SURVO 76, an interactive statistical data processing system for a desk computer

SUHVO 76, an interactiue

statistical data processing system for a desk cornputer

S- lrlugtoncn, He l"ginki

'.. PRINCIPLES OF SURi,O 76

SURTTO ?6 i= å ståtisticat' data Frocessing s)rstem

intended to cower ö rride rånEe o# actiwities irr comFrltationaI' statistica-

Ttre €iURVO ?6 ey=te,m li-3 bG'€rl deEigned esFeciall:r for ttte rrG€ds o# Etåtisticiåni in both teåcF.ing ånd reeearclt *rork årrd its aims år€ sligFriIy dif#er€nt frore tlroce of cpnverrtionål statisticål Påckäg€!5 generally awailable for data årr€f':/sis-

giURUO ?6 i3 ån i-'l3,€Lg.gEåi4lE svetem arrd nc' special i(fb descr.ibing l'anguage .3r code ie needed'

In itg Prsgent. #r:rrn it has been irlP l€metrt€'d En å degk comFuter ^UIANG eeOO urhich Provid€å suitab1e meang Sor.

råpi.l i'lterchånge of information between t|*re sv5tem and tlrc ssctr-

suRul 76: 2

TFre r.|ser c€'| irrBtgr|tl.y rercl-r årry pErrt o+ hiB dsta fcrr insFection- Equrl'ly imeortant is å rseid åcc€,fis to tFre di++el.errt rr('duI.GE (prograrrs årrd subroutines) of tFre statistic€I By3terr to get än idaa of horrr ttre system r.rorl<s ånd to rnrlce tem,'atråFy modificåtiorrs

ånd en1argeme'lts to the lrrodrrIEs-

Due to irrteråctiwity a rlre? krrrrrrringt tlre main

rr'.incipf.€€ .rf ståtit3ticåI' coilrputing cårl f,'earn to u=e

SiUR\,'O ?6 by just starting to ure it without any

detåi l.ed instructiorrt-

No progråmming e'xFcric'nce is neces€€Fy in ståndård åFrr lic€ti.tn of SURVO ?6 but in Erore advånced ^usG!

command of tA€iIC årrd måin con=truction FrinciP1e€

of SUrtUO ?6 is eseential-

SiURt.,O 76 enp l.oys BåSIE as a sctr.trce language in a fairLy extended form inc1uding månv additiorral, matrix, sort årrd alFhanumeric statements-

Using the editing facilities o+ ^U|ANG eeOO ttre system modifications can lt€ rnade easily and instårrtlv-

' Even intenacti\re 6y€t€m= åre sometimes +rustrating sirrce they ma)z in ttreir Grhrrr gentle rrra)r ccrmpel tFre user to å long unproductiv€r conversation srithout

a natursl exit- In SiURTO ?6 thiå depe'ndance is åv.tided by sp1itting the, progFams int.å a lot o+ 5må1I module€- tdtren the us€r becotnes exhausted uritlt € certåin

module tre cårr interrupt ttre conver€åtion ånd cåII any of ttre neigtrb('ur.ing modul'ee by pressing one single key .rn the kevboåFd' urittrrrut l"reging c.fntåct r.ritfr Frewious stege= of ]rir Job.

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It 1r ryadrtlt lb-t rnrrv sd-tisticisns do not. Iike ttr thank tD t'aFrrr of cornPrrtet PrPgr-rnt- Tlrcv Pre+er

c*ryanl out tlulr colPutåti.gn. ln rninor €tePs in the

ord* thay llkr. Ttrrlr pro#crenceg hawe bern tskerr

l-Dto con.ad.rataon l.rr ttrc

?6 g:rstern urhich csn

i" l-n a-ny rlrpactr br oPrrrtrd likG - deBk G€lculåtor u.Lth ttaFy rPqrg.ffu1' klYr.

