*

. . .

/ /

. )sisylanA ataD yrotarolpxE(

. .

. )tolp xoB( tcartsbA ni elor tnatropmi na syalp atad lacitsitats fo ytilibaliava ehT ytefas htiw slaed hcihw hcraeser siht fo ecnatropmi ehT .ssecorp gninnalp siht fo evitcejbO ehT .seulav sreiltuo dna srorre morf atad lacitsitats fo nredom gnisu yb atad lacitsitats ni seulav reiltuo eht enimreted ot si yduts .sdohtem cirtemarap htiw meht gnirapmoc dna sdohtem atad yrotarolpxe tnatropmi niam eht, sretpahc ruof otni dedivid neeb sah hcraeser ehT cirtemarap eht dna sdohtem yrotarolpxe ehT-1:era dehcaer snoisulcnoc seulav reiltuo eht gninimreted ni meht neewteb noitairav dewohs sdohtem .atad eht ni ni desu dohtem tseb eht saw dohtem tolp xob eht taht dewohs yduts ehT-2 .atad ni seulav reiltuo gninimreted

" 6991 , / *

".

1-1

{ )seulav reiltuO( }

.

. )seulaV reiltuO(

)8791 ttenraB()5( :

)rorrE noitaluclaC( - 1 .)srorrE gnidroceR( - 3)srorrE gnidaeR( -2

.

( )

)4( : 0891

( ) -1 ( )

. -2

. -3

.

: 8791 ttenraB

. (srorrE gnilpmaS) -1 )ytilibairaV tnerehnI( -2

- 3.

. )1691,ssorB()9(

)2791,hguaphsiK()81( .

)6791,iruoboJ-LA()61( .

)8791,ttenraB()5( .

.

)esaC cirtemaraP( )noitubirtsiD lamroN(

)esaC cirtemaraP-noN(

.)sisylanA ataD yrotarolpxE(

-2.1

.

)sisylanA ataD yrotarolpxE( dna ,faeL dna metS ,tolp xoB(

)tolp xoB rednifegnaR .

-3.1

)5571,hcivocsoB()5(

.

)2581,ecrieP()4( )n( )K(

)K( )rorrE fo metsyS( )ecrieP(

) ( 1 knk ) ( .n/k

)3191,thgirW()3( .

)n( )3191,niwdooG()61( )1-n( )1-n(

5291 . .

)5291,niwrl()51( )s(

) ( (. )

5391 nospmohT)61( .(6991 ) .T

.

sbburG)31( 0591 )noitalupoP lamroN( n

sbburG)31( .

. )stnioP egatnecreP( K )egappliS( 8491 relletsoM)12(

0591 yekuT & relletsoM)22(

.

)1691 regniZ()03( ( )

.

1791 nallimcM)02( nallimcM

. laudiseR mumixaM()

.

(. 6991 ) .

2791 gnirnetteK dna naksedananG)21(

. gnirnetteK dna naksedananG

. )snoitacoL etairavitluM( )srotceV negiE(

. 2791 hguaphsiK)81( .

3791 namkceB dna erooM ,nejteiT)72( )laudiseR dradnatS(

.sbburG

5791 flhoR)42( tseT paG dezilareneG() )sreiltuO etairavitluM(

.

5791 ttocserP dna nhoJ)42( .

6791 iruoboJ-LA)61( siweL dna ttenraB)5(

. 8791 0891

. )1((8891)

.tolp xoB )2((0991 )

. tolp xoB )3((3991)

.tolp xoB

.

4.1 sisylana atad lacitsitats sisylana atad yrotarolpxE

. yekuT

0791

.

. .

)seulaV rettal(

)elitrauQ tsriF( )naideM( drihT( )elitrauQ

. )tolp xoB(

. .

(41) 1.4.1

.

.

)sdohteM lacihparG((( 41)) 2.4.1

yillaH

0281

2781 )ssergnoC lacitsitats lanoitanretnI( 2581 .

yekuT

.

. -2

: 1.2 ( 1)

)cirtemaraP(

. )sisylanA ataD yrotarolpxE(

2.2

)snoisnemiD owT( )esac etairavinU( )sledom noissergeR(

.

1.2.2 .)etairavinV(

(.31 ))sbburG( : 0591 sbburG

)n( sbburG

)n( )1-2( .

