Notities en voorbeelden bij de statistische theorie van proefopzetten

(1)

Notities en voorbeelden bij de statistische theorie van

proefopzetten

Citation for published version (APA):

van Heck, J. G. A. M. (1982). Notities en voorbeelden bij de statistische theorie van proefopzetten. (DCT

rapporten; Vol. 1982.017). Technische Hogeschool Eindhoven.

Document status and date:

Gepubliceerd: 01/01/1982

Document Version:

Uitgevers PDF, ook bekend als Version of Record

Please check the document version of this publication:

• A submitted manuscript is the version of the article upon submission and before peer-review. There can be

important differences between the submitted version and the official published version of record. People

interested in the research are advised to contact the author for the final version of the publication, or visit the

DOI to the publisher's website.

• The final author version and the galley proof are versions of the publication after peer review.

• The final published version features the final layout of the paper including the volume, issue and page

numbers.

Link to publication

General rights

Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain

• You may freely distribute the URL identifying the publication in the public portal.

If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement:

www.tue.nl/taverne

Take down policy

If you believe that this document breaches copyright please contact us at:

openaccess@tue.nl

providing details and we will investigate your claim.

(2)

(3)

(4)

(5)

l a r

r....

-7

~2

i

....

I

A *

.-

.

....

-

#

-

...

E

₁

I . . .

7 a

c

(6)

s

OT

(7)

(8)

(9)

(10)

xs

1-

(11)

-

d

7 5 -

(12)

(13)

(14)

(15)

(16)

(17)

-

L-44

-

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(28)

(29)

(30)

(31)

(32)

k

(33)

(34)

2 U

v

2 I

-f

O 0

O

b

(35)

(36)

(37)

(38)

(39)

(40)

(41)

(42)

-57.2

4

/

-

R.l

t

I

i

5

3 5 %

33r

964 3383

&.h.

33-1-

37 r-

F‘

270.32 67-20

(43)

(44)

o

O"

t

a

--T -i

o

1 I

NI

CJ

b

I

u

\\

(45)

(46)

(47)

(48)

(49)

(50)

(51)

=

(52)

“3

- f

3 i

- f

-!

4

(53)

De

A ,

(54)

(55)

(56)

o

PARAMETER ESTIMATE

0.2û450E 02

O.11703E

O2

0.80583E O1

0.12703E

O1

PARANETER ESTIMATE

(C)

0.450OOE

O1

0.98422E

O1

0.17067E

O1

13)

0.42344E

O1

(57)

V A

R

I

AN C

E

-

C O V

AR

I

A

Tti

C

E

PIA

T

R I X

PARAMETERS

*

F O

R

1

2

3

4

1 0.13410E

O0

-0.60983E-15

0.30491E-14 -0.12789E-O7

2 -0.60983E-15

0.26820E-01 -0.30491E-15

0.12789E-08

3 0.30491E-14 -0.30491E-15

0.13410E

O 0 -0.63945E-08

4 -0.12789E-07

0.12789E-08 -0.63945E-08

0.2682OE-01

VEI

R I

A

IJ

C

E

-

C O V AR

I

A N

C E

PI

AT

R I

X

PARAWET ERS

F O

R

1

2

3

4

1 0.53641E

O 0

-0.26820E

O 0

-0.53641E

O0 0.26820E

O 0

2 -0.26820E

O 0

0.74501E 00 0.44701E

O 0

-0.38741E O 0

3 -0.53641E

O 0 0.44701E

O 0

0.80461E

O 0

-0.44701E OU

4 0.26820E

O 0

-0.38741E O 0 -0.44701E O 0 0.29800E

O 0

6

(58)

(59)

(60)

Uoí3ts

1 fl73 /?o=

O.18750E 02

6;-

0.64583E

O1

I

fil=

0.19382E

O 1

@'=

0.54850E

O 0

4:

J

0.48436E

O 1

"1=0.89317E O1

~

~ = G S 1 7 2 7 5 E

O ?

A = 0 . 4 2 3 2 2 E

O 1

E 3

(61)

(62)

(63)

0.18850E

02 0.64557E

O 1

0.20070E

O 1

1 0.56208E

O 0

0.48008E

O 1

A

0.85247E

O1

O948568E

O 1

0.43371E

O1

(64)

(65)

(66)

(67)

(68)

(69)

1_1

X6

-2

-1

O

I

2 -2

-1

O

1

2 -2

-1

O

1

2 -2

-1

O

1

2 -2

-1

o

1

2

7 7

9 %

.

-2

-1

- 1

-1

O

o

O

0

1

2

_I

-

3.15

14.42

32.35

75.01 -36.18

-3.74

7 . 9 8

20 .43

65.37 -39.71

-&.66

5.34

23.56

65.84 -35

.06

-4.77

10.74

26.16

70.67 -24.39

7.80

18.58

36.14

78.77 a-

-

34 -1

o

I

2 -2

-I

O

1

2 -2

-1

O

1

2 -2

-1

u

1

2 -2

-1

o

1

2 -z

-

362

I_

-2

-1

O

o

1

2

2 -27.75

4.53

13.21

30.67

73.88 -38.68

-4.80

7.24

23.34

68.37 -37

-33

-7.81

4 - 0 9

22.97

65 - 8 8

-35.00

-4.21

8.04

25.58

68.79 -25

- 2 5

8.72 18,70

1

34.14 ,

79.34 ,

,

(70)

-.

0-02

8 o

(3

o

Q

o

O Q l O

' O

c)

O

o

o.

12.5

13 -

0.0

33 o

o

6 o

O

0.0 I 4

0 o

-0.020

o

z)

(71)

/

c

o

6 6)

Q

o

B

(72)

(73)

(74)

(75)

(76)

(77)

(78)

Xf

-1

- 9

-1

o

1

1 .-

--

(79)

(80)

(81)

o

O

_z,

B

Q

o

&9

o

8 G

a3

o

(82)

(83)

T

c=--

-1

- 1

-1

o

O

o

O

0 O

O

1

1 I

I

1

1 -

-

9kz

7

-

- 1

-1

0 o

o

1

1 -1

- 1

-1

O

1

1 -1

-1

- 1

O

o

O

I

1

s _ 3

-i

o

1 - 1

o

1 - 1

o

1 -1

o

1 -1

O

1 - 1

i)

1 -1

o

1 -1

O

1 -1

u

1

__I ___I I_ PI_

- 1

1 o

'i

o

-1

o

1 o

-1

4 -1

I

o

1 o

-1

1 -1

O

Cl

I

- 1

-1

o

1

al " I

-

(84)

(85)

,

__s

-1

'I

U

1 O

-1

O

-1

1 -

-

-1

o

'I

-1

cl

o

1 -1

-

(86)

(87)

(88)

L _

x3

__II_>

-

-3

-1

1

3 - 1

-3

3

1

3 -3

-1

3

1 - 1

- 3

-

ID

x1,

=

-1

-3

3

1

3

1 -1

- 3

1

3 -3

- 1

-3

-1

1

3 -

3uE

===?

