Statistical graphics in SURVO 76 EDITOR

RESEARCH REPORT

Statistical ^g raphics in SURVO 76 EDITOR

BY

Seppo M,ustonen

No.33 ^{Febru ary 1982}

DEPARTMENT OF STATISTICS UNIVERSITY OF HELSINKI

SF OOlOO

HELSINKI

1O

FINLAND

tsBN 951-45-2561-2 tssN 0357 -9778

S.l'lustonen:

Statistical

sraphics

in

^SURV0 76

EOITOR t6.e.tg8p I

1. Introduction

The

interactive statistical

systen SUfiVtl ?6 provides several neanE

for ^graphical

representation

of statistical data.

Thpre are nodules

like

DIAGRAI'I and PL0T

for scatter

diagrans and tinre series, HIST0

{gr

histograms and frequency curvesr

CURVE

{sr analytic

ciJrves,

SURFACE

for analytic

sur{aceE

in central projection,

SCURUE

{or

Andress'

{unction plots,

FACES

for

Cherns{{'s faces,

CURVEA

for analytic

curves

in implicit

form.

During SURV0 ?6 conversations

ihe

^graphs

are

created by entering the paraneters _needed

for plotting,

The

plots

may be constructed gradually through geveral steps and various gråphs ⁽

like scatter

diagrams and

cutves) may be conbined

in the

sane

picture.

SURU{I ?5 EOIT0B

is

an extension

of ihe

systen

o{{ering report

^gensr-

ating

and

text

processing

activities.

^EDIT0R

also

includes ^procedures

for interactive

numerical and

stetiEtical

computing

in editorial

node

(l{ustonen 1980, 1981 ).

0n

this

besiE

it is naiural ta

develoF procedures

{or statiEtical

gråphics,

too,

SURV0 ?6 EDIT0R notl includes

a

FLOT operation

{or

these

tasks.

FL0T

is able to

^prsduce,

for

^example,

the folloning

^graphic

represEntations on

the

^graphic IRT:

h,gr,_d"*g*fgp,g

(vertical

_ånd

hnrizontal, rr

frequencieE and

pprcFntagBs,

single

ånd

multiple, pie

chartE,

matrix

diagrämg) scg!.!gl. $.laptp.tnp (wit

h

severä 1 optiona

I

^charac ter'ist"ics i

p r obab

i lity

^p lgts ,

n_Lp!:

.,pf

^trnu

ltip

^le

)

t;p.g"Sgt*eg

p rI+ _I y Lg.-r-u r vF.å s:rd.*tås

i.hsl-ql--q!.uså

As an axanple

let

us consider

the plotting of a ber diagran. In

the upper

half of the display 1.1

ne have

a

data Eet and

a

FL0T operation typed

in the edit {ield. In the louer part o{ the

sane

display

the graph creaied _by

activatins the

FL0T operation

is

preEentEd, Activa-

tion of the

^FLOT operation takes

place,

_{ås always}

in

EOIT0R oper-

ations,

by

{irst

noving

the

cursor

to the

operation

line

and ihen pressins

the

key C0liTINlJE.

5 " l'lu ston Fn

: Statigtica I

^g rap hic E

in

^SURU* ?{' En I TCI R ^1L

.-} 1L.TL}'J -L\JaLe.t-tlJl-

DtåP _{*"å. .1}

I jl

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s

{ 100x 1

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i-l

4 5 6 7

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([]13?9

ä"1'lustsnen

*

*Number'

of

rnåIrs .t1000i i"n

vårisus

åge srnuFg

*

*DATA _{I,IALT S, A ,} B, il

tl

0-14 ^15-ä4 A

$weden 841

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*

Denmarl.<

564

³⁹⁵

*

Fen

Land 5öä

³⁹⁹

n Iceland 3ä

^ää

B

Norway 474

³¹⁶

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-tPLO T I,IALT 5

* t

e5*44 45*e,4

118fi

930

7::r

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ä9

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|]F

14 ftLES Su*red en

Denirrark

Flnland Icelend

l,l

oruöy

1000 2'J00 3000 4 0#fJ 5 000

o-r4 n

^1s-24

^{m ?s-44 m 4s}

⁶⁴

^{ffi 6s-ffi}

Hhen

plottins _bar

_diagrans

_the

FL0T cperation has

onl'/

ane ^påråme-

ter, the

nane

o{ the

data

set to

be

ptatted (in this

^case I'IALE$i" The

data

set

has

to

be de{ined by

a

DATA

specificatisn.

^0ATA {on

line

4}

gives

the

nane

of the

data

set

{I'IALES),

the {irst

and

lest line

a{

observation values (A,B) and

the line o{ the

colunn

labels

^(l'l).

In this

cåse

a plain

FLOT operation ^produces

the

graph Presented in

the

lourar

hal{ o{ drsp.1.1,

bui, various featureE,

of tlre ploi

nay

easrly

be adjusted by neans

o{ eLtra

specifrcationE uhich

are

tvPed

in

ttre

edit fie.ld prior to activation of

the PL0T oPeratron.

For instance, to

nake

tlre

sane graph

in vertical

bars and

in

^per-

centages, ^we add

the speci{ication

IYFE=ZVBAR

in the edrt {ield

^and

after actrvatisn o{ the

FL0T operation we have

S.l'luEtonen

I Statrstical

^graFhics

in

^SURUO 76 EDIT0R 16, e . 198[

[rEP-*fd

SURUO 76 ID I TOR ⁽

[

^] 13 79 $. l'1u Eton en

I

e

4

5 6 7

I

9 10 11

u

J-r-lt:r

14

*

*Number'

nf

^ma

leE

^{( 1000}

)

^rn

*

*DA TA I,IALE $, A , B, I,1

1,1

0-14 15-e4 ^e5*44 A

$weden 841 57f

^11BB

t

D ennar

k 564 ::85

⁷³¹

*

F in lan

d 506 399

^7?7

*

Ice

land ::ä ??