)2-2( )3-2(

. )4-2( (.6991 )

) (..........(.....21) ) (

1

2

1

1

2

2

2

==

=

ii

n

n

iin

n

XX

XX

SS

==

1

11n 1

inX ni

X

) (12..........(.....22) ) (

21

22

2 1

==

XX

XX

SS

i

n

ii

==n

inXi

X2

11

1

) ( ..........(.....23) ) (

1

2

2

12

,12

2 ,1

=

=

=

ii

n

n

nninn i

XX

XXSS

=

= 2

1,1

2n 1

inX nni

X

) (..........(.....24) ) (

1

23

21,2

2

2 1,2

==

=

ii

n

n

ii

XX

XX

SS

==n

inXi

X3

1,22

1

)divaD dna yrrebneseuQ()32( : 1691 )divaD dna yrrebneseuQ(

( k) 2 . . K S*2 )7-2( )6-2( )5-2(

)6-2(,)7-2( )divaD dna yrrebneseuQ( ) . ( )

(

S1* )8-2(,)9-2(,)01-2(: K

. )61( ) ( (.6991 )

) (

....................(..27) ....................(.....28) ) (..........(.........26)

/....................(25)

*1

*

*xam

=====

bnXXS

bxaMbS

bxaMbXX

bXXS

iiiW

i

i

ii

) (

....................(...201)

....................(...29)

*1

*

*1

==

==

SnXX

bxaMbxaM

SxaMnXX

bxaMb

iiWi

iiWi

=

=k

iknX Wii

X1

1

=

=k

iNni

1

.(02) )nallimcM( : ( nallimcM0791)

nallimcM 2 u

)tseT laudiseR mumixaM( Xn ( 11.2)

, Vnv) ( . S

. Xn1 ( 2-21) 1, XX nn nallimcM

Cn) ( . n CS) ( ( 2-31) .

( 2-41) sbburG .

) (...........(....221) ) (

...........(....211)1,

1

,

>>

n

nVn

nVn

XXVS

XXVS

12 ) (

1

= 2=

SXXnn

i nin

1

1

1 =

=XXn

n

i ni

) ( nnn XXXCS +> 12...........(......231) ) (..........(.......241) ) (

1

2

2

,1 1

2

2 ,1

=

=

=n

i i

n

nninn i

XX

XXSS

( 72) )erooM dna nejteiT( : k Lk )3791 erooM dna nejteiT(

kE )n( ( ) )slaudiseR tsegraL(

k k Lk* (: 2-51)

(.2- 61) )erooM ,nejteiT( ( 2-71) Ek

*, LL kk . *, LL kk

k n *, LL kk

Ek k k

* ,, ELL kkk ) ( .

..........(.......251) ) (1

2

1

2

=

=

=n

ii

nk

ik ik

XX

XX L

) (

==

nk

iXXnk ki

1

) (..........(.......261) ) (

1

21

2

* =

=

=+n

i i

n

ik ikk

XX

XX L

) (

=+=

n

ikXXnk ki

1

*

) ( ..........(.......271) ) (

1

21

2

=

=

=n

i i

nk

ik ik

ZZ

ZZ E

) (

==

nk

iZZnk ki

1

== ii ZidXX

.(52) rensoR() : )5791,rensoR(

. )81-2( )n( RR, 12 RK

.)61( i RcitsitatsxaMXab = 2 /..........(......281) ) (

nk aXnk) (

ik2 i

1

==+

21) ( ) (

1

= 22=+

bXanknk

ik i

=1....., IXX on) () (

) () (....................(......212) ) ( ) (

....................(.....202)

,,....................(..291)

111

1

10

1

==

==

kkk

i

k

o

oo

RXabXI

RXab

IIX

RXabXI

2.2.2 . )snoisnemiD owT(

. 2T gnilletoH : -: , XY oo) ( 0791 itayaB-LA)6(

=1..., in) ( , XY ii) ( n

itayaB-LA . )noitubirtsiD lamroN etairaviB(

HPPHPP=

::

1

0

P , XY oo) ( )E( , XY oo) (

E (. 2-32) E) ( (.2-22)

P gnilletoH 2T F gnilletoH 2T 2=P

F F ( 2-42) ( 2-32) , XY oo) ( )2-n(

, XY oo) ( 22 , XY oo) ( > 22 (2-52) .

