THE MANUAL

A l i t t l e STATI STI CS on ATARI ST' s


A col l ect i on of st at i st i cal gr aphi cs and cal cul at i ons
Wr i t t en i n GFA−BASI C
c Thomas Gr ב¶t zmacher , 1 988

V 1 . 3 engl .

Cont ent : Page

I nt r oduct i on 2

1 " Desk" dr op−down menu 4

1 . 1 " St at i st i cs" 4

1 . 2 ACCESSORI ES 4

2 " Fi l e" dr op−down menu 5

2. 1 " Change PRN t o SEQ−f i l e" 5

2. 2 " Load SEQ−f i l e" 7

2. 3 " Make SEQ−f i l e" 7

2. 4 " Del et e f i l e" 8

3 " Cor r el at . " dr op−down menu 8

3. 1 " Cal c. cor r el at i on" 8

3. 2 " Rest or e scr een" 9

3. 3 " Pr i nt cor r el at i on" 9

4 " Mor e" dr op−down menu 1 0

4. 1 " Di sc/f i l e i nf o" 1 0

4. 2 " Rest or e gr aph" 1 0

4. 3 " Gr aphi cs st i l e" 1 1

4. 4 " Qui t " 1 1

5 " Gr aphi cs" dr op−down menu 1 2

5. 1 " Di st r i but i on" 1 3

5. 1 . 1 " 2−D uni var i at e" 1 3

5. 1 . 2 " 3−D bi var i at e" 1 4

5. 2 " St andar di zed" 1 5

5. 2. 1 " X−Y pl ot " 1 5

5. 2. 2 " Regr essi on" 1 6

5. 3 " l ogar i t hmi c" /" Log−pl ot " 1 7

5. 4 " Tr i angel " /" Tr i −pl ot " 1 8

5. 5 " sur f ace pl ot " 1 9

5. 6 " cl ust er " 22

6 " Out put " dr op−down menu 23

6. 1 " Har dcopy" 23

6. 2 " Save Degas" 23

6. 3 " Save Doodl e" 23

Hel l o ever ybody i n t he wor l d deal i ng wi t h st at i st i cal pr obl ems
and needi ng some gr aphi cs t o make f act s mor e i mpr essi ve and easy
t o under st and.

Her e i t i s:

The l i t t l e gr aphi c hel p you' ve needed whi l e VI P ( t he sl owest

spr eadsheet f or t he ST' s) l eaves you wi t h poor ef f ect s.

Anyhow, t hank you f or your i nt er est i n my pr ogr am.

Let me gi ve you some gener al i nf or mat i on concer ni ng t he pr ogr am' s

abi l i t i es:

I t r uns ( what I know) on al l ATARI ST ver si ons

I t can handl e 20 var i abl es wi t h 1 000 val ues each

I t of f er s var i ous gr aphi cs ( t hat can each be modi f i ed)

I t has an i nt er f ace t o DOODLE or DEGAS t o make your gr aphi c per f ect

Cor r el at i on−mat r i ces can be saved as ASCI I −f i l e

I t ' s easy t o use and l i kes t he mouse

A l i t t l e hi st or y:

Bei ng a geol ogi st and wor ki ng i n a geochemi cal l ab I wr ot e my
t hesi s on heavy met al di st r i but i on i n t he aquat i c syst em of smal -
l er r i ver −syst ems. I nvest i gat i ons wer e done concer ni ng sedi -
ment s, wat er and suspended mat t er , l eadi ng t o met al concent r at i -
ons f r om r anges of ppb ( par t s per bi l l i on, mi l l i gr ams per t on) i n
t he wat er t o somet i mes per cent i n t he suspended mat er i al ( ever

hear d of adsor pt i on−pr ocesses?) . So dat a coul d onl y be compar ed
i n a usef ul l manner af t er bei ng st andar di zed. Thi s was done be
t he common f or mul a:

Z = ( val ue − mean ) / st andar d−devi at i on

The second pr obl em was seper at i ng t he ext r emel y di f f er ent val ues
of one var i abl e f r om t he maj or i t y of t he popul at i on. I suggest
t hat you can f ol l ow a l i t t l e bi t . Ext r eme−val ues i n a popul at i on
can ( and act ual l y do) di st ur b cor r el at i ve i nt er dependenci es. So
hi gh cor r el at i on coef f i ci ent s can be wr ong, because t hey r el y on

such ext r eme−val ues. One way t o r ej ect such val ues whi l e cal cul a-
t i ng cor r el at i on coef f i ci ent s i s t o set l i mi t s t o t he popul at i -

Al l t he st andar di zat i on i s done whi l e l oadi ng t he dat a−f i l e, t he

l i mi t s ( r ef er r i ng t o t he expl anat i on gi ven above) ar e def i ned by
you. The f ol l owi ng t wo f i gur es mi ght gi ve you an i mpr essi on of
what I ' m t al ki ng about . Fi g. 1 shows t he nor mal l y di st r i but ed
popul at i on and some l i mi t s i n per cent and st andar d−devi at i on.

