AAYSIS O EQUECY ISIUIOS . Grdnr & G. Grdnr IS 0 02246 8 4 . Grdnr nd G. Grdnr CAMOG COCES A ECIQUES I MOE GEOGAY O 19 (Coces a eciques i Moe Geogay AAYSIS O EQUECY ISIUIOS CAMOG as ee ceae o i a eacig ee i e ie o quaiaie meos i uegauae geogay couses ese es ae amiae guies y o e eaces ye cea eoug o sue ucase as e asis o cass- wok Eac ook is wie y a auo cuey wokig wi e ecique Gaie a G Gaie o coce e escies (eicese Uiesiy a omey o Saosie oyecic 1 A ioucio o Mako cai aaysis - Cois 2. isace ecay i saia ieacios - ayo COES 3 Uesaig caoica coeaio aaysis - Cak 4. Some eoeica a aie asecs o saia ieacio age soig moes - S Oesaw 5 A ioucio o e suace aaysis - Uwi I IOUCIO 6. Cassiicaio i geogay - oso (i e-equisies o eae 3 7 A ioucio o aco aayica eciques - Goa A Kiy (ii e coce o a equecy isiuio 3 8. icia comoes aaysis - S auey (iii yes o aa 5 9 Causa ieeces om icoomous aiaes - aiso II E EE O EAMIAIO O EQUECY ISIUIOS I GEOGAICA ESEAC 1 Ioucio o e use o ogi moes i geogay - Wigey (i esciie saisics 6 11 iea ogammig eemeay geogaica aicaios o e asoaio oem - A ay (ii Ieeia saisics 8 1 A ioucio o quaa aaysis - W omas (iii Causa eaaio o saia ocesses 8 13 A ioucio o ime-geogay - i (i Oe uses o equecy isiuios i geogay 9 1 A ioucio o ga eoeica meos i geogay - K ike III GAICA MEOS O EAMIAIO O EQUECY ISIUIOS 15 iea egessio i geogay - eguso (i Cosucio o isogams 11 1 1 oaiiy suace maig A ioucio wi eames a (ii Ieeaio o isogams oa ogams - Wigey (iii Cumuaie equecy gas a oaiiy os 20 17 Samig meos o geogaica eseac - C io eac (i Cocusios 24 1 Quesioaies a ieiews i geogaica eseac - I COMAISO EWEE OSEE EQUECY ISIUIOS A E OMA C io eac ISIUIO 19 Aaysis o equecy isiuios - Gaie G Gaie 26 (i Aaysis ase uo mome measues 20. Aaysis o coaiace a comaiso o egessio ies - Sik 28 (ii Gaica esimaes o mome measues 1 A ioucio o e use o simuaeous-equaio egessio aaysis Oe meos o assessig skewess a kuosis 3 i geogay - o (iii e W es o omaiy 35 Oe ies i eaaio (i 37 ( o-aameic oea gooess-o-i ess h r, Cnpt nd hn n Mdrn Grph 3 (i e eecs o ouies a oe isuaces o oma prdd b th Std Grp n Qntttv Mthd, f isiuio o aa th Inttt f rth Grphr. 5 r dtl f brhp f th Std Grp, rt t th (ii Coice o meos o comaig equecy isiuios Inttt f rth Grphr, I Knntn Gr, ndn, S.W.. wi e oma isiuio h r pblhd b G Abtrt, Unvrt f Et Anl, rh, 4 , t h ll thr nr hld b ddrd. V SAEGIES O USE WI O-OMA AA (i Assumios o e iea moe 7 I IOUCIO (ii Saegies i e assumios o e iea moe ae 48 o saisie (i e-equisies o eae (iii yes o asomaio 51 is mooga is iee o oie a coeie summay o meos I wic may e use o assess e isiuioa caaceisics o aa use COCUSIOS 55 i geogaica wok We assume o e eae oy a aiiy o eom sime aimeic oeaios aoug a asic uesaig o e use GOSSAY O EMS USE 5 a meaig o sime saisica ess wou aso e a aaage I e eciques ouie ae o e aie o age amous o aa e SYMOS USE 1 e aiiy o asae sime aimeic oeaios io comue coe EEECES is aso ecessay ose uy coesa wi e coce o a equecy 3 isiuio may wis o omi Secios I-III A gossay o ems use (iaics i e is icue o age ; is aso icues symos use i omuae (ii e coce o a equecy isiuio aa aayse i geogay oe cosis o a seies o igues wic measue some aiue o e geogaica individuals cocee Geo- gaica aa may o eame e e yie o wea e ui aea o a se o aises e aeage soe o a seies o aiage asis o e aua aia o a ume o meeooogica saios; e iiiuas i ese eames ae aises aiage asis a meeooogica saios eseciey Geogaica iiiuas may e eie egios aig a aea ee suc as amiisaie uis o aiage asis o may e egae as eig oi ocaios suc as iusia eeises o meeooogica saios Eac igue i suc a se o aa is eme a vrt wis eac measue caaceisic is eme a variable. o eame e weae a a seies o meeooogica saios may e escie y aiaes suc as emeaue aia a umiiy eac oseaio eig a aiae Some imessio o e age a aeage aue o a aiae may e gaie y meey ookig oug a is o aiaes u o e sake o simiciy o caiy iomaio i goue o geeaise om is oe moe useu Eac seaae aue i a se o aa as geae imoace we i is cosiee i eaio o e oe aues as a o a umeica isiuio a as a sige isoae oseaio eseaio o goue aa is usuay eecue y eaaio o a equecy iagam usuay i e om o a histogram. o eae a isogam e aiaes ae goue io casses sowig ow may iiiua aiaes a io eac cass is is eme e equecy o eac cass a a iagam sowig ese equecies i asceig magiue o cass aues i e om o a a ga is cae a isogam e aoe ieas ae iusae y e oowig eame usig iy yeas o aia aa as e se o aiaes (ae I igue I ese ae a suse o seecio om a ossie yeay aia oas A suc ossie aia oas ae e population o iees a sma suses seece ae samples. 