^e9

B

Nnrway 474 316

^5::4

f;

*FL0T _{t'lALt5_}

* TYFE =TUtsA ^R

*

vår'iouE åge ^gr0upg

45-64

6s-

9::0

⁵⁸⁵

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468

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Flnland Icel.and

^Nonrray

o-14

n

^1s-a4

ffi

^?s*44

m ^{4s*64ffi 6s-} ffi

Several

extre speci{ications

are

available

dppending on

ihe

type o{

graph

in ^question.

Each

speci{ication

has

a defautt

value uhich cor- responds

ts

some

kind of a

standard

alternative.

Thus even

without

any

extra specr{icatirns a

reasonable

plot

should be obtaj.ned, as a1r'eady seen

in Disp.l.l. ^In fact, rn this

case

the de{ault

valups

o{

the

extra specifrcatrons

correspond

to the follouing

s,et up2

S.l'lustonenl

Statrstiral

^graphics

in

5URU0 76

EDIT0R 16,r,198ä

4

D-rge'å#

E. 1*

^*Number

nf

ma

les

t:!.000

) in vsrisus

ågB _sr'$ups

3* 4

^{*DA TA l'lAlt S, ff} , El, ^f,l

5

^l-l fi-14 15-ä4 ä5-44

45-64

65*

6

^{A Stl *d}

en

^S4

I 571 11S8 9:r0

5fr5

1 *

D enmar

k 564 :r85 ?:rl 5:t?

³⁰⁸

8 *

F in lan

d 506 ::99 7X7 468

^ä0ä

I * Iceland 3ä äA tg ä0

ICI

10 n Narnray 474 316 534 44ä

^ä51

11

^*

1ä

^{*F Ltl} T l{Alt S-

tg

^*TYF t=HBAR DEUI[[=S

l-4

^*H0l'trE =10CI ,

?ö

^{$ I Zt} =6{10 , 4 St]

15

^# SCALE =ö , 1ö00 n ä 0t]0., SSSS , 4 00* , 5öfi0

16

*SHADIT'IG=0,ä,4,7,9

17

^ILEGENS=-

ls

*HEADäR"[EFf,_ i$å9Fry"_g[*mLH_S

19

*XSIU=ä,9,1 YSIU*f;,5,tr F'[N=L

ä0

^*

el

^*

ää* ä3*

0bserve

that the

order

of the extra speci{ications is innaterlel. If

a specification

appears several

tines in the edit {ield, the {rrst r,rilI

be used.

In

order

to

have several

plotting

schemes

in the

sane

field, albor- der line o{ the forn lt. ... ^{(as line}

21 above) can be

set to

rso-

late

then {rom each

other.

^The data

setg,

defined by

the

DATA

specr{i- cations, åre,

hor,lever, 9lobaI and accessible

fron

any

subfield

lirnited by

the *.,... _lines.

To gain

the

nexinum adventage

o{ this

technique,

the

user may create

edit {iies

containing ready made

ptotting

schemes

{or

subsequent app-

Iisations. Typically,

from one tlell-designed

plotting

scheme geveral

variants

nay be

rapidly

composed by

editins

sone

of the extra apeci{i-

cations.

At thp

end

of this report

an appendix

including

several reedy-nede

plotiing

schemes together

sith the {inel

output

t+ill

be prese'nted.

Hence,

the

user nay

easily

^generåte

his

ot,tn solutionE ofi

the

basis

of

theEe exanples.

The next chapter

t.litl

be devoted

to a

nore thorough account on the

PLUT operation

in

various fonns

o{ plots.

The

plots in the

appendix are alEo

to

be used as an

rllustration of the {acts

^presented.

During

the actual sork at the

computer

infornation

needed

fsr ^plot-

ting

nay be obtained by using

the inquuy

system

o{

5URU0 76 EDIT0R.

The keyword PLOT? displays

all the essentials

nelated

to the

^PL0T operation and

to rts extra

specrfications.

i.

^{$URV0 76}

[DI'filR

([i"t973

S.l"tustonpn

{100x100}

S.l,lustoneni

Statistical

^graphrcs

rn

5URV0 76

EDIT0R 16.e.198e

5

2.

^The PL0T.opBqation and 1_ts

exira

speci{icatrong

The

{ollowing

chapters

will

cover

the rules for

^using

the

PL0T

operation

in ^ptotting

varioug types

n{ statistical

^{graphs. Exenples}

ane given

in the

appendix.

AlI

forms

nf the

^FL0T operation

require that the

data

to

be plotted

rs

presented under

a

DATA

specifrcation.

DATA inane

of the dala set),L1,LI,L::

de{rnes

a

data Eet on lineE

Ll-L?.

Each

line

includes one observation

vector in the

{orn.{name

o{

observation)

X(f) X(2) .., X(l'l). Line

^LS specr{res

the

names

o{ the

varrables

X(1),...1(l'1

).

Note

also that tlre line lebels Ll,Le,L3 ny'be either integers

or Eymbolic

(a

_character placed

in

^tl-re

control

colunn),

2.1

Bar and

pie

diaqrams PL0T .iname

of a

data set)

plots a

h,ar diagrarn

o{ a

^data

set

de{ined by

a

DATA

speci{ication, Piotting is controlled

by

the follskring ertra specifications

typed in

the edit {ipld!