) () ( ) ( ) (..........(.....222)

2

11

2

2

2

2

2

xy =+

xy

y

y

x

XuYupXuYu xp

E

2..........(.....232) ) () ( ) ( ) (1

12

2

2

2

2

SS xyxy =+

rXXYYSYY

SXX

r E

) (+ 21..........(........242) ) (npF = TPnp

p=2 ) (

nFTn

3222

=

) () ( ) ( ) (..........(.....252)

21

12

2

02

2

02

2

xy =+

oo

SS xyrXXYY

SYY

SXX

r T

)sledaM noissergeR a ni sreiltuO( : sledoM noissergeR a ni sreiltuO )4( a-

YBBXU ioii =++ 1.......262) ( i )elbairaV tnednepeD( Yi

)sretemaraP( 1, BBo )elbairaV tnednepednI( 2 ~,,1...,(voc,) == iij UNOinoij ) ( )rorrE modnaR( Ui

erauqS tsaeL( 1, BBo : ( 2-62) )snoitamitsE

eybbX iioi = 1..........(.......272) ei

. Vei) ( ( 2-82)

. (2-92)

) () ( ) (/1..........(...292) ) ( ) (

1..........(.282)

1

22

1

2

22

=+

=+

=

=n

iiii

i

i

n

ii

ii

XXXXnesn

se

XX

XXn Ven

mumixaM( s / |ie xaM| 0691 (11)leinaD )laudiseR dezitneduts etulosbA

2791 (8)reparD dna neknheB ( 2- 03)

)t( )reiltuO tnadrocsiD(

namkceB dna erooM t =0.1,0.50,0.10) ( 001= n

.)03- 2( txaMeS ii = ..........(.......203)

ei 5791 ttocserP)71( . S ( 2-03) Si S

2791 reparD dna nekheB)8( )sretemaraP( (q) 2 ()/ nqn

( 2-13) ( q=2 ) (. 2-23) t*) (

*, tt (.6991 )

) () (

=

=

=

=

=

=

=

==

n

iiii

i

n

iii

n

iii

i

Zee

tnxaMz

nxaMee

xaMeen

txaMenqSn

SnqSn

1

2

*

1

1

2

*2

2

....................(223)

/

/

/....................(213)

)4( - b .sledoM raeniL lareneG a ni sreiltuO

-: YXBU =+ ..........(.233)

: Y

n1 )selbairav modnaR tnednepeD fo rotceV( : X

nk +1] [) ( )selbairav modnaR tnednepednI fo xirtaM( k+ 11] [) ( )sretemaraP fo rotceV( : B .n (1) )srorrE modnaR fo rotceV( : U

( 2-33) B ei) ( (. 2-53) (. 2-43)

( 2- 73) ( 2- 63) ei) ( ( 2-83)

( 2-93) ( 2-04) )e(VOC-V

. ( 2-14) ei) ( (. 6991 )

) ( ) () (..........(........263) ] [

..........(......253)..........(....243)

12

1

====

eIRUVroCBXX

BXXXY

VroCeIR = 2..........(.........273) ) ( ) (

ei )73-2(

] [) ( ) (1..........(........283) ) (1

2

12

= =

ii

iii

rraVeXXXX

X i Xi =1 rXXXX iiii ) (

2) (....................(.293) ) ( ] [

2

==

UIRUnq

eSeenq

]xirtaM ycnetopmedI[ IR] [ : : ( voC-Ve)

en SIr = 22 ....................(.204) ) () (............................(....214) ) ( ) (

22

==

Ireenq

SIr

ii

iii

ei) ( =/ Mes iii

)laudiseR dezitneduts mumixaM( . mi () 1691 (62) natnakirtS

T (. 2-24) . 5791 ( 91) dnuL

ei ii TxaMeSn => ..........(.....224)

sisylanA ataD yrotarolpxE. 3.2

( sisylanA ataD yrotarolpxE) )tolp xoB( )fael dna maets(

.)tolp xoB rednifegnaR( ,y) (

( )faeL dna maetS 2-3-1

. )margotsih(

)dirbyh(

. -:

:1

((6 01 05 04 002 06 98 09 44 23 96 87 93 07 89 001)) :

-:

. 1 )stigid gnidaeL(

(0 1 3 4 5 6 01) (.maets )

.2 . )tigid laniF(

( 0) ( 6) (6) ( 1) ( 0) ( 01)

. ( 5) ( 0) . ( 1)

)sevaeL( )mets(

. )faeL dna mets(

(1) 61 = N 1C fo fael-dna-metS

0.1 = tinU faeL 6 0 1 0 1 2

2 2 92 3 4 40 4 6 0 5 7

90 6 )2( 80 7 7 9 8 5

80 9 4 0 01 2 ;002 IH

( 002) ( 1)

.6991 )dolp xoB( -2.3.2

tolp xob . )7791 yekuT(

( 2-6) )seiremmuS rebmuN-5(

)emertxE rewoL( naideM = 2Q() )elitrauQ rewoL = 1Q(

()elitrauQ reppU = 3Q )emertxE reppU(

.

.

1Q -3Q( 1Q 3Q .1 % 05 )egnaR elitrauqretnI =RQI( )RQI = .

. )naideM( .2 )emertxE rewoL , emertxE reppU( .3

)RQI*5.1 -1Q( )shtgneL reksihW( )RQI*5.1 +3Q(

.)seulav reiltuO(

yekuT )htdiw xob( .4 .n) (

. % 5 )hcton( .5

neMRQI

1.85() :

. : n . : Me

)emertxe rewol dna emertxe reppU(

)2.on elpmaxE, tolp xoB( (.6991 ) )AA1(

)tolp xoB redniF egnaR( 2-3-4

)tolp rettacS( .

rednifegnaR( )tolp xoB

. )X( )Y( ( )

)shtgnel reksihw(

)seulav emertxE( . )x( )y(

)seulav emertxE(

(.6991 )

-3 -: 3-1

)seulav reiltuO(

)sdohtem cirtemarap(

)sisylanA ataD yrotarolpxE( .

3-2

.

93.0 50.0- 31.0- 42.0- 44.0 - 81.0 22.0- 36.0 84.0 3.0 - ( 2) 01.0 02.0 4.1- 60.0 10.1

. a- ( 2) 6791 61 iruoboJ-LA

( 04.1-) sbburG )kE( eroom dna nejteiT

rensoR . )10.1( ( 04.1-) ,)10.1(( 04.1-) ( 2)

1R,2R )812.2=2R( )375.2=1R( *27.2,*86.2

.rensoR

. -b )tolp xoB( :

( 2) . ( 2) ( .)04.1-

(2)

20000RAV

05.1

00.1

05.0

00.0

05.0-

00.1-

05.1-

(3) :

(3) 1C fo fael-dna-metS 51 = N 01.0 = tinU faeL ;41- OL 4 0- 2 223 0- 5 01 0- 7 110 0 )3( 32 0 5 4 0 3 6 0 2 0 1 0 1 1

( )04.1-

( )04.1OL

- sbburG erooM dna nejteiT )10.1(( )04.1- ( )04.1

rensoR .

(3)

75.0- 766.0- 314.0- 836.1 166.0 901.0 335.0 43.0- 800.1- 650.1- 341.0- 769.0 909.0- 840.0- 931.2 512.2- 405.0 092.2 055.0- 702.1

. -a

rensoR 6791 iruoboJ-LA)61( . 3

-: 3

: .1 : nallimcM

) () ( ) ( ) (4.10120.927

2.922.93120.46011.5410.736

2*

1

>+>

nnn XXXCS +>

.nallimcM 931.2 , 6092.2 sbburG - : -2

931.2 , 092.2

0.9206 42.998

51.92102

2== ,1

S nn S

-650.1- , 512.2

0.978 42.69812.698

2

2== 1,2

S

S

=0.50 ( 3) . 9625.0

. sbburG

erooM dna nejteiT -3 ( 3) E= 61*20.614) ( . E= 20.735) (

. . ( 3) -b

(.3) ( 4) :

( 4)

10000RAV

00000.4

00000.2

00000.0

00000.2-

00000.4-

)faeL dna metS( :

( 5) .

( 3) nallimcM

)tolp xoB( )fael dna mets( .