On tlr. Iåf'lC eeOO krybogrd th'rr

'rt 3e sPeciål'

, +unctlon kryr tdrnof.rd Iry Fo,F.a,.-.,F3t-) which can be d.+,arr-d rr riLtrtartg polntr #or dl#flrent rlodu LeB- I I'l AUffrO ?6 lha funct.lonr .t+ th.te kevs \'årv dePendine : otl !}t. BuRvo ?6 rodul. ar| ul.. Thr ugrr n€t knoq,irrg I' r*hl-ch F-kry to Prarr lalt' c-n -lrråya r€sctrt t" ltey

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lrotrht.Ghd'.rFl.yront.}rrGRTttrr+unctioneofå11

i'' .l otlrrr F-kryr cFelrtiwl l.n 3ir. Prlrant rituation-

,; trclr F-ttrrt, hrdr to - -aclr'tanc€ .t+ quettions

ii br g|utrro ?6 rhAch hrwl t-o Dl -n.5.Fed bv the

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l; ttt. lrholr da-lotlu. ir dirrelavcd on ttre CRT and

,; rllst tlar ryrtar to g,Lwc thG st-r ilany.comments and l, ;;;-".;.-:;; ;;

";--cc'ntert r.ithout anlr wsste or

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il -11luntrcrg crith r iugg.Ftion for an

urtticFr is

1 e.intrd -+trr tl'ra qu.ltion.

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' ' To ilJ.vr good .rratåttionc SURlfil 76 triee t-o remember : thr prcwiotr= rctaor|* erf ttre ugar GtF Gven to guess

rrrtrrt trr niglrt tttarpt rrert- If the uB@r å!tr€e5 witFr th. sug|gection of SURUO ?6 tre rlcrel'y Preeses the RETURN key- othenwisc lr: nust r.rite his own Etnturclf -

dnw ?6: r

Esch i'rtrrchsn!'c of qrrortl.otlr rrrd arrrr,arr t'..dr

etrentuöll:z to a eorilr o# colFrrtttLonr -nd d.t++crent äcttong- The rGsul,ts are dirpl-y.d rrn the CRT-

Ulh€tt the ccrfltputstiotts are finir]rtd the u3Gr ctn rcl.ect anotlrer F-strrt- Gertrl-n F-stårtr -rG Fa3arvad for tn-rrrfcrring th. ras, ltr ju=t obt-Ln.d fron tlrt ccreen to thr Frl-rrt.r crr tor a-ving thet on ditk -. lntcr- mrd!,att rlcLrltr +or rubtcqLrent -n-I'yri= sittr othcr

SURT4O ilods !rs-

Tlfr SURt,tf ?6 rodul'-r prrfortrtin3| v-ri.tuc rtrtLrticrl' :ntt'y*cl c€lrr ccr-crF-r-tl -nd uBG the !-me ort-gLfr-I' datr #i1cg or l-nteF;.d.1-rte Frslrtta rtthout -ny r.rdi- +icationr rt.lcnevcr thir is strt.l'rtac-l1y r--r.trl-ble-

Erclr st-tirtl-crl' rcahod inctudrd,.an g;URTO ?G lrrs berrr tF1itt.d ints fr-l1 rrcrdsl.er and it is tha u-er's re3p(tnaLbility to corbl,ni. them in r rtae('nabI.c uav entloying F-ktyr. It rould, of ccrlIFle , bc 'casy tl' corrncct .tLfferent rubrodules in a #l-rcd ordcF' but tlr.n t,itc user uould br rt ttre mercY o+ the sy3tcrt - äir undösiFsble but unftrrtunåtely tyPicå1 +cåtsr€ ar+

tnärry rtatisticål conput.inE packåges.