1

3 -Y

-1

- 1

-3

3

1

3

1 -1

-3

-1

1

3

(89)

Cf

u3

(90)

1 . 6 4 5

1 . 9 6 0

2 . 3 2 6

2 . 5 7 6

2 . 8 0 7

3 . 0 9 0

3 . 2 9 0

3 . 8 9 7

4 . 4 1 7

u

tweezijdig

5 %

2 %

1 %

0 . 5

%

0.2 %

0.i

%

0 . 0 1

%

0 . 0 0 1

%

(91)

1 6 7 8 9 1 0 11 12 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 25 30 35 40 5 0 Aantal v r i j h e i d s g r a d e n Y = 2 0 E e n z i j d i g : P ( 0 . 8 0 &

<

o ) = P ( 1 . 3 6 5

>

u ) = 0.95 Tweezijdig: P ( 0 . 8 0 - &

<

Q

<

1.36 2) = 0.90 1.92 1 . 8 0 0 . 7 2 1 . 7 1 0 . 7 3 1 . 6 5 0 . 7 4 1 . 5 9 0 . 7 5 1 . 5 5 0 . 7 6 1.52 0 , 7 6 1 . 4 9 0 . 7 ’ 1 . 4 6 0 . 7 7 1 . 4 4 0 . 7 8 1 . 4 2 O . 78 1.4u 0.79 1 . 3 8 0.79 1 . 3 7 0.80 1 . 3 6 0 . 8 1 1 . 3 1 0 . 8 3 1 . 2 7 0 . 8 4 1 . 2 5 0 . 8 5 1 . 2 3 0.86 1 . 2 0 .975 . 9 5 “1 0.45 0.52 0.57 0 . 6 0 0.62 0 . 6 4 0.66 0.68 0.69 0.70 0.71 0.72 0.72 0.73 0.74 0.74 u.75 0.76 0.76 0 . 7 7 0.78 0.80 0.81 0.82 0.84 “2 3,73 2 . 8 7 2 . 4 5 2 . 2 0 2 .O4 1 . 9 2 1.83 1 . 7 5 1 . 7 0 1 . 6 5 1 . 6 1 1 . 5 8 1 . 5 5 1.52 1 . 5 0 1 . 4 8 1 . 4 6 1 . 4 4 1 . 3 8 1 . 3 4 i

.so

1 . 2 8 1 . 2 4 1 . 2 2 1 . 2 0 1 . 1 8 1 . I 7 1 . 1 6

1

a 0.39 0 . 4 7 0.51 0 . 5 5 0.58 0.60 0 . 6 2 0 . 6 3 0 . 6 4 0.66 0 . 6 7 0.68 0 . 6 9 0.69 0.70 0 . 7 1 0.71 0.72 0.72 0 . 7 3 0 . 7 5 0 . 7 7 0 . 7 8

o

.7.9 0 . 8 1 1 . 9 8 , 1 1 . 4 7 0 . 7 3 1 .42 0.75 0.7% 1 2- I .e, 1.54 1.43

1.43’

1 0.82 0 . 8 3 0.84 0 . 8 5 0.86

(92)

-

43-

Definitions:

Qo(z)= 1, #1(4=42. #s(z)=~&~-A(Tb*-

1%

= A , ( r 8

-

&(ha

-

7 ) z), Qr(z)

= = A , ( ~

-ik4( 3n8- 13) za+ &(?as-

1)

(na- Q)},

$,(z) =Ab(*

-

ies(n'

-

7 ) d

+r,L..(

16%'- 230d

+

407) I).

@&) = A s { f l - % 4 d ( 3ns- 31) i

+

r h ( 5 n 4 - llOns+ 329) a 9 - ï i ~ ( f c s - i) (na- 9) (na- 25)}.

The table gives the values of these polynomials, +,(I) for i= 1 ( I ) 0' and is arran@d in rifty SeBtions commponding to eanipltt sizes n = 3 ( 1 ) 5 2 . Tlie urgwiienta z=z,zet-b(n+i) cover the fu:! observational range t-i (i)n for n = 3 (1) 12 and the half-rcruge I = 1 (i)

[?$-!I

for n > 12, when uae is made of the symmetry (antiaymmetry) relatione :

The argument I ie not shown aa much in the table, but the Brst column of each motion givea (6,=A1z, where Al

is 1 for n odd and 2 for n even. The leading coetììcienta A, are chosen 80 that the #&) are positive or negative

hwgere throughout, and are given in the bottom Ikie of each section. Ale0 shown. in the line above the

A,.

ara

the s w of equeree

C

{+,(sr))* for the full range of zt values. Note the errengementa of the sectiona

wG&

prn.

f=1

grew from left to right through consecutive ages up to n=%. From this point onwards the sections P ~ P S ~ ,

from left to right through the top hahm of tEe pagea up to n=40 and then return from right to left through

&e

bottom halves of the

prges.

$&)=#,(-a) for i even, +,(i)= - # , ( - 2 ) for i odd.

n

som4 formulae:

Estimete of coenlcient of bi(z) :

A,

-1

yc q&(%,)/F {+&tr)}'.

Variance of

A,

-IJ$? {+&)}a.

*

Except that for n d 6, i

ie

not taken beyond n-

1. I

I

I - 1 1 -3 1 - 1 -2 2

-1

1 - 6 6 - 6 1 - 1 O -2 -1 -1 3 -1 -1 2 -4 -3 -1 7 -3 6 1 1 1 -1 -3 O -2 O 6 -1 -4 4 2 -10 1) 1 1 1 -1 -2 -4 1 -4 -4 2 10 2 2 1 1 3 -1 -7 -3 - 6 6 6 6 1 1

I

B

6

1

20 4 20 I 10 14 10 70

I

70 84 180 28 262

I

1 I n = 8 n = 9

!