Fi g. 1 :

You wi l l get a sl i ght l y bet t er i dea of how ext eme−val ues i n a

coupl e of sampl es mi ght di st ur b t he cor r el at i ve i nt er dependen-
ci es ( and t hus t he cor r el at i on− coef f i ci ent ) by l ooki ng at t he
next f i gur e ( 2) . Thi s exampl e i s r at her i deal i st i c but deal i ng
wi t h l ab−dat a, you wi l l somet i mes have even such st r ong ef f ect s.

val ues

Ok, as a shor t i nt r oduct i on I t hi nk t hi s i s enough, mor e mi ght be
t oo much and you wi l l pr obabl y get scar ed of t hat l i t t l e st at i -
st i cs t hi s pr ogr am of f er s. The f ol l owi ng pages wi l l gi ve you st ep
by st ep al l t he i nf or mat i on you need f or each dr op−down menu and

f or al l possi bi l i t i es t o change gr aphi cs i n t he way you want t hem
( you shoul d send me your suggest i ons f or i mpr ovement s) .

_______________________________________________________________

_______________________________________________________________

Thi s pr ogr am di d make a l ot of wor k ( and st i l l does) , i f you have
ol der ver si ons I wi l l send you t he newest when r ecei vi ng a f l oppy
and a st amped envel ope. Thi s manual pl us pr ogr am wi l l char ge you
wi t h 30. − Mar ks ( about 1 0 pounds or 20 $) , when you or der i t pl ea-
se i nser t a f l oppy wi t h t he pr ogr am' s ver si on you have, i f i t

i sn' t t he l ast updat e, I wi l l copy i t t o t he di sc and send al l
back t o you. I f you don' t have t he pr ogr am yet , t hi s wi l l be t he
r i ght way t o get i t . Pl ease r ecogni ze t hat t hi s pr ogr am i sn' t
publ i c domai n any mor e, so be honest and don' t spr ead i t wi t hout
payi ng.

_______________________________________________________________

Thomas Gr ב¶t zmacher

Von Br andi s St r . 1 2

51 00 AACHEN

Feder al Republ i c of Ger may

_______________________________________________________________

_______________________________________________________________

1 " Desk" dr op−down menu

1 . 1 " St at i st i cs"

Cl i cki ng t o t hi s you get a t i ny copyr i ght −message, t hat has a
bui l t −i n hel p t ext ( j ust t wo pages gener al i nf or mat i on) . Bewar e
of t he r egi st r ed number of your pr ogr am−ver si on, t hi s pr ogr am
i s' nt publ i c domai n any mor e, but al most f r ee of char ge ( be

honest ) .

1 . 2 ACCESSORI ES

The l at est ver si on al l ows you t o use t hese l i t t l e hel per s whi l e
r unni ng t he STATI STI CS pr ogr am. Unf or t unat el y t he GFA−BASI C does

not suppor t t he accessor i es ver y wel l , ever yt i me you use one t he
backgr ound of t he deskt op ( i n t he wel l known gr ey) wi l l appear
r i ght wher e t he accessor y was bef or e. That ' s why you can use t wo
r ef r esh−r out i nes t o r est or e t he ol d scr een ( I ' m sor r y f or t hat ,
but I can' t avoi d i t ). One r est or es a cor r el at i on−mat r i x ( i f you

have cal cul at ed i t bef or e) , t he ot her r edr aws t he l ast gr aphi c
( or any ot her scr een) . Anyway, wi t h t hi s l i t t l e t r i ck accessor i es
ar e usabl e.

2 " Fi l e" dr op−down menu

2. 1 " Change PRN t o SEQ−f i l e"

One of t he f i r st pr obl ems was t o get an i dea of how number s and
st r i ngs can be r ead i nt o a pr ogr am. A spr eadsheet ( l i ke VI P−PRO-

FESSI ONEL) has t he opt i on t o save par t s of a spr eadsheet i n ASCI I
t o di sc, and spr eadsheet s of f er i n my opi ni on t he best way t o
l i st , mani pul at e, cal cul at e and sor t dat as of any ki nd. That ' s
wher e t hi s r out i ne st ar t s. You use a spr eadsheet t o gener at e your
ASCI I dat a−f i l es or any edi t or ( i . e. WORDPLUS wi t h WP OFF) . By t he

way, VI P ( r ef er t o LOTUS 1 23 manual s) saves i n ASCI I , when you t ake
t hi s way: / Pr i nt Fi l e Range ( opt i ons possi bl e) Go.