(5 ) 1C fo fael-dna-metS 02 = N = tinU faeL 01.0 2- 1 2 1- 1 1- 3 00 0- 7 5569 0- )4( 0134 0 9 1 0 8 9655 1 4 2 1 3 6 2 2 21

(4) 62.4 25.4 93.4 76.5 54.4 93.4 03.4 13.4 46.4 92.5 21.4 26.5 75.4 06.4 92.4 36.4 28.4 15.5 21.4 14.4 80.5 65.4 37.4 87.5 04.4 62.4

. a- -:

)sbburG( : 87.5 :

0.97 6.5614.19

2

2

==S nS

21.4 : 0.49

6.5615.738

2

2== 1SS

21.4 ,87.5 17.0 .sbburG 4

)erroM dna nejteiT( : :

2.425.874.186/0.94

1

1=

=RR

R= 1*2.39 .)rensoR(

-b . :

-: 45.4 )naideM(

13.4 )1Q( 28.4 -)3Q(

21.4 )L( 15.5 -)U(

(.4) ( 6)

(6)

10000RAV

00.6

05.5

00.5

05.4

00.4

.)26.5 ,76.5 , 87.5(

(7) : (7)

N 1C fo fael-dna-metS 62 = 01.0 = tinU faeL 11 4 2 3333222 4 9 555444 4 )6( 7666 4 11 8 4 7 0 5 6 2 5 5 5 5 4 ;65 IH ;75 ;65

)IH(

.

: 3.3

. (5)

22.3 41.2 64.3 64.2 72.3 86.2 49.2 4.2 3.3 67.3 86.3 4.3 97.3 52.3 :X 89.1 19.2 98.2 65.2 10.3 14.2 27.2 81.3 89.2 70.4 25.3 17.3 92.3 33.2 19.3 58.2 :Y 22.2 46.2

. ( 5) -a )tset 2T gnilletoH( 6791 61 iruoboJ-LA

( 5 ) )70.4,4.2(

-: |is/ie| xaM=t . i e

=+ 1.90.63 yX ii

16.2 / es ii )70.4 = y ,4.2 = x(

)70.4 ,4.2( )6.2 = *t(61 .

)y,x( - b( 8) ( 5) )tolp xoB rednifegnaR(

.

(8)

00.205.200.305.300.4

X

00.4

05.3

00.3

05.2

00.2

Y

)y ,x( .

.

(6) 2.04 3.24 5.34 2.44 1.24 3.64 1.54 3.74 8.74 5.84 2.44 05 9.94 3.15 : X 0.43 8.13 1.86 1.56 2.27 7.18 6.48 9.87 2.92 6.88 59 0.78 9.59 4.001 5.401 5.201 : Y 5.25 3.76

-: ( 6 ) -a :

: E : XY == 013.8,076.3) (

E= 8.68

) (8.50

322

2

2

==

T

Fn Tn

> ET 2 . xY == 00 13.8,76.3) ( : = txaMes ii

: =+ 12.82.4 YXi

. t )00.2( / es ii es ii

61)9.2 = *t( 3.24= x , 1.56 = y

(.6991 ) ( 6) - b

: (9)

( 9)

00.0300.5300.0400.5400.0500.55

1X

00.011

00.001

00.09

00.08

00.07

00.06

00.05

Y1

)3.76 = y , 8.13 = x(

.

-4 : 1.4

-:

sbburG .rensoR erooM dna nejteiT

sbburG . erooM dna nejteiT

2

resnoR

erooM dna nejteiT sbburG . nalliMcM

( 6991 )

.

. ( 3)

erooM dna nejteiT rensoR . sbburG

.

2T )y, x(

t )y, x(

.

)y, x(

. )y,x( )2x , 1x , y(

(.)2x , 1x , y

)y,x(

. : 2.4 .1

nalliMcM rensoR nejteiT sbburG sbburG .

rensoR .

.2 t 2T

tolp xoB rednifegnaR .

.3 .

.4 .

.5 . )faeL dna mets(

.6 .)tolp xoB( )erooM dna nejteiT(

.7

. )tolp xoB( .8

()erooM dna nejteiT .6

)tolp xoB( .9 .

.01 )tolp xob rednifegnaR(

)y ,x( )y ,x( )y ,x(

. : 3.4

: .1

. xoB rednifegnaR dna ,fael dna mets ,tolp xoB .2

tolp .