TYPE, SCALE" SHAOINS' LEGEND, HEAOER, TEXT, HOl'tE,

SIZE, XOIU, YDIV, EAF, SPACING, PLAN" LI}1ITS,.FEN, FRAI.IE,

A.1.1.

^TYFE

TYPE speci{ieE

the type of the bar

diagran

in the

PLUT operation.

0e{ault is

^TYFE=HBAR

(hsrizsntal

_bar

_diagran}.

The

alternatives

arE

TYFE=UBAR

vertical bar

diagran,

TYFE=ZHBAR

horizsntal bar

diagran

in

percentages,

TYPE=lUBAR

-

vertical bar

diagram

in

percentages,

TYPE=l'tHBAR

nultiple horizontal

ban diagran,

TYPE=l,lUBåR

nultiple vertical bar

diagran

TYPE=P IE

rnuitiple pip

diagran

tfntal

åreå Fropontional

to

cslunn sun)

TYPE=XP IE

nultiple ^pie

diagran

(t'otal

area=constant)

TYPE=i'IATRIX

natrix

diagram

nith

shåded

cells

according

to the

data values

a.1.e.

scALE

SCALE=tlst value),'iEnd

value),.,.,{nax.va}ue}

specifies the

Ecale and

the scale labels

on

the X-axis in

^{HBAR dia-}

grans and on

the Y-axis in

^VBAR diagratns.

I+

^SCALE

is nst

^given,

scaling

and

labelling is

automatic and EelectEd by using

the

valueE

in the

data

set

as

a basis.

Hence, when automatic

scaling is

used, no

overflow

o{

bars

in ^the

^{gnaph may occut.}

SCALE=- neanE

that ihe

(automatic) scale

uill not

be displayed.

S.l{ustoneni

$tatistical

sraphics :.n SURU0 76

EDIT0R 16"t.198e

⁶

E.1.3.

^SHADING

SfiADING=i,hst

o{

shading values

0,1,e'...,10) or 0,-1r-8,...,-10 or

0r11,le'13'14

specifies a

shading

{or

each

section of the bars.

The vålues

0,1'e,...

rå+er

t0

tones {rom

u*hite" t0 "black"

(on Paper),

I+

SHAOING

is not given, the

shading valueg ^depend on

the

nunber ^g

of variables {sections) to

be

plotted.

$ection

i siil

^{then have sha-}

ding

value R0UND(11*(i-I)/g,0). For eranPle,

i{

^g=5,

the de{auIt

cor- responds

to

SHADIt'lG=0,?,4, ?,9.

E.

I.4.

^LEEENO

LE0END ={str ing*}, rthou t-.spac es)

gives

a declaration for the dif{erent

shadings specr{red autonatrcally

or

by $HACIING.

Oefault is

an errPtv

string {r.e.

no

decleration,

but

list ^o{

^shadings

is ^plotted),

^{LEGEND=- neens}

^that all

declaratrons are osritted.

A,1.5

^HEAOER

HEADE R=.lstr in ^g-t,, itl-rou t-sPac es)

gives

a title to-be plotted in the

upper

le{t

corner

o{ the

^prcture

area.

De{au

lt rs

HEADER=r.tyPe}

-D IAGRAl't-0F-i.datai

Since

underlining is

^ignored

in ^plotting,

undenline

the

whole

text

or use

'-' in

^place

o{ a

blank.

HEA0ER=- neans

that

no header

is ^plotted.

l'fore

text

mey be

plotted

by

e

TEXT

speci{ication.

e.1.5.

^TEXT

TEXT={Iist

of text

^nanes}

lists ^the

variouE

text

nanes. Each nenber

o{ this lrst

has

to

be

defr-

ned

in the edit {ietd in the

^forrn

{text

nanp}={text

to

be

plotted},t,y,{size},{x

spacing),.iy ^EPacing) where

xry år€ the

coordinates

(in piatting units) n{ the first

character

o{ the tprt, 4size} (optional} is the letter sire

(de{eult=l), and .ix spacing),{y

^sFacing}

toptional) are

character spacing paraneterg tdefault=8,0).

{text-to-be-plotted}

has

to

be

a Etring without

EPåce5, Since under'-

tlning is

ignored

in plotting"

underline

the

t.lhole

text or

use

'-'in

plece

of a

blank.

?. 1.

?.

^H0I1E

Hfll,lE=<,x coord. )

,.-y

^{coord. )}

specifies the location of the

lo1xer

left cotnpl o{ the

^gråPh 1alth re5-

pect of the current

home

Position of tfie

pen. Coordinates

are

^given rn

p

lotting units.

Default

^i.s H0l'lE=100,?0

for bar

diagrans on

the

^{graphic CRT,}

H0l'lE=0,0 in ^other

^cåEes,

S,l'lustoneni

Statistical

sraphics

in

^SURVO ?6

E0ITOR 16.4.$ge

¹

S.|lustonen!

$tatrstrcal

^graphics

in

SURUI 76

EDIT0R 16.ä.196e I

e.1.15.

LIi'IITS=11,1?,.,.

L ll'lITti=L 1, L? , . . .

(in

PL0T operation

{or natrix

dragrans TYFE=i'IATRIX) sPecr{ies

the

uFper

linits {or the

classes

s{ the

data va}ues ^Ea

that the class i ^{consists o{}

^values

X: L(i-1){Xt=L(i).

tdhen

plotting the ceils

belofiging

to class i t{ilI

^{be shaded}

according

to the ith

shadins speci{red bv ^SHADING.

3,?.