Ther e ar e onl y f ew t hi ngs t o keep i n mi nd when gener at i ng a
dat a−sheet :

− Var i abl es' names must not be l onger t han f i ve char act er s

and no BLANCS ar e al l owed i n t hem ( t hat ' s because t he r out i ne
separ at es t he names ( and t he dat a) by means of t he bl ancs
bet ween t hem) . " Al 2O3" i s r i ght , but " Mn O2" i s wr ong, and wi l l
be i nt er pr et ed as " Mn" and " O2" , l eadi ng t o wr ong var −names f or
al l f ol l owi ng var i abl es.

− Var −names and dat a must be seper at ed by at l east ONE bl anc

Her e' s a exampl e f or a cor r ect dat a sheet :

Mn Pb Zn Dept h

1 25 30 1 000 256

25 5 1 200 1 000

5 0. 5 1 700 2000

Negat i ve val ues somet i mes l ead t o pr ogr am−cr ashs because of un-
al l owed cal cul at i ons ( i . e. l og of a negat i ve val ue) . The mor e i m-

por t ant f act i s t hat t hi s pr ogr am does NOT l i ke mi ssi ng val ues,
t hey def i ni t i vl y l ead t o wr ong r esul t s. You must i nser t a some-

Now what does t hi s r out i ne act ual l y do?

I t t r ansf or ms t he dat a−sheet ( as descr i bed above ) i nt o a sequen-
t i al l y st r uct ur ed f i l e , so when wor ki ng wi t h t he pr ogr am a once

t r ansf or med f i l e wi l l l oad f ast er . The new f i l e has t hi s st r uc-
t ur e:

3 ( No. of var i abl es ( st ar t i ng at 0) )

2 ( No. of val ues ( st ar t i ng at 0) )

Mn ( f i r st var −name)

1 25

25

5

Pb

30

5

0. 5

Zn

1 000

1 200 and so on . . . got i t ?

Usi ng an edi t or t o wr i t e your dat a−f i l es you shoul d ment i on t hat

t he End Of Fi l e ( EOF) must f ol l ow di r ect l y under t he l ast dat a−
l i ne. I f you l eave some empt y l i nes beneat h your dat a, t he pr o-
gr am wi l l t ake t hi s as zer o ent r i es t hus l eadi ng t o a wr ong num-
ber of dat a−l i nes. Some user s r epor t ed t r oubl es when af t er t he
l ast var i bl es' name t her e i s no f ol l owi ng bl anc, t hi s bug has

been ki l l ed i n ver si on 1 . 31 E wi t h r egi st r at i on−no. " 88−05−. . . " .

As you mi ght see now, t he cr eat i on of t he pur e dat a−f i l e i s t he
most i mpor t ant st ep when usi ng t hi s pr ogr am. The savest way t o go
i s usi ng t he bui l t −i n r out i ne f or f i l e−cr eat i on, al t hough you
t hen mi ss a f i l e i n a f or m you can use i n your t ext s. The second

savest and i n my opi ni on t he best way i s t o use a speadsheet ( I
mean VI P−PROFESSI ONAL) t o gener at e a dat a−f i l e.

2. 2 " Load SEQ−f i l e"

The f i l e cr eat ed by t he r out i ne descr i bed above wi l l be l oaded by
t hi s opt i on. You get a l i t t l e gr aphi c t o shor t en t he t i me ( whi l e
si t t i ng i n f r ont of t he scr een and wai t i ng) , t he var −names wi l l
be di spl ayed whi l e l oadi ng. Af t er l oadi ng al l dat a ar e r ecal cul a-
t ed i nt o a st andar di zed val ue ( r emember t he i nt r oduct i on) . Af t er

al l you get t he t i me needed f or cal cul at i on and you can st ar t yo-
ur wor k. Ver si on l at er t han " 88−05−. . . " gi ves you a cal cul at i on
of t he memor y used by your f i l e.