I

-7 7 -7 7 - 7 I -6 1 6 -13 23 -6 -3 -3 7 6 3 -17 9 -1 - 6 3 9 -16 -6

i

1 -6 -3 9 16 -6 3 -3 -7

-

3 17 9 6 1 -6 -13 -23 -6 7

7 7 . 7

1 1 -4 28 -14 14

-

4 4 - 3 7 7 -21

11

-17 - 2

-

8 13 - 1 1

-

4 22 - 1 -17 Q Q

-

9 1 O -20 O 18 O -20 1 - 1 7 - 9 9 9 1 2

-

8 -13 -11 4 22 3 7

-

7 -21 -11 -17 4 28 14 14 4 4 990 408 'O 2,772 2,002 1,980 168 264 2.184 108 816 264

e

1

4 *

*

t

,

i

3

t

*

l'j

t i

-3 6 -1 S -1

I

-2 O 1 - 7 4 - 6 -1 -3 1 1 -6 16 0 - 4 O 6 0 - 2 0 1 -3

-1

I 6 16 2 O -1 -7 -4

-

8 2; 8:

i

15; 8:

i

1 i *

14

n = 10 - 9 6 -42 18

-

6 8 -7 2 14 -22 14 -11 -6 -1 36 -17

-

1 10 - 3 -3 31 3 -11 6 -1 -4 12 18

-

6

-

8 1 -4 -It 18 6

-

8 3 -3 -31 3 11 6 6 -1 -35 -17 1 10 7 2 -14 -22 -14 -11 9 6 4 2 1 8 6 8 330 8,580 180 132 2,860 660

(93)

i n = l l n r 12

I

1 4,

$4 $8

4.

I -11 65

-

33 33

-

33 I1 - 9 26 3

-

27 67

-

31

- 7 1 21

-

33 21 11 - 6

-

17 28

-

13

-

29 26

-

3 -29 19 12

-

4 1 4 - 1

-

35 7 28

-

2Q

-

20 -3 6 1 -4 - 4 O 4 4 -1 -6 8 156

ts

15

-

40 29 36

-

12

-

40

-

12 38 29 16

-

48 11,220

if0

-6 16

-

30 8 - 4 6 8 -6 - 3 - 1 22 -6 -2 - 6 23 -1 -1 - 9 14 4 O -10 O 0 1

-

3.5 3

-

19 6 -17 7 1 9 26 11 66 - 7 28 20 -20

-

19 12 44 4 -26 -13 29 26

-

21

-

a3

-

21 11 - 3

-

21

-

67 -31 a3 33 33 11 1 2

a

4 6 110 - Q

-

14

-

8 -23 - 1

-

22 6 - 8 16 30 4 -1 -6 -6 8 4,290 868 286 672 6,148 16,912 12,012 8,008 1 1

i

fr

2 3

4 is

n = l 4

-

13 13 -143

-

11 7 -11 143 -143

-

77 187 ,

-9:;

1

-8 -6 - 4 -3 - 2 -1 0 22 -11 11 O 99

-

68

-

22 22 83 -66 18 8 -11 43

-

26 22 -20 -20

o

-40

a

6 -96 - 5 8 -84

-

10 7 11

-

13 1 64

-

14

o

84 - Q 2 - 7 - 2 - 6 - 6 - 3 - 1 - 1 - 8 Be -132 132 -11 227 185

1

Di3

-

92

-

28 96 -13 -139 67 63 -146

-

25 24 108

-200

i'

81.240 236,146 138,1363 497,420

1

I (i72 3.m2 810 725 II

L

*

Izr

fts

2

t

4 *

a%

* I

I n= 16

I

n a 16

i

-7 -8 -0 91 -91 1,001 -1,001 1,144

-%

1

62 -13

-

429 19 35

-

869 979

-

65 -11 36 21 9

-

465 273 -143

-

91

-

91 143 143 -221 143

I

-117

-

39 69 87 46

-

25

-

76 - 4

-

8 -3 -29 -2 -44 -1 -63 O -66 68

-

704 44 178 61

-

249

-

751 197 49 261 -1,000 50 27 621

-

676 -126 O 766

o

-200 - 9 - 1 261 -2OL 33 - 7 - Q 301 -101

-

I7

-

6 -16 265 23 -131 179 129 -115

-

3 -19

-

1 -21 83 189

-

46 280 89.780 10,581,480 37,128 8,466,480 426,380

i,aw

I

1,007,760 201,552 6,iia 470,288 77.620 I

L

(94)

$1

4 a

4*

Q'

4,

$1 9%

4 s

4'

Q'

4'

-8 40 -28 62 -104 101

-

17 68 -63 68 -884 442 -7 25

-

7 -13 91 -169

-

15 44 -20 -12 676 -65.0 -6 12 7 -39 104

-

78

-

13 23 13 -47 871 -377 -6 1 15 -39 39 65

-

11 6 33 -51 429 169 -4

-

8 18 - 8 -16 17 -2 -20 13 -1 -23 7

o

-24 O 408 8,876 1.762 -24

-

36 128 - 3 - 8 3 93 17

-

88 2 31

-

66

-

85 36

o

-120

-

9 -10

-

7 -22

-

5 -31

-

3 -37

-

1 -40 42 -36 -156 42 -12 -583 35 13 -733 23 33 -683 8 44 -220 48 1 439 145

-

209

-

440 100,776 16,796 1,938 178,296

1

23.258 6,953,544 2,941,884 23,250 28,424

n=

19 -9 -8 -7 -6 -6 -4 -3 -2 -1 O 670 1 61 -204 612 -102 1,326 34

-

61)

-

68 88 -1,768 19 28 -388 98 -1.222 6 89 -453 68 234 - 6 120 -354

-

3 1,235

-

14 126 -168

-

64 1,352 -21 112 42

-

79 729

-

26 83 2?7

-

74

-

214

-

29 44 352

-

44 -1,012

-

80

O

396 O -1,320 213.180 89,148 13,666 2,288,132 24,515,700 1

f

*

3% n-21

4 s

$*

4 a

4 4

4'

A

-

10 190 -286 969 -3,876 6,460 - 9 133 -114 O 1,938 -7,106 - 8 8% 12 -Oio

3,ass

-6,392 - 7 37 98 -880 2,618

-

9i8 - 6

-

2 149 -615 788 3,996 - 5 - a 6 170 -406 -1,063 6,076 - 4 - 6 2 166 -130 -2,354 6,088 - 3 - 8 3 142 160 -2,819 2,001 - 2 - 9 8 103 386 -2,444 -1,716

-

1 -107 64 540 -1,404 -4,828

o

-110

O

594 O -5,720 770 432,630 12 1,687,020 201,894 6,720,330 614.829.70(

1

3

L

n=20

41

+a

4 a

$4

4.