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SURlrO ?6 can be run in llANG eeOO instal'låtigtr5 hrvanl I crntral Frocessing unit uit-h a memorv of at leart EIOK' a GF'IT tti.,ipIåy' a <tua1 removsbI'e f'I-r:eev dlrk drLwc' a Frirrter ånd r elottnr. trllren the

AUnVO ?6 dyrtem ic i|l LrtG onr of ttr€ dislr drives ie rttarvad +Gtr the SURvo ?6 Progr-r disks ånd ånother ir for the ur.r'* drta and Po3a.'-b1c additional

PrcD9?-l'r-

SURl.rO ?6 Cotraartr ct+ - cintr-I nodule and various gtrtlttic-l trrdulG3' of rhictr ona at å time cån be itr ula togathrr rath thr ccntnal nodule- Ttre central rctdllle taka3 c-ra ct+ tlta cGt-ctPaF-tion between t!-te d.lf{rnrnt' r'l'rtl-rttcaI roduler rnd it clrntairrg svstem rubfoutlllar, a-9. +or d-t- tr'rrns#äre betureen ttre

carrtr.rl -nd dirk naacrFy- Ttrur thG user need5 not worr:r -bout tlrG loc-t.lon o+ hLr d-tå during comFl.ltåtions'

Thr nurrbcr of €IUR\|O ?6 rnodul'cs is not limited

Lrr !n),, utay- Nrc, rodu lat c-tr br gg'nerated €lvetr in arr i-'lteractivG noda by consul.tlng å lråL+ PrePaIted

module FRaHE- EtrtPlovirrg FRåI{E to build urt å new frodul'e glraranteat ttrat tlr. rtodttl'e urill be comPatilrl'e urittr the rcquir.i.nts o+ the €iURUO 76 sv€teilr-

Uhen 5iURV[I ?6 l-. lo-dcd. fnorr disk a Ligt r:#

alternative rrrodubl is ditPlayed ctn the GRT and th3 user trss to rllact ttre trlodul,e Fre wants to LrsE.

ner t:

STATISTICAL DATå PROCTSSIIIB gY TEil SURU] ?6

1= llEilU ^?= GUIDE 3r DATå ^it= DåIAP 5= llll ⁶⁼ C0Rl ^?. $lRT ^{0= CHIilCE}

9= TAE-E ¹⁰⁼ PLOT ^11' OIåGlAlt l2= FRllllE

l3= LIIREG ¹¹⁼ ll0NLItl tS. PCilP ^{16= SPECTR$I}

17- AN0tå ¹⁹⁼ HIST0 ^19- FACTA ^{?0= IESTREG}

?1. CIIRVE ^ee= ilåTnI ffi. 0ISTRIBS ^{P1= tlAMlUA} 25. DISCRI ^?5= CLASSI ^A?r LllEo ^{e8= SURFACE}

?9' OåTASIRT

s€LECT A SURVtt 75 ltoDltE 0{t}lER 0R NållE)?

sunn ?5: 6

If ttre uscr rel-cti rr|'dub no-.a (llENU), hr gttr

on the ERT I l.ict of rll. SUR\rO ?6 l'odrtlci l,ith r tlrort descriptiorr of their +unctienr-

Thir I'ist ie reproduc.d in Apprndix a-

A nore ttrorosgh dercription o# at€lt nodrr lp crn be obtained on tha ERT by =el'ectl-rrg thc nodul. in

quE3tiorr- Tlr! rrcrduh

''rrgent6 its åctavitl-ac i'lctuding|

€r list o# operrtiwe F-ctart= and eventuglly sornc sp€ciå1 instructionr-

llodul.c no-P Lr - €}URIO ?5 teaclrer GUIDE shich is årr i-ntcråctive Pro9r-t irr itsetf and givet Lnf<rr*

rnation pGrtitrent to ttro SURITO ?6 ryrt*n during tlre ccrn\ref*sstion- Aft.r cctnsulting GUIDE th. ulaF wil'l be reädy to cåll rny guRl',tl lodrrl.c to suit hl-s Pr..r€rrt needs-