S-catter diågrans PL0T {data) ,':.inage

linei

ohere

tlre

image

IinB

has

tlre forfi "

XXX YYY SSS

I " Plots a

Ecatter diagran

of a

data

set

de{ined bv

a

^0ATA

speci{ication {or the vari-

ables

in the

XXX and YYY columns.

5SS

(optional) is a

nask

for the

narks

of the

sbservations

in

^the

gnaph

(like

nane

o{ the

observatian

or

an

indicator variable).

I (optional)'is _a

_nask

{ot a nissing

value

indicator.

^Charactens

'gpåcg','0'

^ånd

'-' ^åle

^codes

^{{or the}

misEing values,

Flotiing is controlled

by

the following extra sPeci{ications

^typed

in the edit field:

XSCALE, YSCALE, XLABEL, YLABEL, P0INT, LINE; ^GRID

HEADER, TEXT, HOI'IE, 5IZE, XDIV, YDIU, ^FEN, FRAI'IE, CONTOUR' TREND.

PL0T {data) , +.x variEb lei

,'lv

variab le}

nakes

å scatter

diagram

o{ a

data

set

de{ined by a SATA

speci{icetion {or the variables {x

vaniable} and

{v variable).

The

ertra Epecification åre the

^same

es

those

for the

Previoug

{orn

of PL0T

{or scatter

diagrans.

e.2.1.

XSCALE

X$CALE=r,nin. vålue) ,.'?nd value) , r.3rd value) r . . .

" {.tr1sx. value)

specifieE the

scale on

the

X

axis

and

the scale

labels.

I+

^XSCALE

rs not given, scaling

and

labetling rs

automatic' XSCALE=',scale type) , r.nin. veluei , {änd value) , ' ^{. . ,';max.} value}

specifies a

nonlinear scale on

the

X

axis

and

the scele

lebels-

{scale type) is

ane

o{ the alternatives

L0G, L0GIT, PR0BIT, S0F, EXP, ARCTAN.

e.e.e.

YSCALE

Y$f,ALE={rnin. valuei ,':.änd value)

" *l3rd velue} , . , . _, ^{.mår, veluei

specrfies the

scale on

the

Y

axis

and

the

Ecale labels.

If

^YSCALE

^{rs not givefi, scaling}

^and

^{labellrng is}

^autonetic.

YSCALE:r:.gcå

le

type),.lmin. ^va lue), {2nd va luei, . . .,'.nax - va lue)

speci{ies a

nonlinear Ecale on

the

Y

axis

and

the scale

labels.

{scale type) is

one

of the alterneiives

^{L$G, LIGIT, FRIBIT, fiflR,}

EXP, ARCIAN.

2.4.3.

^XLABEL

XLABf L =..str ^{rn 9} .-t|| l-thou t.'Epac es)

gj.ves

a title ior the

X

arrs.pefault rs ^the

^name

^{o{ the}

^varrable.

iLReEL=- neåns

thåt the label rs onitted.

S.lluEtonen!

$tatisti.cal

sraphics

in

^$URVO ?6

EDiTOR 16,e.1981

^g

A;8.4.

^YLABEL

y1-gggl

=.: str r n 9_withou ^t _{_spac} es)

gives

a trtle for the

Y

axrs. Default is the

nane

o{ the

variable.

YLABEL=- neans

that the label is onitted.

2.e,5.

P0iNT P0 IN T=.;c harac t,er )

speci{ies the

Eylnbol

{or the

observation

points in the

diagram.

De{auIt,

is a

small

point.

A nore

flexible

way

o{

narking

is

^provided

by

the

5SS nask on

the

inage

line, 8.P.6.

LINE

LINE=*:.line type)

,.lline

thickness) ,

{tine

label}

.

speEifieE

the line

type

especially in plstting tine series but

can

also

be used

in scatter

diagrans

to join

consecut,ive points.

i+

LINE

is

missing,

the points are not joined

t,ogether uhen

plotting a scatter

diagram.

{Iine typei is

an

integer n=0,1,?,..,,1ä indicating the

brskeness n{

the line

⁽ⁿ⁼⁰ means

a solid line).

.r.line

thickness) (optronall is

an

integer 1,?,3,...

^De{ault=l.

{Iine labeI) (optional) is a string uithout

spåces

to

be plotted as

a lebel at the

end

o{ the

tirne

series.

De{ault=no labet.

4"e.7.

^GRIp

GRID=..X,Y

or

^XY)

draws

stnaight lineE parallel to the x-axis

^(ERID=X)

or the

^y-axis

{ERI0:Y)

or both

^TGRID=XY) ihrough

the points indicaied

by XSCALE (TSCALE) and YSCALE, respectively.

GRIO=,'.x Etep, ystep)

Horks as

the {inst

GRID,

but

uses

the

steps

dxstep),{ystep)

shen

drawrrg

the grid. I{ a.step

^paraneter

is

negative,

orly a snall

tick is

^{draun instead}

o{ a line

segnent.

e.e,8.

coNT0uR

CONT0UR=epsl, eFgä, .

..

BINIJRtl=E {X },E ^(Y ),S(X ), 5(Y ),Corr ^(X,Y )

determineE

ihe

contour

ellipses to

be

piotted

on

levels epsl,epse,...

on

the

basis

of the

tuo-dimensional nornal

distribution

de{ined by a BIN0Ri{

Epecr{ication. I{

^BINORI'I

is

missing,

the

parameters

åre

estim- ated

fron the ptotted _data.

The parameters

epsl,eps?,.., re{er to

the

probåbilities o{

an observation

lyrng inside the ellipse.

Perticularly,

epgl=0 causes

the princlpål

_axes

to

be

plotted.

Exanplel C0NT0UR=0,0.5,0.9,0.99 BINOR|i=O,0,1,1,0.70?