2. 3 " Make SEQ−f i l e"

Somet i mes onl y smal l dat a−sheet s ar e necessar y and you don' t want
t o l eave t he pr ogr am, t hi s opt i on of f er s you a possi bi l i t y t o

gener at e your dat a−f i l e . You ar e asked f or t he number of var i a-
bl es you want t o ent er and f or t he number of val ues f or each
var i abl e. Then you get t o t he I NPUT−SCREEN. Cur sor movement s ar e
poor l y suppor t ed ( sor r y), but i t does t he j ob. Af t er you have
ent er ed al l dat a you ar e asked f or t he f i l e' s name, under whi ch

you want t o save your dat a. Thi s f i l e i s " r eady t o use" by t he
" Load SEQ−f i l e" r out i ne ( r ef er 2. 2) .

2. 4 " Del et e f i l e"

Somet i mes you may wi sh t o del et e a f i l e ( i . e. a ASCI I −dat a−sheet
af t er t r ansf or mat i on, or a saved scr een you don' t l i ke anymor e) .
J ust cl i ck t hi s opt i on, a f i l esel ect −box wi l l appear and you can
choose t he f i l e you want t o di sappear . Af t er sel ect i on you ar e
asked ( j ust f or bei ng sur e) i f you ar e consci ous of what you ar e

goi ng t o do, and t hen t he f i l e i s gone.

3 " Cor r el at . " dr op−down menu ( Cor r el at i on−coef f i ci ent )

3. 1 " Cal c. cor r el at i on"

Thi s opt i on cal cul at es a mat r i x of cor r el at i on−coef f i ci ent s f or
al l var i abl es you use i n your l oaded f i l e ( i n t he exampl e gi ven
above I ' ve cal l ed t hem ONE, TWO, THREE, et c.

I n t he r i ght −hand upper par t you get i nf or mat i on of t he number of
dat a t hat f i t i n t he l i mi t s you di d set bef or e ( r emember what

t hese l i mi t s ar e good f or , t hey r ej ect " ext r eme" val ues) . The
coef f i ci ent cal cul at ed i s t he so cal l ed pr oduct −sum−coef f i ci ent ,
a cal cul at i on of t he RANK−cor r el at i on−coef f i ci ent ( SPEARMAN' s)
i s not j et i mpl ement ed, but wi l l f ol l ow soon.

The ext r ema−l i mi t s you use t o speci f y t he bor der s of your " val i d"

popul at i on can be set ( and changed) i n t he " MORE" opt i on usi ng
t he " Gr aphi cs st i l e" ent r y, f or mor e i nf or mat i on r ef er t o 4. 3
( Gr aphi cs st i l e) .

3. 2 " Rest or e scr een"

Her e' s t he opt i on t hat r est or es t he scr een af t er you have used a
accessor y or i f you j ust want t o swi t ch f r om t he gr aphi c t o t he
l ast cal cul at ed cor r el at i on ( wi t hout cal cul at i ng i t once agai n) .

3. 3 " Pr i nt cor r el at i on"

You can send t he cor r el at i on−mat r i x t o a pr i nt er ( t he " ESC−
sequences" ar e i mpl ement ed f or EPSON pr i nt er ) , or you mi ght save

i t on di sc by choosi ng t he opt i on " Fi l e" . The scr een i s saved as
ASCI I −f i l e t o t he di sc you speci f y and you mi ght r ead i t i nt o any
wor dpr ocessi ng−syst em. That ' s what you shoul d do, when you use a
di f f er ent pr i nt er or have mor e t han 1 0 var i abl es, you j ust use
t he pr i nt er −dr i ver of your wor dpr ocessi ng−syst em.

4 " Mor e" dr op−down menu

You mi ght wonder why I j ump over t o t he l ast dr op−down menu, but

her e you f i nd one of t he most i mpor t ant opt i ons t o change t he
gr aphi cs t he way you want t hem ΓêÆΓêÆא† " Gr aphi cs st i l e" .

====א†

but al t hough swi t chi ng t o t he l ast dr op−down menu l et me descr i be
t hem i n t hei r or der :

4. 1 " Di sc/f i l e i nf o"

Thi s opt i on gi ves you i nf or mat i on about t he cur r ent f i l e you wor k
on and al so about al l ot her f i l es i n your home−di r ect or y endi ng
wi t h " SEQ" ( r emember , t hese f i l es ar e used by t hi s pr ogr am) . You

get f r ee memor y and di sc space t oo.

4. 2 " Rest or e gr aph"

As t he opt i on r est or e sr een i n t he " Cor r el at i on" dr op−down menu
you can use t hi s opt i on t o r est or e t he l ast gr aphi c−scr een.
That ' s usef ul l i f you cal l ed an accessor y or i f you want t o
swi t ch t o ( and back wi t h t hi s opt i on) t he l ast cal cul at ed cor r e-
l at i on.