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tic-I d-t- proccrll-ni} lyltrr- Untatr now the emPl-råsis

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: hög blen on thr rort tD-dl-tiatnrl. rnd elementarv 4orms . o+ anltvrlr (cf- Apprndfu 'l-) rrhaclr gtive å rråturåI.

nI b-eir #or tlre dev.t'oPrrnt of thr 3v.tem-

Il EURUO ?6 ttr. frno!|lrrnl o# +ledans' editins ånd tranl#orrang datr lrrr,l rrcciwed sP-ciäI attention-

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i fne roduhg DåTA -nd DåTåa h-vr bcan Plårrn€d to cr:ver

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I --r.ioul -ctLvitirr Ln thLg fl-rtd tc rnake the svstem se1+-e.rn'Lrinid in tlr*a rreptct.

Onr of th€ b-3l.c PtlrrciPl.s in SUR\,O 7€ is tl-iåt anv plrt.nt'l. t'ly irneortrnt obeerwrt,l.ont or intermediåte

Fetulir crn bc urrd LlD fubsltqurnt'GotlPutåtiont without lrtrå lD.rdl-+.lcatl-on: o+ tlre lvstem-

SURtttl 76 al1owg bGtth warirblri and observatisns to be l'-b.llcd r*itlr -I'Phanufreric rlrrt€3r Ttris måkes the FGrsult- ilrore raadrbI'a -nd rnonitorini the comeutåtions eåBi€F-

Eåch siURVO ?6 rDoduI'c'ig sr.tPPoged to telL continu- ously on the CRT elrat it' iå doing- Ftrr instånce' rrrl-ren

observrtions are, Proc€3sed the syrEtom Prirrt€ clll the CRT t-hc tlåtnG o+ thc observåtion to lre dealt r4itF.

nex t-

3- e - ^GRAIII{ rC, REFSESiENTJITIONF Elcrt-lr tl-re ^p tr-otter an d tlre C ttT f crr rråsr-ra Lå z in gl etstistica I data

suRul 76: I

€rr* € wa l"uab I-e d evic es

an d tlreor etica L

mode l"s-

siUR\,O ?6 crn ^p l.ot, for inst,Ence, scatter diagrarns' time +eries' -nåx'ytical qurrrat gnd surfaces- To begin grith, th6 graphB -r. usuårlly FI'ottad rsPi-d1v but insccur-tel'y afn tlrc CRT- lrltren tlae user finds that a certain graeh is LntGrestirrg rnd deset'vcEt c l.rrser cxgmination hG cåtl rrril'y tr-n3+€F it orr P{EPen in a rrcrr.G åccu1.åte forrn rr€irtg the 3l lotter ctF the trrinter -

ulhårl rtråki-ng sraPhs [,.rr:/ gmall ntrLgances like pl'åcirrg prcrP€r mrrks rnd irrdicsttoni ctn cct*crrdinate .rcs rD-y ån'lcty the gser- Therc+ore it ir wqluable tlr-t ttre =ystett cått ccttnc to the -rescue of ttre uBGr .fn erobl'ems of th-t kind- ThttB tiUR\lO ?6 täk€s care o+

scälirrg l'f ttre rrariabl.ec if degircd arrd it als(' s€lect3 'nice" msrking Poants on the aaxGt qccording t.o tFre size ('+ th€ gnaelr (determined bv the rrser) and the rärrge of tfre viriöbles to be Plotted-

It is al'sct essential' that the uscr can emPlcr:r rrarir:rus pl.otting rnodqlalt rcne å+t€r årrotlt€'r. for t-tre same eicttrre to ctrmbine gråPtrt- It rna:r be use#rrl to hawe. f{)r instance' a tiae seriee ätrd tome o# its ccrmlrcrtr€lrrts in the eane pi-cture- Likewi6€' å+ter

making a scåtter di-agråm ttre Ltter migtrt urisFr t<r decide wtrat kind o+ m(rdel Bltctuld be +itted' estimste ttre model and return t-g Pf.('t a 1ineå.r ctF nonl'ineår regresgicrtt cltFtte ctn ttre same gräPl-r-