S.l'lustoneni

$tatrstrcal

sraphicE

in

5URU0 76

EDIT0R 16.e.198e

10

e.e.9.

TRENo

TREND=CL,EP',.. (at

_nost

5

parameterE)

deternines

lines parallel to a lineer irend ta

be

plott*d' If

the

trend is

^Y=aX+b and

the residual

variance

rs sfe,

then

the

lrnes t:61+[+f,s and Y=aX+b-Cs

{or

C=f,I,CP,,.

}rill

be

plotted.

For exanplå,

TREND=O causes

the trend itsel{ ts

^be

^draln.

^The

^{trend iE}

estinrated by

the

^(JLS method from

the plotted deta,

However,

i{

^{a BIN0RI'1}

^speci{ica-

tion is

^{given (see}

e.e.g), the trend will

be computed åccslding

to

the correEponding binormal

distribution'

3.?;10. 0ther specificetions

HEADER (see

?,1,5i,

TEXT

^(sEe

ä,1,6),

^l

HOt'lE

^(see

2.1.7),

SIZE

^(see

?.1.8), XOIU

^(see

?.1.9),

Y0Msee ^ä.1.9), PEN

^{(see 2.1.1?),}

FRAt'lE (see 2.1,13).

?,3.

Time series

PL0T ideta)

,.linage line)

nhere

the

irnage

line

has

the

fonn

" TTT YYY 5SS I

^u

plots _the trne

senies YYY

fron a

date

set

defined'bv

a

^0ATA

speci{i- calion.

The

tine axis s,ill

be

labelled

by

texts

aPPearing

in the

^TTT

co lunn.

5$S

toptional) is a

nask

for the

^menks

o{ the

observation Points

in the

graph ⁽

like the

namee

sf the

obtErvations

or the

values

o{

an

in- dicator variable).

I (optisnal) is e

mask

{ar a

missing value

indicetor.

Characters

'gpåce','0'

ånd

'-' ^årå

^codes

^{{or the}

misEing vålueg,

Plottins is controlled

by

the

{ollouring

extra sPeci{rratisns

tvped

in thp edit freld:

^TSTEF, TSCALE, YSCALE, XLABEL, YLABEL, F0INT, LINE, GRID" HEADER, TEXT, HOI.IE, SIZE, XDIV, YDIV, ^F'EN, FRAI'IE, TRENO.

2.3.1.

^TSTEF

TSTEF =.:.Iabe l

lrng

step) , ,imarking step)

specifies the labels

ånd

the

^pornts

to

be narked on

the trne

axis.

{labelling stepi specifres the

^gap between

the

TT'I labeIs end

{rnarking

step} (optional) the

stEP

for the

sma}} marks an

ihe

axis.

e.3.e.

^TSCALE

TSCALE=.Ilist

of

TTT labels)

speci{ies ihe labels to

be

ptotted

on

the tine axis.

^TSCALE can ^be used

joinily

r,rith TSTEP

for additional

^mankings.

S.1'lustaneni

$tatisti.cal

graphics

in

^suRUO ?6

EOITOR 16.e.198e

11

ä,3,ii,

{Jtl-rpr sFecrfrcatinrrs

The f o l lowing specr{tcationE t+lot'k åF those

{or

scåt.ter dragråm$, YSCALT (Eee

e"il,ä),

XLABTL (sep e"ä.i,i

), (de{ault iE

XLAFEL=TIl,1[) YLABTL ⁽ Eee ?.?.4 ) ,

P0INT

^(Eee

f;.e,5),

LINt

^(Eee

?.?.6i, ^(de{ault

rE l-INE=0,1,_)

GRID

^(see

?.?.?),

TRtl'lD ⁽ see ?.?..9 ) _, HEAOER ⁽ see e. 1.5 ) ,

TEXT

⁽ Eee e. 1.6 ) ,

fiil ^i;;-

^{ä.1.1 ),}

SIZI

^iEee

e"1.8i,

XDIU

{see

I.1.9}, YDIU

^(see

e.1,9),

FEltl

^{i see ä, 1. lP i} , F

RAI'lt

i see

L

1. 1:i ) .

gfilollit'e

on nornål _e FL0T .ldata) ,,:image

line)

uhere

the

image

line

has

the forn "

FFF tiSS

" ^plots

^{on nornal probabi-}

lity

^paper

the

FFF

variable

from

a

data

set

de{rned by

a

DATA

speci{r- cation.

The PFP colunn

nust

be Eorted

in

ascendrng order before

plot- tins.

SSS

(optional) is a

nask

{or the

marks

of the

observations

in

the graph,

- FiEtting

nay be

controlled

by

the

sane

extra speci{ications

as

in ^plottins scatter

diagrans ^(see

?.?.)

Note

also the possibility of

^using

the probit

trans{ormation by

the speci{ications

XSCALE and YSCALE (see

ä.?.1-2}.

?.5. Plottinq text

In addition to

^HEADER and TEXT

specifications

^(see

p.1.5-6) _text

nay be

plotted {reely

on

the

^graphic screen by using

the

PL0T oper-

ation in the {orm

PL0T TEXT,

Activatron af

FL[]T TEXT leads

to tlre displayl

COORDINATES:

X=

O,

Y=

^O

PLOTTING TEXT:

SELECT: 0=STARTING

F0INT,

T=ENTER THE TEXT, RETURN(EXEC)=$T0F C;CHARACTER

SIZE,

S=CHARACTER SFACING, F=FEN

0n

the

^graphic screen

å

cupsor

is blinking in the low-Ie{t

corner (coordinates l=S,Y=0) and

it

can be moved

in

^steps

o{ 5 p}otting

units by

the

arroul-headed F-i<eys

or drrectly to a specific point

by pressing

0

and enterrng

the

new coordinates.