+e

-

19 67 -969 1.938 -1,938 1,938

-

17 39 -357

-

102 1.122 -2,346

-

16 23 86 -1,122 1,802 -1.870

-

13 9 377 -1,402 1.222 6 -11

-

3 639 -1,187 187 1.497

-

9 -13 591

-

687

-

771 1,931

-

7 -21 653

-

77 -1,351 1,363

-

6 -27 445 603 -1,441 195

-

3 -31 287 948 -1,076

-

988

-

1 -33 99 1,188

-

396 -1,716 2,660 4,903,140 31,201,800 17,656 22,881,320 40,031,400 2 1 %?

s-P

iLp

fiö

n=22 $1

$4

$8 4 4 $6

A

-

21 36 -133 1.197 -2,261 646

-

19 25

-

67 57 969 -646

-

i7

ia

O

-

670 1,638 -546

-

15 8 40

-

810 1,598 -170

-

13 1 85

-

776 663 306 -11

-

6 77

-

563

-

363 668

-

9 -10 78

-

268 -1,158 637

-

7 -14 70 70 -1,554 303

-

5 -17 55 366 -1,509

-

30

-

3 -19 35 685 -1,079 -338

-

1 -20 12 702

-

390 -620 3,612 96,140 40,562,340 7,084 8,748,740 4.903.14 2

t

*

3% +to

(95)

.---

»=23 - _-I

A

9,

9. 9'

96

4 s -11 77 -77 1,4G3 -209 3,553 --__ - __

___

-.

-

10 66 -35 133 76 -3,230 - 9 37

-

3

-

627 171 -3,553 - 8 20 20

-

950 152 -1,292 - 7 5 35

-

955 77 1,207 - 6 - 8 43

-

747

.

-

12 2,754

-

6 -19 45

-

417

-

87 2,985

-

4 -28 42

-

42 -132 2,076

-

3 -35 35 315 -141 50 1

-

2 -40 25 605 -11G -1,166

-

1 -43 13 793

-

U 5 -2,405

o

-44 O 868 O -2,860 1,012 32,890 340.860 35,420 13,123,110 142,19 1 ,06C 1 1 . 1 1

1

1% $6 l b o

--

n = 2 6

-

___I_ 91

h

A

h

$6

4. -

12 92 -606 1,518 -1,012 19,228

-

11 69 -263 253 253 -14,421

-

10 48

-

55

-

517 748 -18,810

-

9 29 93

-

897 753

-

9,899 - 8 12 196

-

982 488 2,052 - 7 - 3 259

-

857 119 1,229

-

6 -16 287

-

597

-

236 5,142

-

6 -27 286

-

267

-

501 3,635

-

4 -36 268 78

-

636 8.028

-

3 -43 211 303

-

631 391

-

2 -48 149 $43

-

500

-

7,050

-

1 -61 77 803

-

275 -12,375 O -52 O 858 O -14,308 i .3w i,48û,û5û 7,8û3,9W n = 2 1 -I__

_ _

$1 9 9

9,

9. Or

94

- 2 1 187

-

847 33 1,463 -3,9';1

-

15 05 745 - 1 6 3 2,07 1 1,045 -13

-

17 949 -137

1

U9 3,271 -11

-

53 1,023

-

87 -1,551 3.951 _ _ _ _ _ _ _. - 23 253 -1,771 253 -4,807 4,öOî

-

19 127

-

133

-

97 3,713 -4.760

-

17 73 391 -16; 3.553 -?,14ï - 9 - 8 3 987

-

27 -2,721 3,183

-

7 -107 Slil 33 -3,171 1,410

-

3 -137 419

-

6 -125 GOB 85 -2,893

-

6U5 103 -2.005 -2.525

-

1 -143 143 143

-

715 -3,675 4,600 17,760,600 177,028,920 394,680 394,680 250,925.40i 2 3

I%

3% f ü 1% n = 2 ö

41 9,

9 a

91

A

9. -

-25 50 -1,150 2,530 -2.530 6,325 -23 38

-

598 506 500 -4,JOI -41 27

-

161

-

759 1,771 -6,072 -19 17 171 -1.419 1,881 -3,608 -17 8 408 -1,U14 1,326 46 -15 O 660 -1,470 482 3,090 -13

-

7 637 -1,099

-

377 4,672 -11 -13 649

-

599 -1,067 4,624

-

9 -18 606

-

54 -1,482 3,231

-

7 -22 518 466 -1,582 1,033

-

5 -26 395 905 -1.381 -1,340

-

3 -27 247 1.221

-

935 -3,300

-

1 -28 84 1,386

-

330 -4,400 5.850 :,aû1i,Goo 48,384,i8U n=27 ~

41 A

$4

4 4 9 6 9 6 -13 325 -130 2,990 -16,445 1,495 -11 181

-

22

-

782 10.879

-

1,403

-io

l i 8 15 -1,587 iZ,ì44

-

920 -12 260

-

70 690 2,530

-

920 - 9 61 42 -1.872 9,174

-

122 - 8 10 60 -1,770 4,188 592 - 7 - 3 6 70 -1,400

-

1,162 1,018 - 6 - 7 4 73

-

867

-

6,728 1,096

-

6 -107 ?O

-

282

-

8,803 885

-

4 -134 62 338 -10,058 424

-

3 -156 60 070

-

9,478

-

101

-

2 -170 3 6 1,285

-

7,304

-

584

-

1 -179 18 1,648

-

3,960

-

920

o

-182 O 1,638

o

-1,040 1,638 101,790 2,032,135.560 712.0ío 66,448,210 22,331,16( 3- 1 3

*

sl-

$3

1.0

--

n = 2 8 - ~ -

-91

9 8 0 3

94 A

4.