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Orrr rttrrct.l.wr fcrture o+ the faANG geOO comPuten ir tlrft v.raOul afLthnetic oPerations cart be eerformed ärld ratultr dirpkycd *iust bv oPerating the mactrine

I,ik. - nort-I crlculator- To a ce'rtairl exte'trt ttris alro -PPl'i:3 to natrix oPergtions-

Ia +a'al', howcwer, that thege ctPG,råtictlls €15 rBuch are not 3oFhisticåted enctuglr for the mu lti+åritrus conputltLonrI' ncrds o+ ståtisticians- It is often derl-rrb 1r to t15v. i.n ctPPortunitv tct continue certain cornputltLont fnå'lu-ll'y å+ter ttre standard routines fr-v. br.n Prrforred utith SURVS ?6 modules on otlr€r prcrt,r-tl- For thlr turPcrse the sy€tem cotrtåins a rnodu l. c- 1l'ed IiATRI -

Iittr I{ATRI tlra uaar c-n PeF+orm s wide' r.€nge of mrtn.Lr ctpar-tl-ct'rr url.ng tt.lc cctmPutei lLke a calculåt.ar-

In ilATRI all tFrc F-krys are defined +or \råri-olls

ilätrir ot'cratitrnr l-ncluding matrix in\rersiotl . eiglen- wglucg ånd vactcrrlf +Grr ryrnrnetric måtrices. eartition- ing and coilbi'li-trg nrtriccs-

Ttr€ lltricee reqrt.l.rad 55 åtl inPut can be keved in riänu-1l'y or trsnrf.rFrd +rorl different- E;URI,O 75 +il'eg;, R.ru1tg c-rr Itc r€ved in special matrix fi1es fcrr htcn oPcrstionr-

In tlre cantral taactry ttrere ig sPace' for three rratricas onI.y (tl.o ('PcDands X'Y ånd Gtn€r resul"t- Z)- An e=scntial +Eåtura clf IIATRI is ttt€t tFre rnodr-rle doee a ket of br:ol<-ka.Parrg ånd 1åbele eåch regult r.rith a name cctFrei=PctndLrlg to ttre ordinar)z rtåtFix

notstion- Hetrce slttrouglh

"*= .r=-t hå5 to sPl.it mgtrix #ormulåe into brsic oeerations wl-rictr are

corried rfut trv singla F-keyB he alwa)rs hss on tFre CRT l.alre,le o+ th. 1åt.3t oPerand= arrd resu I'ts in allno5t notmaI' rnrtrix nartqtiatn-

lru

3.4- RANDSI.I DATå SIäII-ATION

In many rretlr{'dol.ogLcaI' conrid.rrtiorrt -nd ttactring situations it ir uf.+ul to -n-lyra -rti#.lel-rl' F,lnd.f,m dåtö r*hoer orLlin ir parf.ct t'y kreFn-

P1årlning| Gr+ such Grp.pir.rrta c-lr ba rubat:ntLally

#acilitåt.d. by .r|rloying - aURVO ?6 nodulr call.d cHANct rrtriclr aa - r-rrdo- drtr lrnaratctr-

Tlr. user hrr to cr.atr thr rtrt.arntt nrrdtd to generatc - tyPlc-I obt.rv-tLorr oh.{ch ir donl accoFding to thc .an.truct.aonr t.lwrn ltv CHåNGE. Ei.v.rrl n^lb- routiner -p. iilr.dtrtrl'v rvl.l'hblr Lrr CHANGG to grnrrrte paauatcr F-ndor wrrirtlr fror rärioua dlrtri- butaorrr-