.3 . )y ,x( = txaMes ii) ( )erooM dna nejteT(

.4 .

1. )1988" ( " .

2. )1990" ( " .

3. )1993 " ( .

4. )1980 " ( .

5. Barnett, V. & Lewis, T.(1978) Outlier in Statistical Data, John

Wiley and Sons, New York. 6. Al-Bayati, H.A.(1973)Procedure for Detecting Observation in

Samples two related Variables, The Proceeding of the Ninth Conference of Statistics and Computation to Multivariate Statistical Analysis, John Wiley and Sons,New York.

7. Becketti, S. & Gould, W.(1987) Rangefinder Box plot Anote, The American Statistician, V.41,No.2,p.(149).

8. Behken, D. W. & Draper, N. R.(1972) Residuals and their Variance Patterns, Technometrics, V.17,pp(127-128).

9. Bross, L. D. J.(1961) Outliers in Patternend Expremints a Strategic reappraisal, Technometrics, V.3,pp(91-102).

10. Cleveland, W.S.(1985) The Elements of Graphing Data, Monterey, CA; Wads Worth.

11. Daniel, C. (1960) Location Outliers in Factorial Exeperiments, Technometrics, V.2,pp(140-150).

12. Gnanadesikan, R.& kettenring, J.R.(1972) Robust Estimates, Residuals and Outlier Detection with Multiresponse Data, Biometrics,V.28,pp.(81-124).

13. Grubbs,F.E.(1950) Sample Cirteria for Testing Outling Observation, Ann. Math. Stat., V.s1,pp(27-58).

14. Hussin, M. M. (1989) Some studies of Graphical Methods in Statistical Data Analysis ; subjective Judgements in the Interpretation of Box plot, Unpublished Ph. D. Thesis, Keele University, Uk.

15. Irwin, J.O. (1925) On a Criterion for the Rejection of Outlying Observation, Biometrika, V.17,pp.(238-250).

16. Al-Jobouri, S.(1976) Test of Outliers, Unpublished M.Sc Thesis, University of Baghdad.

17. John & Prescott, P. (1975) Critical Values of a Test to detect Outliers in Factorial Experiments, Appl. Sta., V.24,pp.(56-59).

18. Kishpaugh, J.R.L.(1972) Experiments in Outliers Detection in Multivariate Data, M. Sc. Thesis, State University of New York, Stony Brook, NY.

19. Lund,R.E.(1975) Table for an Approxiamte Test for Outliers in Linear Models, Technometrics, V.17.pp.(473-476).

20. McMillan, R.G. (1971) Tests for one or Two Outliers in Normal Samples with unknown variance, Technometrics, V.13,No.1,pp.(87-100).

21. Mosteller, F.(1948) AK-Sample Slippage Test for an Extreme Population, Ann. Math.Stat.,Vol.19,pp.(58-65).

22. -----------& Tukey,J.W.(1950) Significance Levels for a k-Sample Slippage Test, Ann.Math.Stat.,Vol.21,pp.(120-123).

23. Quesenberry, C. P. & David(1961) Some Tests for Outliers, Biometrika,V.48,pp.(379-387).

24. Rohlf, F.J.(1975) Generalization) of Gap Test for the Detection of Multivariate Outliers, Biometrics,V.31,pp.(93-101).

25. Rosner,B.(1975)On the Detection of many Outliers,Technometrics,Vol.17,No.2,pp.(120-135).

26. Strikantan, K.S.(1961) Testing for Single Outliers in a Regression Model, Sankhya,A.Vol.23,pp.(251-260).

27. Tietjen, G.L., Moore, R.H.& Beckman, R.J.(1973) Testing for a Single Outlier in a Simple Linear Regression, Technometrics,Vol.15,pp.(717-721).

28. Tukey, J.W.(1977) Exploratory Data Analysis, Addison-Wesley Publishing Company.

29. Velleman,P.F.& Hoaglin, D.C.(1981) Applications, Basics and Computing Exploratory Data Analysis, Boston, M. Sc., Duxbury Press.

30. Zinger, A.(1961) Detection of Best and Outline Normal Distributions with known Variances, Biometrika,vol.48,p.(457).

)AA1(