-27 117 -585 1,755

-

13,456 13,455

-

28 91 -325 455 1,495

-

7,475

-

23 67 -115

-

395 8,395

-

12,306

-

21 46

cfr

-

879 9,021

-

8,783

-

19 25 171 -1,074 7,866

-

2,163

-

17 7 255 -1,050 4,182 4,138 -16

-

9 305

-

870 22 8,310 -13

-

23 325

-

590

-

3,718 9,682 -11

-

36 319

-

259

-

6.457 8,401 - 9 - 4 5 291 81

-

7,887 6,139

-

7

-

63 245 395

-

7.931 84 1 - 6 - 5 9 186 655

-

6,701

-

3,485

-

3

-

63 115 840

-

4,456

-

6,936 - 1 - 6 6 30 936

-

1.500

-

8,840 7,308 2,103.660 ' 1,354,757,040 96,004 19,634,160 1.771.005,38 2 1

1

+i $0

Ifr

(96)

%be/

4 4

p h /

dq

Percentage Points

of

Chi-square Distribution

a n 0.995 0.99@ 0.975 0.950 0.900 0.10 0.05 0.025 0.010 0.005 1 O.ooOo39 0.00016 2 0.0100 0.0201 3 0.0717 0.115 4 0.207 5 0.412 6 0.676 7 0.989 8 1.34 9 1.73 10 2.16 11 2.60 12 3.07 13 3.57 1 4 4.07 15 4.60 i 6 5.14 i7 5.70 18 6.26 i 9 6.84 20 7.43 21 8.03 22 8.64 23 9.26 24 9.89 25 10.52 26 11.16 27 11.81 28 12.46 29 13.12 30 13.79 40 20.71 60 35.53 120 83.85 0.297 0.554 0.872 1.24 1.65 2.09 2.56 3.05 3.57 4.11 4.66 5.23 5.81 6.41 7.01 7.63 8.26 8.90 9.54 10.20 10.86 11.52 12.20 12.88 13.56 14.26 34.95 22.16 37.48 86.92 0.00098 0.0506 0.216 0.484 0.831 I .24 1.69 2.18 2.70 3.25 3.82 4.40 5.01 5.63 6.26 6.91 7.56 8.23 8.91 9.59 10.28 10.98 11.69 12.40 13.12 13.84 14.57 15.31 16.05 16.79 24.43 40.48 91.58 0.0039 0.103 0.352 0.711 1.15 1.64 2.17 2.73 3.33 3.94 4.57 5.23 5.89 6.57 7.26 7.96 8.67 9.39 10.12 10.85 11.59 15.34 13.09 13.85 14.61 15.38 16.15 16.93 17.71 i 8.49 26.51 43.19 95.70 0.0158 0.21 1 0.584

1

.O6 1.61 2.20 2.83 3.49 4.17 4.87 5.58 6.30 7.04 7.79 8.55 9.31 10.08 10.86 11.65 12.44 13.24 i4.04 14.85 15.66 16.47 17.29 18.11 18.94 19.77 20.60 29.05 46.46 100.62 2.71 4.61 6.25 7.78 9.24 10.64 12.02 13.36 14.68 15.99 17.28 18.55 19.81 21.06 22.31 23.54 24.77 25.99 27.20 28.41 29.62 30.8i 32.01 33.20 34.38 35.56 36.74 37.92 .39.09 40.26 51.81 74.40 140.23 3.84 5.99 7.81 9.49 i i .O7 12.59 14.07 15.51 16.92 18.31 19.68 21.03 22.36 23.68 25.00 26.30 27.59 28.87 30.14 31.41 32.67 33.92 35.17 36.42 37.65 38.88 40.1 1 41.34 42.56 43.77 55.76 79.08 146.57 5.02 6.63 7.88 7.38 9.21 1O.M) 9.35 11.34 12.84 11.14 13.28 14.86 12.83 15.09 16.75 14.45 16.81 18.55 16.01 18.48 20.28 17.53 20.09 21.96 19.02 21.67 23.59 20.48 23.21 25.19 21.92 24.73 26.76 23.34 26.22 28.30 24.74 27.69 29.82 26.12 29.14 31.32 27.49 30.58 32.80 28.85 32.00 34.27 30.19 33 41 35.72 31.53 34.81 37.16 32.85 36 19 38.58 34.17 37.57 40.00 35.48 38.93 41.40 36.78 40.29 42.80 38.08 41.64 44.18 39.36 42.98 45.56 40.65 44.31 46.93 41.92 45.64 48.29 43.19 46.96 49.64 44.46 48.28 50.99 45.72 49.59 52.34 46.98 50.89 53.67 59.34 63.69 66.77 83.30 88.38 91.95 152.21 158.95 163.65 ~ -

Fox n

>

120, x!,, n z r i -

2 +

where za is the desired percentage point for a s!anda:dized n orml

dktfjbution.

L

9n ~~~~ ~~ U n 0.10 0.050 0.025 0.010 0.005 1 3.078 2 1.886 3 1.638 4 1.533 5 1.476 6 1.440 7 1.415 8 1.397 9 1.383 10 1.372 11 1.363 12 1.356 13 1.350 14 1.345 15 1.341 16 1.337 17 1.333 1 8 1.330 19 1.328 20 1.325 21 1.323 22 1.321 23 1.319 24 1.318 25 1.316 26 1.315 27 1.314 28 1.313 29 1.311 30 1.310 40 1.303 60 1.396 120 1.289 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.71 1 1.708 1.706 1.703 1.701 1.699 1.697 3.684 1.671 1.658 12.706 4.303 3.182 2.776 2.511 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.021 2.000 1.980 31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.71 8 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.413 2.467 2.462 2.457 3.423 2.390 2.358 63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.01 2 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.791 2.787 2.779 2.771 3.763 2.756 2.750 3.704 2.660 2.617 a = 0.995, 0.990, 0.975, 0.950, and 0.900 follow from tn.l.-a = -tnia

(97)

(98)

3 x 3 .4 B C B C - L C A B

EXAMPLES

OF

L ~ T I N

SQUARES

4 x 4 A B C D A B C D A B C D . i B C D B A D C B C D A B D A C B 1 D C C D B A C D A B C A D B C D A B D C A B D A B C D C B . 4 D C B A

í i)

(ij) ( i i i ) (IV) 5 x 5 A B C D E B . i E C D C D A E B D E B A C E C D B A 7 x 7 A 3 C D E F G B C D E F G A C D E F C A B D E F G A B C E F C A B C D F G A B C D E G A B C D E F 6 x 6 A B C D E F B C F A D E C F B E A D D E A B F C E A D F C B F D E C B A

s

x s A B C D E F G H B C D E F G H A C D E F G H A B

D

E F

G

H A B C E F G H A B C D F G H A B C D E G H A B C D E F H A B C D E F C

73b-e/ A B

E ~ A M P L E S

OF

GRAECO-LATIN

SQUARES

3 x 3 4 x 4 -12 B/3

cl

. i a

B/3

C;)