4. 3 " Gr aphi cs st i l e"

Thi s i s t he mai n opt i on t o change gr aphi c set t i ngs, al l by mouse
and on ONE scr een. Ever y set t i ng you change can be saved t o di sc
by t he opt i on " SAVE" . " LOAD" on t he ot her hand get s t he set t i ngs

back f r om di sc. You may choose any name you want ( endi ng wi t h
" . PAR" ) , i f you cal l t he f i l e, t hat must be i n t he home di r ect or y
of t hi s pr ogr am, " DEFAULT. PAR" i t i s l oaded when st ar t i ng t he
pr ogr am.

The speci f i c opt i ons f or each gr aphi c ( some set t i ngs ar e val ue
f or mor e t han one gr aphi c) wi l l be descr i bed i n connect i on wi t h
t he gr aphi c i t sel f .

One gener al set t i ng i s t o choose wet her sampl e−number s shal l be
di spl ayed or not .

4. 4 " Qui t "
Thi s opt i on i s t he one you
need af t er some t i me of ST

sessi on.
I t l eaves t he pr ogr am

wi t hout any savi ng.

5 " Gr aphi cs" dr op−down menu

Thi s dr op−down menu f i nal l y i s
t he one t hat you need t o choose
t he di f f er ent gr aphi cs. The si n-
gl e opt i ons i n t hi s menu ar e onl y

sel ect abl e i f a dat a f i l e i s l oa-
ded ( l ogi c, i sn' t i t ) . The f ol l o-
wi ng t ext wi l l gi ve you a det ai -
l ed descr i pt i on of ever y si ngl e
menu−ent r y and of t he possi bl e
changi ngs you can make by usi ng

t he " Gr aphi cs st i l e" scr een,
descr i bed above.

Ever yt i me you sel ect one opt i on you wi l l be asked f or t he adequa-
t e var i abl es. Thi s i s done by a si mpl e wor ki ng sel ect r out i ne,

you j ust cl i ck t o t he var i abl es you wi sh. A smal l l ogi cal t est i s
i ncl uded t o pr event nonsense ( i . e. cor r el at i on of a var i abl e wi t h
i t sel f ) .

I f you sel ect ed somet hi ng you don' t wi sh any mor e, cl i ck t o t he
" NO" but t on, t hen t he sel ect i on i s done once agai n. Ther e i s no
way out of a gr aphi c i f i t once i s sel ect ed, you al ways have t o
r un t hr ough t he ent i r e r out i ne unt i l t he dr op−down menu head
( " Gr aphi cs" ) i sn' t i nver t ed any mor e.

5. 1 " Di st r i but i on"

5. 1 . 1 " 2−D uni var i at e"

Thi s opt i on i nvokes a gr aphi c t hat di spl ays a bar −di agr am st i l ed
di st r ubut i on. The separ at i on i s al ways 1 /1 0t h of one st andar d−
devi at i on. That means you get a di st r i but i on pat t er n based on t he
STANDARDI ZED dat a, what makes i t easi er t o compar e popul at i ons of

di f f er ent uni t s.

Usi ng t he " Gr aphi cs st i l e" opt i on ( r ef . 4. 3) you can change t hi s
gr aphi c i n di f f er ent ways. Changi ng t he " EXTREMA−LI MI TS" wi l l
change t he x−axi s scal e ( i n uni t s of one st andar d−devi at i on) . The
second set t i ng " pl ot −scal e" makes i t possi bl e t o change t he si ze
of t he gr aphi c f r om t he f ul l −scr een di spl ay t o a smal l er squar e−
si zed st i l e. The next opt i on ( scal e) makes t he x−axi s' uni t s

swi t ch f r om " SYMBOLS" ( what you see above) t o " NUMERI CAL" st i l e,
by r epl aci ng t he symbol s wi t h t he val ues t hey r epr esent . The l ast
opt i on gi ves you t he possi bi l i t y t o choose t he " pat t er n" of t he
bar s i n t he di agr am. St r i pes, bl ack and none can be choosen.

