1 9 7 3> Sa l t L a k e C i t y : Ut a h St a t e De p a r t m en to f A g r i c u l t u r e , pp . 8 6 - 7 Ma p m a k e r s f r e q u e n t l y a r r a y th es e t yp es o f d a t a i n

s e q u e n t i a l o r d e r a s a p r e l i m i n a r y t o p r o c e s s i n g t h e f i g u r es i n t o c a t e g or iesfo r s ym bo l i z a t i on .

^ . Fo r a mo r e s o p h i s t i c a t e d a n a l y s i s o f m a p s a s c o m m un i c a t i v e d e v i c es s e e : Ro b i n s o n , Ar t h u r H ., a nd B a r b a ra B . Pe t c h e n i k , " T h e M a p a s a C o mm un i c a t i v e S y s t e m , "Th e Ca r t o g r a p h i c J o ur n a l , v ol . 1 2 , N o . 1 ( J u n e 1 9 75 ) ? p p . 7 - 1 5 .

5 . Al so s e e Rob i n s o n , Ar t h u r H . , a n d Ra n d a l l D. S a l e , E l e me n t s of C a r t o g r a p h y,3 rd e d i t i o n , New Yo r k : J o h n ¥ i l e y a n d S o n s ,

6 . Dobso n , M i ch a e l W. , " S y m bo l - S u b j e c t M at t e r R el a t i o n s h i p s i n T h e m at ic C a r t og r a p h y, " Th e C a n a d i a n C a r t o g r a p h e r , v o l . 1 2 , N o. 1 ( J u n e 1 9 75 ) P P . 5 2 - 6 ?

7 . Ar e a l s t a n d a r d i z a t i o n o f d a t a fo r c h o r o p l e t h m a ps i s a c h i e v e d b y co n v e r t i n gs imp l e e n u me r a t e d d a t a t o r a t i o s . I n th e cas e o f ma p B i n F i g u r e 5 > th e c r opl a n d a r e a o f e a c h c o u nt y w as d i v i d ed b y i t s to ta l l a n d a r e a t o d e r i v e t h e r at i o , c r o p l a n d a s a p e r c e n t a g e o f t o ta l a r e a .

8 . Mor r i s o n , J o e l , M e th o d P r o d u c e d E r r o r i n I s a r i t h m i c M a p p i n g , Ca r t o g r a p h y

D i v i s i o n Te c h n i c a l M on o g r a p h N o . C A - 5 , Wa s h i n g t o n , D.C . : Am e r i c a n C o ng r e s s

o n S u r v ey in g an d M a p p i n g ,

9 . Ar nh e im , Ru do l p h , A r t a n d Vi s u a l P e r c e p t i o n , Berk e l e y : Un i v e r s i t y o f C a l i f o r n i a Pr ess , 1 9 7 1 , p . M l .

10. T h e s e m a p s a r e t a k e n f ro m t h e u n p u b l i s h ed P h . D . d i s s e r t a t i on r e s e a r c h ofTh e o d o r e S t e i n k e a t t h e Uni v e r s i t y o f K an s a s .

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contemporary statistical maps evidence of spatial and graphic ignorance

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