The

text to

be

platted is to

be entered and edrted by

{rrst

^pressrng

T then by

typing

and/or

edrtrns the tert

and

finally the tert

rs

plotted

by preEsrns RETURN(EXIC)

Ihe character Erze

(de{ault 1)

and spåcrng (de{.-lult 10"0) nay be

set

by

ll

and

$

respectrvely.

S.flustonen!

Statistical

^qråphics

in

5URV0 7b

EDIT0R 16.e,15äe

1ä

All selections

^made by

the

user

0rll

be dispiaved on

the

normal screen

as

{ollowsl

COOROINATES:

X=

1OO, Y= 4OO PLOTTING TEXT:

SELECTT S=$TARTING

P0INT,

^{T=Ei'ITER TllE TEXT,} RtTURI'IttXE[ i=$T0P C=CHARACTER

5IlE,

$=Ci{ARACTER SFAIING, ^F=FEN

TCICIRDINATES OF THE STARTIHG FOINT

(X,f)?

_1ÖO,4OO O,Ö tex t

I

TeEl åä-ån å?fiå/.$!t*

[I.IA RAI TE R $ I

ZT I

il$RIlfii'ITAL ^SF'AC

INt]-l

^1*

VIRTIIAL SPAI

ING?

^O

PTFN 1

$ince

all the

parameters

[ån

be entered

repeatedly'

several

texts

nay be

plotted

durrng

the

^salne

activation o{

^{FL0T TEXT.} 0bserve

that

PEN

?

nay be used

for

erasing

text

previouslv Plotted.

Return back

to editorral

node takes pls'-e bv RETURN(EXE[).

e"9.

Clrve+ ång

As seen

in P.8.8-9

some

curves, like

contour

elliPses

and lines

parallel to e llnear ttend,

nay be

plotted direetly in

connpction

with scatter

diagrams,

To produce ilorE conplicated ^graphs

o{ analytic

^curves,

a

special fonn

of the

PLOT operation

is

available.

The equetion

o{ the

curve can be

uritten

according

to the

uset's

own

notation either in the

{ornr PL0T Y(X)={unctiontX)

or in ^the

parametric {orm FLoT X (T)={(T),y (T)=g(T)

The

{unctisns

appearing

in tl'e

FL0T operatxon måy

include

symbolic parameters

(pj., rho,

speed) whose values have

to

be gi.ven in

the

form {Farameter}=.lnuneric

valuei

(Pi=:4.1416, rho=0.99, sPeed=?O)

in the edit {ield.

In addition, at nost

two parameters Eån be given as cycling

parameters

in the

form

{paraneter)=({irst value),{last

value),'isteP).

Then

a

one-

or

two-paraneter

fanily o{

curves

will

be

plotted in

the sane coordinate systen.

The

plotting

åreå

is specifred

by

the

XSCALE and YSCALE

specifr*

cations

^(see

?.2.1-2),

The

de{ault is

XSCALE=-10,0,10 YSCALT=-10,0,10.

The

plotting

_rånge

is

^given

in the torn X=';{irst value),':.Iåst

value},

{step). I{..step) is noi ^given, l/100 o{ the plotting

rånge

is

^used

as (step). If the plotting

range

is not given, the total

range ^given bv ^XSCALE

will

be ^used.

In the

second {orm

o{

^PL0T above

the

range

rs

^given

rn the

form

T=.l{irst

value)

,.-last

^value} , ^{r.steP) .}

In

both {orns X and T can be replaced by åny

other letter or

ilord.

S"l{ustonen:

$tatistical

^gr,aphics

in

^5URV0 76

EDIT0R 16.e.1g8e lg

sone simple curve

plottine

schenesi (The

plsts _are in the

appendix,)

FL0T Y tX )=10*Stri{ tX }

HEA0ER=F*trg.lrgnp_ X:l

t-l.."lsr-J:1"d.*it.1

^GRID=XY

PL0T

Y(x)=xtn /

n=1,4,1

HEA0ER=[.pnIgul

j.-iltere.Ft

f

oI

^{F=å,]Fr. ,}

-

^lVo XLABEL=YearE GRID=XY XSIALE=0, 5, 10, 15,ä0',e5, :i0 YSCALT=0, 10, e0, i:0, 40,50,G0, ?0

F =5, 15,

1

^X =0, :;0, 1

FL0T Y (X )=(1 +F' /100)+X

XSCALE=-I0, 0, 10 YSCALE=-IO, 0, 10 XDIV=l, 8,

I

^Y0IV=l, 8,

1

SIZE=500, 500 X=-10, tr 0, .

0e5

HEADER=Y=100/ tX-5 ) / _{X+5 )

/X

^GRI0=XY

FLOT Y (X )=10fi1{X*5i/{X+5}/X

alllrrlrt

HEAOER=Contoqr

ellipses

XSCALE=-IO, 0, 10 YSCALE=-IO, 0, 10 XDIV=l, 8, 1 Y0IU=l, 8,

1

SIZE=500,500 s1=5 s?=3

rho=0.9 t=0,6.?83ä

^GRIO=XY

eps=0.5,0.9,0.1

PL0T X ( t,)=sltEqr ⁽ -ä* log ⁽ 1-epE) )*cost t ),

Y ( t ) =sP* sqr ⁽ -2* log ⁽ l-ep s ) )*sin ^t t+arcsin ⁽ rho ) )

HEADER

XSALE=-3, 0, 3, 6,

I

^YSCALE=0,

0.5 5ll[=]99,

400

a=0,6,0.5

b=3

s=l t=0.3 p=0.?

c=0.39894

(=l/sqrtE*pi))

PLOT Y

(l

)-p*s/s*sr ^{p (} -. 5* t tX-a ) /s ) fP ) + ⁽ 1-p )nc./s*exp ⁽ -.5* ^{( (X-b} )/t)+p )

H E A D E R =F''jU ^a h g 1.,*,t..$ åg+, n,gf ., f L r c-}g p XDIU=l, 8,

j.