Dil

By

Cr A,+

Bd

A;. Cr Cj? Ay BI. C/3 Dr A6

&J

D /

C6 Ba A$ I 5 x 5 7 x 7 I Ar B$ C;J D6 EE A r BP

C J

DO EE Fd Gti Bd CE Dx E3

A;$

BO CE D+ E)/ FX G,3 ,4;*

C$

Dy Eh AE Br Cij D r EP

F;,

Gij Ae Byí

DE Er .i$

B;)

C+ D:)

EO

FE Gqi Aij Bx Cb

El

A0 BE

C-A

D,3 E6 F,/ Gx A@

B I

CO D E

F$ G I 4 d BE Cqi D I , EZ

GE i d

BI/

C-Z D,;

r.*

Fd

There

is

no

6 x 6

Graeco-Latin square. Graeco-Latin

squares of Size 8 x

9 x 9. I i x i I , and 12 A i7 exist:

larger squares are unlikely

to be of

practical

(99)

RANDOM

PERMUTATIOXS OF

9 i

8 6 2 2 4 5 4 5 8 3 9 6 5 2 2 4 9 8 2 9 8 6 6 5 6 3 5 6 6 5 1 1 3 9 1 2 2 3 3 9 8 1 8 3 7 6 5 1 3 8 3 6 9 1 6 3 7 4 3 5 9 3 2 5 2 5 8 1 3 5 7 5 6 9 5 4 2 6 6 1 7 4 4 9 6 1 3 3 7 5 9 4 8 8 8 5 4 1 8 7 2 2 8 8 2 5 4 4 5 3 7 5 2 2 4 5 9 9 8 4 5 8 5 9 1 6 1 2 7 7 1 1 5 1 9 4 4 5 7 9 6 8 1 8 2 9 6 1 4 5 4 7 8 6 9 7 4 2 5 2 2 5 5 4 4 4 8 8 1 3 9 7 6 6 8 1 9 9 1 1 3 9 4 1 9 3 3 3 7 3 6 5 1 4 1 1 5 9 1 1 2 9 9 3 8 8 6 2 5 7 9 1 8 4 8 1 7 9 7 6 2 1 7 4 3 8 2 7 3 7 C I 1 6 C 6 6 4 2 6 6 5 7 2 4 3 3 5 6 6 2 8 7 5 2 8 2 6 1 7 2 7 4 6 3 5 3 7 9 2 8 7 7 9 1 3 3 1 1 3 4 7 7 7 7 6 3 3 9 8 1 8 2 5 1 9 1 6 5 8 1 2 3 2 3 7 2 3 7 4 7 9 9 4 6 6 5 3 4 8 9 5 3 8 2 1 6 4 4 6 8 4 9 9 1 4 3 3 7 9 9 3 4 5 9 3 2 3 6 1 2 3 7 5 9 6 1 7 5 4 8 4 5 9 1 3 7 1 8 5 7 1 9 1 3 6 9 8 1 5 6 4 4 9 2 7 4 9 8 2 4 7 2 1 9 6 7 2 8 7 5 5 6 6 2 8 8 4 3 7 2 5 7 3 1 5 5 3 2 5 5 2 2 9 6 7 2 5 9 5 3 2 6 1 8 6 2 4 3 9 6 5 6 2 1 3 4 5 6 3 9 3 2 4 4 4 7 5 1 7 2 9 8 6 8 5 9 9 2 5 9 3 2 2 s 2 9 2 4 8 4 2 6 4 2 7 9 7 5 6

}

8 9 4 3 3 3 6 1 2 7 2 8 8 6 9 4 8 7 7 4 1 2 5 9 4 7 6 1 2 7 2 8 6 7 3 1 1 6 2 1 8 4 6 4 1 9 1 1 3 2 2 1 8 5 7 3 7 5 6 2 5 8 2 9 6 4 7 1 3 7

,

3 8 1 6 4 1 3 9 3 3 7 5 3 5 4 1 9 3 1 6 5 6 1 5 5 8 7 3 8 4 1 1 9 1 8 I 9 6 8 7 5 5 8 4 7 6 4 3 7 7 3 7 6 5 4 3 9 4 7 8 6 1 1 9 7 8 8 6 8 8 9 7 4 2 4 2 1 2 2 6 2 8 6 5 2 2 6 1 8 4 7 1 2 1 8 3 9 7 7 4 3 4 6 1 4 7 8 5 9 8 7 8 3 9 2 3 1 1 6 5 9 7 7 2 9 3 5 4 4 7 8 3 4 1 1 7 6 5 8 1 6 9 6 4 5 9 3 1 3 7 5 7 4 2 8 8 9 9 4 5 8 2 9 6 1 7 4 6 3 3 6 9 8 3 7 8 1 7 7 6 3 6 6 7 4 8 9 7 1 6 7 1 5 7 8 5 6 5 2 4 6 6 2 5 9 8 1 4 5 9 2 2 2 8 7 5 5 9 1 5 9 5 5 9 4 6 2 3 3 6 4 7 6 5 3 4 2 5 6 7 4 7 1 9 5 4 5 9 1 2 1 4 8 5 1 6 6 9 3 9 4 3 4 9 2 9 9 1 9 2 1 7 9 2 6 1 3 3 2 2 9 6 3 6 1 6 7 7 8 9 4 3 8 4 1 3 5 6 5 1 1 8 8 8 9 2 5 3 4 5 2 5 7 7 8 5 4 1 5 9 8 2 5 4 3 7 4 3 8 3 5 8 2 6 3 6 4 7 7 6 9 8 8 9 2 3 2 2 4 6 1 3 8 3 3 4 9 4 6 8 1 2 2 7 7 1 4 8 1 7 2 3 3 3 5 5 1 1 8 8 9 8 9 6 3 3 9 7 5 9 7 3 2 3 5 8 1 1 7 6 1 2 2 6 6 3 7 3 8 2 7 4 1 7 6 7 8 9 1 3 7 2 5 7 7 5 2 6 6 7 2 2 7 8 1 3 4 8 8 5 9 8 1 9 8 9 7 9 3 8 8 9 2 1 9 2 7 2 3 3 9 5 1 7 4 4 5 3 2 7 6 7 3 2 3 2 3 8 6 b 5 8 3 8 2 6 5 6 2 8 1 4 4 8 5 2 4 9 5 1 9 8 2 4 5 5 9 9 9 4 5 1 4 3 4 6 9 5 6 9 3 7 8 8 4 9 5 3 9 8 8 1 5 2 9 6 6 4 5 9 4 5 5 5 7 7 9 6 2 9 i 6 8 4 4 2 3 7 7 6 8 6 6 1 4 6 9 3 1 2 7 4 8 9 4 2 6 7 1 2 8 4 7 7 7 3 5 4 9 3 9 1 1 6 1 5 3 9 4 6 4 7 4 9 3 5 9 9 6 2 8 3 1 7 8 4 6 2 5 5 4 1 6 1 7 4 4 4 9 2 6 8 8 2 2 1 6 7 8 6 3 7 6 1 8 7 8 6 4 9 1 2 9 4 1 8 3 7 5 5 1 2 3 3 7 4 1 1 6 1 3 8 8 4 8 1 3 5 3 3 9 1 4 3 1 6 5 5 1 3 2 2 2 2 1 5 6 5 5 5 3 2 5 6 6 5 4 2 8 3 2 4 8 6 2 6 4 2 4 1 3 9 8 1 9 7 4 7 4 9 6 1 3 4 1 4 8 1 1 5 7 6 5 7 1 8 7 7 2 7 8 3 1 1 6 8 3 7 2 6 5 8 5 6 7 2 4 1 9 5 9 4 9 2 3 9 3 6 6 6 6 3 4 3 4 7 5 8 2 3 5 8 1 6 7 1 3 2 8 2 4 3 2 8 7 3 7 8 4 8 1 9 4 4 9 3 5 6 8 3 5 1 9 3 9 6 6 2 8 3 2 5 3 1 6 9 5 4 7 6 5 5 4 5 7 2 2 3 9 4 5 9 9 4 8 2 9 3 5 4 9 1 5 3 4 4 6 4 9 4 8 2 5 3 4 1 3 2 3 9 6 1 8 1 7 7 6 5 1 6 9 7 5 6 2 4 7 6 7 8 8 1 1 5 8 3 6 7 1 3 6 1 6 9 2 3 5 7 3 2 9 2 3 7 1 1 6 7 7 7 1 5 3 5 5 6 9 8 3 3 1 7 6 6 9 8 6 3 7 1 8 8 9 2 8 4 1 1 9 9 3 2 4 9 3 7 2 4 9 2 9 2 6 2 1 7 9 8 5 2 7 9 7 8 4 4 7 1 5 5 1 8 2 5 5 4 8 6 8 8 2 4 9 4 1 3 7 9 7 5 5 8 9 2 8 2