5. 1 . 2 " 3−D bi var i at e"

Thi s opt i on gi ves you a 3 D−di st r i but i on gr aphi c of TWO var i a-
bl es. I t i s a way bet ween t he pur e 2 D di st r i but i on descr i bed

above and t he st andar di zed XY−pl ot t hat wi l l be di scussed bel ow.
I t i s r at her f i xed i n i t s f or m, al ways di spl ayi ng t he sect i on
f r om −3 st d t o +3 st d ( st d=st andar d−devi at i on) . You can choose
t he i nt er sect i ons i n bet ween one st d, di -
vi di ng i t i nt o 2 ( 1 /2) , 3 ( 1 /3) or 4 ( 1 /4)
st eps. The ot her t hi ng you can change i s t o

di spl ay bl anc col umns or have some pat t er n
wi t hi n. Agai n t hese opt i ons ar e avai l i abl e
i n t he " Gr aphi cs st i l e" scr een. The co-
l umns hi ght can be changed i n t hr ee st eps
i f you desi r e.

5. 2 " st andar di zed"

5. 2. 1 " X−Y pl ot "

Don' t be conf used by al l t he l i nes i n t he pl ot above. As you see

t hi s r out i ne gi ves you a st andar di zed X−Y−pl ot of your dat a. The
sampl enumber s r epr esent t he l i nes i n your or i gi nal dat a−f i l e.
Ther e ar e a l ot of possi bl e changi ngs concer ni ng t hi s pl ot :
HERE

The changi ng of t he ext r ema−l i mi t changes

t he scal e of X and Y axi s

The pl ot can be FULLSCREEN or SQUARE, t hi s

opt i on i s t he same as t he one f or t he 2 D
di st r i but i on gr aphi c. SCALE /SYMBOLS i n-
vokes t he gr aphi c you see above, i f you
sel ect NUMERI CAL a non−st andar di zed pl ot
wi l l be di spl ayed ( i n ver si ons l at er t han

" 88−05−. . . " ) . Ref er t o appendi x 1 ( V1 . 31 E)
about t hi s new f eat ur e.

Er r or bar s can be di spl ayed f or X and Y val ues ( YES) or j ust f or
t he X axi s ( X−Ax. ) . I f you sel ect " NO" t hey ar e not di spl ayed.
Er r or bar s ar e cal cul at ed as t he di st ance of a val ue f r om t he l i -
near −r egr essi on of t he X ( or Y−val ue) .

5. 2. 2 " Regr essi on"

I f you see a X−Y pl ot on your scr een i t i s possi bl e t o use t hi s
opt i on. I t of f er s sever al possi bl e r egr essi ons and di spl ays t he
equat i on of t he r egr essi on chosen.

I n det ai l you can choose:

− l i near r egr essi on

As t her e ar e t wo possi bl e r egr essi on−l i nes you may
choose whi ch one shal l be di spl ayed, " bot h" i s ano-

t her opt i on. You have t o t hi nk of t wo di f f er ent di -
r ect i ons you l ook at t he dat a, so t wo r egr essi ons
can be seen. The angl e bet ween t he t wo r egr essi on−
l i nes i s di r ect l y r epr esent i ng t he cor r el at i on, r =1
means t hat bot h l i nes ar e congr uent . I f a si ngl e r e-
gr essi on i s choosen t he equat i on wi l l be di spl ayed.

− nonl i near e r egr essi on

You have t he oppor t uni t y t o sel ect a equat i on of se-
cond or t hi r d power , t he equat i on wi l l be di spl ayed
t oo. Thi s opt i on somet i mes does' nt show t he r esul t
you expext al t hough t he cal cul at i ons ar e r i ght .

I t ' s j ust because t he r egr essi on i sn' t f i t t i ng.

What you shoul d do i s t o cal l al l possi bl e r egr essi ons and sel ect
t he best f i t t i ng one. Then agai n sel ect t he X−Y pl ot and onl y
cal l t he best r egr essi on. I n t hi s way you get t he best r esul t .

Usi ng t he t wo di f f er ent XY−PLOTs ( non/st andar di zed) you get
equat i ons cal cul at ed upon t he dat a you use, so t he equat i on of
t he st ar dar di zed dat a di f f er s f r om t he one of t he r aw−dat a. Al -
t hough bot h r egr essi ons descr i be t he SAME st ochast i c behavi our
and mi ght l ook ver y si mi l ar t o you, don' t f or get t he base of t he

cal cul at i on ( r aw−dat a or st andar di zed dat a) .

5. 3 " l ogar i t hmi c" / " Log−pl ot "

Thi s opt i on i nvokes a l ogar i t hmi c X−Y pl ot . You can change f r om
X−Y mode t o t he di spl ay of a sum−cur ve, what i s somet i mes usef ul
t o i ndi cat e abr upt changes i n a var i abl es st ochast i c behavi our .
The gr i d at t he exponent −bor der s can be set or di sabl ed.