_YDIU=l,S,

₁

SIZE=500,500 T=0r

6.1ffil

R=-lCI, 1ö,

L

ind=0, 1,

I

F'LtlT X {T i=Rrcil${ Ti+indxR, Y { T )=R*SIN t T

}+u-ind

irR

As seen

fron

tFre preceding eranples,

the extra speci{ications

of

scatter

diagrans {see

E.?.1- )

can be used

in

curve

plotting,

_too.

Thus

analytic

curves may be

plotted

on ån

eårlier scatter

diagran

or

on

a tisre series plst.

s.l,tustonen!

statistical

^graphics

in

^{$LRUO ?6}

^{EOITOR 16.P.1å8å}

¹⁴

In

curve

plottins

sone

addrtional

specr{rcattong can

also

^be

enp loyed.

8.6.1. FILL,

YFILL, OFILL, IFILL

r

rLl={.dendityi,r.intial value},t{inal

^value}

draws

line

segments

parallel to the

Y

axis

{rsal

points

_on

the

cutve

to the

X

axis in

i,he

interval speci{ied

^bv

r'initial velue}

and

*ifinal value). $e{ault iS ^the

^whole

Flstting

^rånge.

{densitv)

^{(an integer}

1,?,3,..)

^giVes

^the

^{9åp between}

^{the line}

^{segments using}

^the

^curve

plottins

steF

as the unit.

YFILL={densrtv),'linitral value),'ifinal

valuei

,";;;;'';;ir-;;;' j;;;;-;;";i

_on

_*,e

_curve

_{to ihe}

Y exis.

0FllL*{density}

,'iintial

^{value} ,}

^{.{inal

^value}

ir-"i-"it*tnative {orn a{

^{the FILL}

sPecification for'

curves

of

the

{orn

X(T}=f(T),Y(T)=g(T) ^and

ioins the points

on

the

curve

to

origo

for

valueg

qinitial _value) {

^T

_'i {{inal

^value}'

IFlLl={density},.iintiai

^{value}, {fina1. value)}

norlrs as $FILL

bgt ioins the points

^an

the

curve

to the intiai

^point

of the

curve,

ä.6.E.

^ROTATIT]N

R0TATI0N={an9le

in "},{x),';Y;

notates

fhe

^graph by {angle

in "}

^usrng

^{the point} {x}'{y}

as the centen

of rotation. Default is

R0TATI0I'I=0,0,0.

4.6,3. INTEöRAI

^:

INTE0RAL={constant}

{or

curves

o{ the

{orrn

Y(X}*{{X}

^rescales

the

{unctiorr. be{ore

plotting

so

that the integral o{ {tx) is

equal

to {constant},

The range

sf in- tegration is the

^5åne å5

that {or plotting.

^{By using} INTEGRAL=I, {or exåmpler

density

{unctiohg can be

plotted without giving ihe

^cumber-

sone corstants åPPeåring as

coefficients in the

{unction'

e.6.4. Plsttine o{

^an

integral

{unction

PL0T INTEGRAL Y(X)=f(X)

plots the integral

functron

o{ {(x).

^{The range}

{or the integraiion

and

plottrng is

^given

in the forn

^X={lotler

limit),{upper linit}'

{step). If

^these

lirnits are not given,

^x$cALE deternrnes ^then and 1/100

of tlre the

rangE

is

used as {step)

Tlre

extra speci{ication

^{INTEGRAL (Eee}

2.6.3)

can

also

be ^emploved

in

connection

with

^{FL0T INTEGRAL}

thus pernritting plottrng

o{

cunulative densrty

functions o{ probability distributions,

^{or

exEnp

le.

Furthernore, by using YSCALE=PRIB1Tr:.. (scale _values).

..

the

cunulatrve

functions råy

be

plotted

on nornal

probability

Påper.

S.l,lusionent

$tatistica:l

sraphics

in

^$URW ?6

E0ITttR 16.g.1gge $

REFERENCES

I'lustonen,

S.

^(1980),

Inieractive analysis in

^SURV0 ?6, Proceedings in Computetional

Statistics,

Ed.by l,l,|1.'Barritt and 0.tdishart, e53-e59, Fhysica-Uerlas, hlien.

l{ustonen,

S.

^(1980), SURU0 ?5 EDIT0R,

a

^new

toal {or interactive stat- i.stical

courputing,

text

and data nenagenent, Reseårch Report No.

19,

Dept.o{

Statrstics,

Univer'sity

o{

Helsinki,

l'lugtonen,

S.

^(1981), SURU0 ?6 EDITBR,

a

nert

tool {or interactive stat-

istical

computrng,

text

and data nanagenent, ^(RELEA$E

2),

Re-

search Report No.24,

0ept.of Statistics,

Unrversrty o+ Helsinkr, llustonen,

S.

^(1981), SURVU T6 tDIT0R, Estrrnation

o{

regression nodels,

Research Report No.ä9, Dept.

of Statistics, University

o{

He

lsrnki

flustonen,

S.