Taken, by permission

of the authors

and publisher, from

9

15.5 of Expei.inzenta!

I

d e s i v s by W.

6. Cochran and

6.

M.

Cox,

John

Wile! and Sons, New

York.

(100)

7 12 15 15

1

13 3 8 16 7 3 1 4 5 1 4 I 1 8 16 14 15 1 4 9 1 6 3 2 16 10 13 5 4 6 1 3 7 2 6 14 6 10 4 10 15 2

1

13 12 10 7 12 9 15 7 5 2 10 16 2 11 8 8 9 13 14 3 6 8 11 9 4 11 I 5 12 i1 16 5 4 3 9 1 2 i1 8 16 5 5 2 2 8 8 1 4 6 1 3 2 13 6 14 12 4 16 16 8 6 3 9 4 9 15 12 10 3 3 10 11 12 13 16

1

13 14 8

1

14 14 2 9 4 4 6 4 1 2 15 5

1

11 10 5 3 5 6 7 12 7 15 15 15 10 11 10 3 2 7 9 7 7 1 1 13 16 9 1 1 1 6 7 4 8 9 I5 11 3 11 10 16 4 5 12 4 1 4 1 9 5 7 3 13 14 15 16 l i 2

1

14 3 10 16 16 13 11 13 9 13 4 15 2 3 12 9 14 1 14 6 10 13 12 5 11 3 22 6 10 7 2 8

9

8 1 0 6 2 7 6 2 1 6 4 15 8 16 5 8 12 15 7 1 3 4 10 4 16 5 1 4 4 6 8 2 2 2 15 14 7 12 15 8 1 2 6 9 7 1 4 9 14 5 16 7 10 15 11 8 9 7 1 1 6 6 1 4 4 10 3 16 2 1 8 1 1 3 1 9 7 1 4 2 6 12 1 9 10 15 3 3 12 11 5 10 15 11 5 13 8 13 13 3 3 16 i 6 5 1 2 11 _- - ._

RANDOM

PERMUTATIONS OF 16 2 7 16 10 2 10 11 10 13 5 13 3 14 9 13 6 2 6 2 1 6 9 14 13 8 6 5 13 2 11 7 i 5 1 9 1 4 14 4 15 3 3 12 16 3 4 8 11 9 8 12 14 7 8 12 6 15 8 15 5 16 1 4 10 11 5 12 3 12 7 7 10 16 5 4 14 9 1 6 1 15 11 13 1 13 2 16 16 4 3 8 I1 5 9 15 11 10 11 14 10 5 12 10 6 4 16 2 2 12 6

1

15 12 5 11 7 8 14 15 5 3 7 15 16 1 4 6 14 3 11 8 15 9 6 3 7 1 0 5 7 13 2 14 3 9 8 12 12 13 4 2 1 4 6

1

7 l t . 13 1 8 1 0 9 9 4 6 5 2 8 1 5 15 9 10 I 3 9 16 li 7

1

5 4 1 3 6 8 2

1

1 4 16 5 1 6 6 9 3 4 7 13 1 11 14 13 8 3 5 13 12 2 4 13 10 1 3 1 2 4 2 11 15 8 2 7 14 7 15 14 16 4 11 7 10 11 8 10 6 15 12 10 14 16 9 6 3 12 5 12 9 13 16 13 5 3 2 15 1 13 14 16 9 12 16 6 3 5 14 7 12 14 10 11 15 11 8 I1 8 14 13 12 8 7

1

15

1

3 16 12 5 1 1 7 9 6 9 15 4 4 11 4 4 14 10 9 8 5 2 3 5 10 2 9 6 6 3 1 0 7 1 2 5 2 7 10 13 2 4 1 6 1 3 8 1 6 14 15 7 13

13

11 7 13 16 i 13 2 9 1.5 6 8 5 1 2 3 9 5 8 1 4 7 3 3 12 5 14 12 7 10 6 9 11 4 1 6 2 6 5 10 1 15 5 14 15 4 11 8 i 6 6 13 16 12 15 1 9 8 1 8 9 3 1 0 4 4 12 14 3 10