Anot her t hi ng you mi ght choose i s a mi xed l ogar i t hmi c/l i near di s-
pl ay, pl ease r ecogni ze t hat onl y t he Y−axi s can be l i near , you
al ways sel ect f i r st t he X−var i abl e and second t he Y−one.

To si mpl i f y t he pl ot t i ng a aut o−scal e f unct i on i s i mpl ement ed,

5. 4 " Tr i angel " / " Tr i −pl ot "

Thi s opt i on i nvokes a gr aphi c t hat gi ves you an i dea of t he r el a-
t i on of THREE var i abl es i n per cent . You have t o r ead such a di a-

gr am l i ke t hi s:

The cor ner of t hi s t r i angl e r epr esent s 1 00% of t he var i abl e of
t hi s cor ner . That means i f t he f i r st chosen var i abl e ( t he f i r st
i s t he l ower l ef t edge, t he second t he l ower r i ght edge and t he
t hi r d on t he t op) i s i . e. 56. 9, t he second zer o and t he t hi r d al so

zer o, t he poi nt l i es r i ght i n t he l ef t l ower edge. So i f al l
t hr ee val ues ar e t he same ( i . e. 230, 230, 230) t he poi nt wi l l l i e
i n t he mi ddl e of t he t r i angel . Thi s pl ot −st i l e i s of t en used t o
descr i be t he mi xi ng and change of t hr ee const i t uent s of i . e. a
mi ner al .

Because a f ul l t r i angl e ( cover i ng t he f ul l 1 00%) i s not so use-
f ul l when l ooki ng f or onl y smal l changes, you can change t he

A l ast f eat ur e i s t he si ze of t he mar ker s, t hat can be changed i n

t hr ee st eps. I f you want sampl e−no. i n your t r i angl e, you shoul d
choose t he mi ddl e or l ar gest mar ker s.

5. 5 " sur f ace−pl ot "

A f i l e l i ke t hi s a b c d e

0 0 0 0 0

0 1 1 1 0

1 2 4 2 1

0 1 1 1 0

0 0 0 0 0
wi l l gener at e a sur f ace l i ke t hi s:

Thi nk a l i t t l e about i t , i t ' s r at her si mpl e.

Ther e ar e many opt i ons t o change t hi s gr aphi c:

I t i s possi bl e t o swi t ch f r om t he r aw−dat a t o
st andar di zed val ues ( DATA : RAW / STAND. ) . The
scal i ng i n Z−di r ect i on can be changed usi ng t he

opt i on AUTO SCALE ( Yes / No) .

I f you sel ect SI ZE : MAXI you get a f ul l scr een
di spl ay , when chosi ng t he MANU−opt i on, you ar e
asked f or t he hor i zont al and ver t i cal si ze of
t he pl ot , t he best way i s t o t r y i t .

The FRAME but t on swi t ches t he pl ot ' s f r ame ON

and OFF. I f a f r ame i s di spl ayed, t he BASE ( a
gr i d) can be added.

The PATTERN of t he sur f ace can be changed t o whi t e ( =no pat t er n) .
When a f r ame i s act i vat ed you can i nvoke t he scal i ng, t hat of f er s

you t he opt i ons NO ( no scal e at al l ) , YES ( var i abl e−names and LI -
NE−number s ar e di spl ayed) and SKI P ( var i abl e−names and ever y
SECOND l i ne−number ) .

Thi s SURFACE−PLOT i s l i mi t ed t o 20 var i abl es ( as t he whol e pr o-
gr am) , you r ecei ve good r esul t s wi t h not mor e t han 20 dat a−l i nes

i n your f i l e. Pl ease r emember t her e i s no pr ocessi ng done as i nt er -
pol at i on or anyt hi ng l i ke t hat , YOU have t o do i t when " st i l i ng"
your f i l e.

5. 6 " cl ust er "

Thi s cal cul at i on i s not j et done i n t hi s r el ease. I ' m sor r y f or
t hat , but t he al gor i t hms I want t o use ( SPבäTH, H. ; " Cl ust er ΓêÆAna-
l yse−Al gor i t hmen" ) ar e wr i t t en i n FORTRAN and t he t r ansf er t o
Gf A−Basi c i sn' t t hat easy because t he FORTRAN−guys wer e gr eat

f ans of t he Mr . GOTO ( you know t hat l i t t l e j umper ?) , so I have t o
f i x a whol e new st r uct ur e t o t he r out i nes. What you get i s a l i t t -
l e gr aphi c of a ver y, ver y si mpl e " ad hoc" cl ust er i ng al gor i t hm.