^(1981),

Statistical

conputing

nith a text editor,

Conpu-

tational Statlstics,

ed.by Herbert &ining and Feter Nåeve, 3e?-348,

Helter

de

Gruyter, Berlin,

L

=,3

4 ::'

t=D

7a Lo9

J-r.

.Le .1-3

l-4r-5 i.6i-7 L€la9 eoe1 e&

a3

S.l{ustCInpn;

StatrEtrral gråpiirrs in

^{SURU0 16 [DIIUR 16.} e " 198ä 1"6 NOTE

The PL0T operation has nou, been extended

to

^produce

three

dinren-

sional

^graphs

of analytic

^gur{aces

in central proiection.

^{The actual}

graph

r,rill consist o{ a proiection

on

a

Plane orthogonai

to the iine fron

EYE

to origo.

The sur{ace can be defrned

in the

{orn

PLST

Z(X,Y)*f,unctisntX'Y)

^nr

PLOT l( (T, U)={(T, U),Y (T, 1J)=9 (T, U), Z(T' U)=h(T' U).

The space cutves

characterizing the

surface

are

selected by CURUES

speciflcations.

^The graPh can be saved

step

bv steP

in

the

edit {ield

^{by using}

^a

^PL0TLINE

specification

and

it

nåv bp rePlotted by

a

PLOT FILE operation.

In replstting the speci{ication

EDIT mav be used

{or editing sf

lhe graph. The

plot wrll

then åppe€r steP by step and

th€

user nay

edit the plotting

_steps

via the

keyboard.

l- suRuo ?F EDIT|fR (C)19?9 sl't{ustoi€n (eloxl.oo)

*$f!6

E1p2

* *

*PLoT z<X.Y)-?rtxP(

*

(-X*X-Y*Y, /? ^>

:*

*X:-5,5, _{- P} lbY:-5-

=. -?

FLgTL INE =B

*X -C ^URIIE !i'=-5 , 5 *o - 5

*Y _-CURiUIE S=-5, 5, - 5

*xD IV=,O, a, o ^YD IV,=O, a, O SIZEry$lL, $,LL FRAHI*O

*PLoT FtLE,ExPa.B- / HoHE-,t'4oo

e u,ase,-råg o.-al-e D'-3.-t- u'-4'-? t'-1r-l- u'-g'-? u'-4'-a u'-4'- ru'-3'-eu'_4.-LU.-4'-aU.-a._au'-4.-eU.-3'-?D._4._1D'-4._eD

* D,-4.-e o,-a,-i o'-+'-e D' -4,-e 9.-1 '-1 9'-4'-e D'-"1 '-e D'-q'-? ^Ö + D,_4._e o._o._ä o.-o.-t- D,-ä.-e D'-4'-a D'-4.-e o,-5i*e o,-4.*e ^D

* O.-a,-a

*..,

o.-5.:? D'-4'-a D'-5'-e -tc-

* ( P 1ot-i-j"ng *tcP* -f ttr edit'Lng, '

x l.ridd-n l.inaa åra Fanovcd aemiruton-ticållv)

f

$,l'iustonen

I

Statrstica

I

^gråFhicE

in

^SURUCI ?6 tD I TfiR 16"1" 19ää 1?

{ll[Illå:

^{Graphs senerated}

^trith

^{SUftU0 76 EDIT0R}

lhir

appendir presents

the

usage

o{ the

FLUT operation through examples.

In

eaclr

o{ the {ollowing exhibits the

^graph

is

^{coupled witlr}

an

extract fron the

edj"t

{ield

completelv descr'ibing thB ^FLUT oper- etrorrs

acirvated

arrd

the

^neceEsary

attributes.

Thus

a1l

these

plotting

schenes nay be

easrly

r'egenerated by 5URV0 76 EOITOR on an }Jang 2Q00

inEtallation with

thE graphic ^CRT

ptotter

ä?8P. Furthernore,

the

5URV0

?6 EDITOR DEI'1fiNSTRATI0H

pletter _carries

these

plotting

schenes

(edit {rles

FL0T1,

FLOTI,...i alnost

comPletely.

l'lany

of the

exanples

are reiated to staiisticel

^graPhics

^to

^sho$,

how

pictures

can be used as an

efficient t,ooi in

varis'us research and

teaching

srtuatrons. 0{ rourse,

an immense amount

o{

var'iants

rsuld

^be derived

{ron

some basic ^gr'apl's

or

ås cornbinations

sf

standard

alterna- tives.

Therefore

this

^aFpendix cannot be complete,

but

includeE only sone

typical statistical ^plots.

^The reader having åccess

ts

SURV0 ?6 EDIT0R can

pasily

generate nor'e exåmpies by

nodifying the existing

ones and save

his solutions for

subseguent

applrcatron. In {act,

the

PLOT operat,rsn has ^{nov, beEn} succeg{ully enployed

{ron

February 1981 on

by several SURU0 ?6 users

Hithout wrrtten

docunenl,s on

the

basis"

o{

a

rather restricted

sanple

o{

exanPles.

Also sone

purely nathenaiical

curves and

{anilies of

cutves serve ås

illustration of

hou

to

use ^$URU0 ?6 EDIT0R

in non-statistical

apPlica-

tions.

The appendix

{inally

contains nore conplicated

'artistic' ^plots

displaying the

^pouer

of the 'graphical

language'.

It is inportant to

note

that

some

of the

dynamic aspects, tlhich ap- pgår on

the

screen and are

nost interestins in

^måny cå5e5, cannot be

detected

fren the final

output on PaPer. Nevertheless ^{we hoPe}

that

even these ready-made graphs can give an impression

of ihe passibili-

ties

available.

S.i'tustonen;

Statrstrcal

gråFlircs

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