Thua it Ia aalv lvorr foF an ulrarParirncrd 'PFo- gr-rrrlerr to conrtruct tandqr drtå rccord.lni to r gliv.n rtatirt.ac. I rodrt'- Th. .1ruhtrd falrl ern subr.quantly bc tr.-t.d a3 ord.l.n.r.v drtr ^+.4 1.r bv rrr,.rr5 of 5UR\IO ?6-

. Errp loylnl CIIANCE thr f.trl of dl.ffrrrrrt 'r-ilP IG dirtrLbuti('rlr c,.n ,. 1ro ba dllonrtratcd on tlrr GRT- Tlre urcD trlact3 tlrc dLltr.alutlotl -nd it. Prr-f,rcteFs rnd GHANCE ltartr to t.fia?.rtr oblaFv-tiorlt fnorn ttrat dirtribution- Obrrrw-tionr ,arG Plottod on the cRT .anc å+ter -notliFr a. conrts'ltly flrowLng histogråm-

APPEND ICES:

t-- List o+ SUR9O ?5 nodu hg e- Graptrics cLttr 6UR1IO 76 REFERENFES

=

l{uetonen S-, G}URVO ?6: A etatirtl-cål dåt- Pnocessing slrctem, Rcctrrctr RaPort No.6' Drelrtnrnt of SitåtiBtica' Uniwerri+.Y o+ Hrlrankl., LgaT

Alro lro dilonetratior diBketteE contrining reådy.rede corvcrcttioir rilh ^StlRUl 16 erc rvellable.

This Daper håt bem prepared ssing år sditilt ^{proqrer dev.loPcd in} conlection ritå $tlltltl 76.

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APPEND IX I.: L TgiT OF giURVO ?6 I,IODIJLEE EUIDE: $IfrII} ?6 IEACHER

DATA: DITå $IPUT, SAVIT{G, EDITIilE A}IO TRAilSTORilåTIO}I5

I)ATAE: TRA}ISFERRIIIG AI{O COIIEIilING DATA FILES

II{I: TIIIIåRIåIE STåTISTICS

CIIRR: IEå}IS, STfr}IDåRO DEVIATII}NS A}IO CTIRRELATIO}Is

flIRT: OåTA $NTIilB åM OHER STATISTICS

TåBLE: a{NEilgIOIåL CLASSIFIED FRE0IE}ICY TABLES,

TåH.ES FOR IIESIS A}O STANDARD DEVIATII}NS,

TåH.E EDITI}IC O}I T}E CRT, CHIIS A}IO T TESTS,

T.-ANO E-NY åilåLYSI8 I}F UARIå}ICT

HISTO: ]IIIUARIåIE CLåSSIFIED FREOUE}ICY DISTRIBUTII}Ns, HISTOGRå}IS

PLOT: PLIITTINC å TIIIE SERIES OR SCåTTER DIAGRAI{

(IiAX 1?O OBSTRUATIO}IS, AUTOIIATIC SALING)