6 " Out put " dr op−down menu

6. 1 " Har dcopy"

Thi s r out i ne uses t he TOS bui l t −i n har dcopy−r out i ne, t hat i s
desi gned f or a 9−needl e dot −mat r i x−pr i nt er , so i f you use a 24−
needl er , you have i nst al l a pr i nt er dr i ver whi l e boot i ng. Al -

t hough I never coul d t est a 24−needl e pr i nt er , I pr esume t hat i t
wi l l wor k wel l .

You wi l l see t hat t he upper menu−l i ne of t he scr een i s del et ed,
so t hat you onl y get t he pur e gr aphi c. Thi s i s al so done when
usi ng t he scr een−dump−opt i ons descr i bed bel ow. I t of cour se i s

r est or ed af t er t he end of t he scr een−dump.

6. 2 " Save Degas"

Thi s opt i on asks you f or a f i l ename f or t he scr een t o save and
t hen st or es t he scr een t o di sc usi ng t he DEGAS−f or mat ( 32024
byt es) . Fi r st of al l t he di sc space i s checked f or enough r oom
f or t he f i l e t o come, so usi ng a har d−di sc causes a f ew seconds
del ay.

6. 3 " Save Doodl e"

Thi s r out i ne i s t he same as " Save−Degas" ( descr i bed above) . I t
onl y uses t he 32000 byt es scr een f or mat , t hat i s used by DOODLE

and many publ i c domai n gr aphi c/pai nt −pr ogr ams. I t can al so be
easi l y r ead i nt o memor y ( i f you use own pr ogr ams) by usi ng i . e.
" BLOAD f i l ename, st ar t adr ess" i n Gf A−Basi c.

Pl ease ment i on t hat I wel l t hought of i mpl ement i ng some gr aphi c−
r out i nes as I NSERT TEXT or ARROWS, but I r ecogni zed t hat usi ng

r eady pr ogr ams t o make gr aphi cs mor e per f ect i s t he bet t er way.

Rel ease 1 . 31

Thi s ver si on of f er s you a XY−pl ot r el yi ng on your r aw dat a ( l i ke
VI P−gr aphi cs) . I f you sel ect " scal e" / " numer i cal " t hi s new f eat -
ur e i s i nvoked by r epl aci ng t he ol d XY pl ot based upon t he st an-
dar di zed dat a ( t hat r uns i f you choose " scal e" / " st andar di zed" ) .

The r egr essi ons ar e

cal l ed i n t he same

manner as i n t he ol d

st andar di zed gr aphi c.

Pl ease ment i on t hat

t he equat i ons gi ven i n

t hi s opt i on r el y on

t he r aw dat a.

I n t he st andar di zed XY pl ot t he possi bi -
l i t y t o swi t ch t o numer i cal val ues f or
t he X&Y axi s has been r epl aced by t hi s

r aw−dat a−XY pl ot . I f you di d sel ect " nu-
mer i cal " and cal l t he 2−D di st r i but i on−
gr aphi c t he x−axi s wi l l be di spl ayed nu-
−NEW− mer i cal as i n pr evi ous r el eases.

א½==ol d r out i ne

So l et me r epeat t he new f eat ur es:

You can swi t ch f r om a XY−pl ot based upon
st andar di zed dat a t o a XY−pl ot based on
t he r aw−dat a. Regr essi on and equat i on
ar e swi t ched as wel l . The new XY−pl ot of f er s you a f r ee sel ect i on
of l ower and upper l i mi t s as wel l as an " aut o−scal e" f unkt i on.

The er r or bar s can be di spl ayed i n bot h XY−pl ot s.

The scal i ng i s best when t he mi ni mum and maxi mum ar e not 1 power
of t en ( l i ke 0 t o 1 00) , best r esul t s ar e gai ned when usi ng f i t -
t i ng val ues ( l i ke 20 t o 1 00) . The r eason f or t hat i s somewher e i n

t he scal i ng al gor i t hm, sor r y.

How t o use i t :

You st ar t i t wi t h swi t chi ng
f r om st andar d XY−pl ot ( STD)

t o Cr oss−pl ot ( CROSS) .

I f you i nvoke t hi s gr aphi c,

you ar e asked wet her t o use

t he AUTO−SCALI NG f unct i on

or not . I f You sel ect AUTO−

SCALI NG t he l ower boundar y i s

set as negat i ve upper maxi ma.

As i n t he XY−pl ot wi t h l i near
axi s, you can ent er t hese

val ues by hand.