3 ae I Aua aia (mm 1931-19 Yea Weigo ak o ameo Yea Weigo ak o ameo 1931 131 91 19 1 39 1 193 1 9 197 9 79 1933 9 682 19 111 3 193 115 9 199 137 688 1935 1195 97 195 139 99 193 17 5 1951 1 882 1937 17 117 195 1157 795 193 1 844 1953 820 37 igue e asiio om 1939 13 91 195 1 17 isogam o equecy isiuio 19 11 15 1955 97 9 oe owee a e asiioa 191 13 737 195 93 77 se ia e equecy oygo is 19 113 77 1957 1111 95 oe omie 193 1 842 195 135 99 19 1157 71 1959 137 13 195 1159 7 19 15 13 e aiae cocee is aua aia a e iy aues o oa aia oe o eac yea om 1931 o 19 o e aia saios (Weigo ak a o ameo oie iy aiaes o eac saio e iy aiaes ae eac assige o a cass e cass imis eig a ieas o 15mm isogams o ese aa ae esee i igue I e oea sea o equecies ewee e casses is cae e frequency distribution o e aa a i is wi meos y wic e aue o suc isiuios may e aayse a is mooga is cocee oe a e age a isiuio o aiaes as a coce is ieee o e cass ieas use i e eaaio o e isogam a aoug a equecy isiuio is coeioay isuaise as a isogam i is moe coecy oug o as a geeaise coce eaig o e sea o coceaio o aues ieee o e casses use We ae so a isuaise equecy isiuio i ems o isogams u i we imagie a ey age same aw om a ey age ouaio a e aiaes ae assige o casses wi ey sma cass ages o e aiae e e isogam ouce wou e i e om o a smoo cue isogams ae oe esee i is om o as equecy oygos (igue as ese moe eay acco wi ou coce o wa e ueyig equecy isiuio sou ook ike uiuece y e same ake o cass sie use i eaaio o e isogam (iii yes o aa I as so a ee assume a e aa o coce eese aues om a coiuous age owee i is ossie o ecogise o continuous a drt aa e ome may ake o ay aue wii a igue I equecy isogams o e aia aa o ae I e gie age a i geea ae measue aues suc as aia aea o eica scae is oe o equecy (; e ume o aiaes i eac cass eg o eie aios suc as ouaio esiy o eceage o a is gie aoe eac a e eigs o wic ae ooioa o e use iscee aa cosis o coue aues suc as umes o uiigs equecy associae wi eac cass o umis a ae geeay woe umes I acice e isicio may ecome somewa ue sice coiuous scae measuemes ae a 4 5 iie esouio a aimeic ouig o euces e ossie aues o a coiuous aiae so a coiuous aa may e cosiee iscee i oue o e eaes woe ume eeeess e isicio is a imoa oe as i eemies e way i wic aa sou e ae e eciques escie i is mooga ae iee imaiy o aaysis o coiuous aa aoug ey may aso e aie o iscee aa i some cases; a u iscussio o equecy isiuios o use wi iscee aa is gie y Gaes a Eige (197 ue seciic yes o coiuous aa wic ee o e ecogise icue cose aa wic may oy ake o aues ewee aicua imis as o eame a 1 i e case o may sae measues o a 1 as i e case o eceage aa a oe aios wic may age om o iiiy is isicio emas eaie cosieaio we asomaios ae eig cosiee (Secio II E EE O EAMIAIO O EQUECY ISIUIOS I GEOGAICA ESEAC e caace o equecy isiuios is imoa o a geogaes wo ae ikey o wis o use umeica meos i ay ac o e suec; some o e moe imoa aicaios ae escie eow e ways i wic equecy isiuios may e eamie o use ae is o a ouie a e some seciic aicaios ae escie (i esciie saisics A se o aiaes may e isuay summaise y a isogam u is is o aways coeie i wic case esciie saisics may e use e mos commo o ese ae e n a e tndrd dvtn, a ese escie eseciey e aeage aue o cea eecy o e aiaes a e isesio o aues o eie sie o e mea aue e cacuaio a use o ese a oe measues is escie ue eow (Secio I Caaceisics o equecy isiuios may e succicy summaise y ese sime measues (igue 3A A ee sime om o saisica soa is e use o dl l, wic is e cass aig e iges equecy owee ese saisica soas may occasioay gie ise o eoeous o miseaig cocusios as i e case o equecy isiuios wic ae asymmeic o d, a equecy isiuios wic ae moe a oe moa cass (imoa imoa ec; igue 3 e mea oies a eiey ai iicaio o cea eecy oy o symmeic uimoa equecy isiuios aoug is use is oe oeae o sigy skewe u eeeess uimoa equecy isiuios I is eeoe imoa a e aue o equecy isiuios e eamie eoe suc esciie saisics igue 3 Mea a saa eiaio as esciios o equecy e emoye isiuios A Comiaios o ig a ow meas a saa eiaios esciie use o isogams is ey commo i geogaic eseac; B.