DIAGRA}I: PLOTTIilG å II}IE SERIES OR SCATTER DIAGRAI{

(IIIL iltITED }IITttrR OF OBSERVATIONS,

SALIilE IS AUTI}I{ATIC I}R OETERI{I}IED BY THE USER}

CURI/E: CI'RI'E PLOTTIilG

SURFACE: $IIRFACE PLOTTIIIG I}I CEilTRAL PROJECTIO}I

CHANCE: RåilDOI{ DåTå 6E}ITRATBR,

SIIITLATIO}I OF UARIOUS DISTRIBUTIOilS ON THT CRT

FRAI{E: }IåLF PREPARED SURIJB IIOOILE FIIR INTI RACTIIE COI{PO9ING

IF ^ilET SURU} IIODILES

LINREG: I{II.TIPLE LI}IEAR REB$SSIO}I åT{ALYSIS

RESTREG: IIII.TIPLE LI}TEAR REBf,ESSION ANåLYSIs

TITH LII{EAR PfiRåI{ElER COilSTRAINTS

NO}ILIil: ffiALIilEAR REGRESSIffi ANALYSIS AIID }I{S{L II{EåR OPTII{ I ZATION

PCOI{P: åMLYSIS IIF PRIilCIPåL COI{PI}IIEI{TS,

FRI}ICIPAL AXES S}LUTIO}I F(}R FACTOR ANALY5IS

FACTA: ORTHI}GOilAL ROTATIOT{S fi ^FåCTI}R A}IåLYSIs BI'I THE CRT, GNAPHICAL, ^t/ARtrHAX åTP OUåRTII{åX ROTATIONS SPECTRIfr : ^åUTO. AI{O CRI}5S-CORruLåTI{}NS, SPECTRAL ANALYSIS

I{ATRI: }iåTRIX I}FERåTIOilS $I }TåTRICES Iil SURVO FILES OR

!{]f,TRICE5 GIIEil gY T}IE USEN

DISTRIES: fulåLIES OF HEI}RETICAL DENSIW AND DISTRI8UTION

FtffcTl{t}t5

DI$CRI: I{IT.TIPLE OISCRII{INAT{T åNALYSIS

CLå55I: CLåSSIFICATIOfi OF OS$RVåTIONS I,ISIi.IG I{å}IALAN{}8IS O{€ åND &YES PRBBABILITIES

LIilICO: LTNIIAR COilBI}ååTI{}N5 CIF VARIåS.Ts,

PfrI}IIIPAI. COI{PI}I{ENT, FAETOR AI{I} OISCRII{II{ANT SCORES

DATASI}RT: 5{IRTIN6 A DåTA FI[-E åilo TNAHSFETRIilG THE SffRTTO OATå

${ åT{OT}IEN FILE

COFY: R*PID TRåNSFENS OF OåTA FILES

TDATA: å$ 'DATA' 8UT åUTI}ilåTIE LABELLII{G FOR TTHI SERIIS CI8ffiRråATlCIt{S,

I,IATDåTA: TAåH$FERRIiIG å HåTRIX SåffiD t}N OIS( IN A SURUO ?g

[}åTå FILE

AG6RE: åffGNEGATI8il{ OF OBSERUATIONS

I.IfiLEY: trEXS ALL THg RI}I}TS OF å}I ALCEBRAIC EfrUåTION"

BINORI{: Stril{å*TTOT {}F 8IT'åftIåTE I,I{IRI{AL DISTRISUTIO}'I {iI{ THE CRT

sI}tåLCfi: å SEI{ERAL SITILåTOR FilN TIHE SERIES

CURVEE: åS O[[JR[E'U 8UT ALSO FCIR II,IPLICIT FIS{CTiONS

DEPEND: TESTIilg FOR THE II{DEF,Ei.ISEilIE OF VARtrABLES

SCURUE: TH€ FIHCTION PLOTS I}F I'IIJI-TINIHENSII}NAL DATA

8Y T}IT }IETHI}D OF åNDREHS

N-TEST: TESTS OF NORI{ALIW (SHåPIRO-bIILH TTC" }

},I}I-TEST: TESTS OF HIå-TIil(}RilAL ITY

PRII,IT: '}IEAT' ^PRINTOUT fiF SUfiVO 76 DATA FII-ES

GROUPS: CLUSTENIilG OF CIBSERUATIOHS IACCORDING TO I$$SATå}

FARTCORRs PARTIåL CORNELATICI}IS,

CI}}II}ITIIIilAL ilEANs åilD STAI.IDARD DEUIATIONS

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Thi* t^rilr'k h.aE been supported by the ^Acadeny of Finland and Al...l{fi ⁽ t he State Alcohol l'lonopoLy of Finland ).

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LJrr:ivsrr*ity of Helsink i H*rLl.i'tuskatu L1-13 5F".O0100 HELSINF(I J.0