1

16 11 1 2 10 2 6 4 1 1 2 14 12 9

a

i 10 14 15 1 2 12 6 16 15 16 3 3 12 1 4 15 2 9 8 1 6 4 4 1 3 7 7 9 9 5 14 11 10 11 15 6 12 5 7 8 3 13 11 8 1 1 3 6 3 5 11 10 10 1 2 16 4 5 5 13 15 10 1 4 6 6 7 11 9 14 1 3 2 4 2 1 1 1 6 2 3 8 4 6 6 1 4 8 2 1 5 7 9 7 I 6 11 8 3 15 5 12 5 7 14 9 2 16 1 16 1 4 3 15

11

9 10 16 2 10 10 12 5 12 5 3 1 3 14 4 2 2 4 13 3 16 11 7 8 14 6 13

1

9 10 I 2 6 8 4 9 8

1

11 i 11 1 3 12 3 10 6 1 4 5 15

1

13 15 6 1 4 1 16 8 16 4 15 4 3 10 15 14 9 10 5 13 16 1 7 12 I 12 12 14 7 11 6 3 11 9 3 3 7 1 3 4 9 13 13 6 1 8 4 1 1 5 2 1 6 5 8 1 15 10 7 10 9 1 4 2 8 2 4 13 12 9 6 2 11 5 10 15 12 8 6 11 14 15 3 7 2 5 1 6 10 6 i 8 10 7 5 13 2 14 2 8 4 5 8 13 4 3 10 4 15 13 11 4 7 16 L L 9 15 9 7 € 1 6 l i 1 1 2 10 6 9 12 14 1- ? 2 8 9 14 14

1

4 1: 8 12 6 14 16 5 13 5 3 1 0 9 i 3 6 15 Iô 1.5 1 2 5 1 15 7 13 11 3 7 11 16 5 13 3 1 3 3 l i 4 5 15 5 9 10 12 l b 15 13 6 4 1 16 6 5 1 5 'i S 12 14 8 8 i 1 1 3 1 3 3 5 i 11 1 1 4 4 8 i 7 1 2 7 3 1.5 9 9 I? 15 16 l i 5 2 4 9 1 6 2 6 16 2 6 11 1 10 8 i i 4 13 2 I? 2 10 14 1 4 1 10 6 10 5 7 13 2 10 X 16 1 14 3 3 1 2 2 3 4 16 5 11 8 1 12 6 14 4 13 11 3 9 I? 5 2 10 'i 10 16 1 4 1'3 16 5 6 I 1 4 S 6 I? 9 a 3 i 1 4 4 4 4 15 11 10 i1

io

5 8 15 8 6 11 9 6 1 15 13 15 7 2 12 16 'i 13 15 5

1

2 7 2 3 3 1 2 12 12 1 4 7 1 14 8 8 16 5 1 1 2 9 3 16 3 11 11 s 4 4 6 6 9 l i 10 4 5

1

8 15 9 1 14 2 16 I0 12 4 9 5 12 16 6 10 6 14 10 11 1 3 8 5 15 5 15 7 15 7 13 3 1 13 13 10 6 9 1 6 2 2 14 13 7 14 15

Taken.

by

permission of the authors and publisher. from

4 15.5 of Expertinental

(101)

Korte handleiding voor gebruik van programma XEO

voor

statische theorie

van

proefopzetten.

Rev

2 . 1

---

Aanmaken van het programma:

R

' WERKIE

>XPD

.

CPL

'

Syntax

van

de invoerfile XPD.IN:

(aantal

metingen}

<model

>

<waarnemingen>

waarin

:

(aantal

metingen>

=

aantal uitgevoerde metingen, indien

een

nul ingevoerd wordt, worden alle

waarnemingen in de invoerfile

%remerkt.

<model>

=

definitie

van

hei-

model, dat wordt opgebouwd met

orthogonale polynomen. De syntax van het blok

<model> is als volgt:

{aantal variabelen>

--.-

- -~

VVLIL

elke

variabele

:

<max

orde van polynoom,aan%al njveaus,minimumlmaximu~>

voor elke variabele:

<max orde van polynoom in hoofdeffekt>

voor elke variabele:

<lambdal, fambda2,

. . .

lambda(max

orde pul)>

<equidistant>

met <equidistant>

=

J

<equidistant>

=

N

als

niveaus equidistant zijn

a l s

niveaus

niet

equi-distant

zijn.

<aantal interaktietermen in

model>

voor elke interaktieterm:

(aantaal variabelen In die interaktieterm>

<variabelel,ordel,variabele2,orde2

. . .

>

(102)

<waarnemingen>

=

voor elke waarneming:

<waarde variabelel, waarde variabele2

. . .

waarde laatste variabele, waarneming>

Voorbeeld:

25

2 3,s

I

1 ,

20 3,5,.047,.163

2

1 1,1,.8333333333,2.

1,1,.8333333333,2.

3

2 1,1,2'1

2 112,2,1

2 1,1,212

1.00,0.047,16.^0

f.00,0.016,16.22

1.00,0.105,16.45

1.00,0.134,16.70

1.00,0.163,17.02

5.75,0.@?7,

3.32 5.15,0.076, 6.52

5.?5,@,?05;

9 . 8 1

5.15,0.134,12.94

5.75,0.163,14.67

10.50,0.047,13.05

10.50,0.076,

3.36 10.50,0.105,

6.10 10.50,0.134,

9.24 10.50,0.163,12.23

15.25,0.047,12.81

15.25,0.076,13.19

15.25,0.105,

3.87 15.25,0.134,

6.98 15.25,0.163,

9.94 20.00,0.047,12.82

/*aantal metingen

/*aantal variabelen

/*voor variable

x ( l )

geldt:

/*hoogste

orde: 3

/*aantal niveaus: 5

/*minimum

waardc

van xil):

'1

/*maximum

waarde van

X U ) :

20 /*voor variable x(2) geldt:

/*hoogste orde: 3

/*aantal niveaus: 5

/*minimum waasde van x(2): 0.647

/*maximum waarde van x(2):

0 . 1 6 3

/*hoofdeffekt

x(l)

tot tweede orde

/*hoofdeffekt x12) tot eerste orde

916666661 /*lambdal tot lambda4 voor

x(1)

916666667 /*lambdal tot lambda4 voor

x ( 2 )

/*niveaus zijn equidistant

/*aantal interaktie termen in model

/*twee variabelen in interaktie

1 / *

interaktie

1 =

x(l)*x(2)

/*twee variabelen in interaktie

2 /*interaktie

2 =

**( x ( l ) * * 2 ) * x [ 2 )**

**/*twee**

variabele:: in ii,trxaktie

3 /*Enteraktie 3

=

x(I)*(x(2)**2f)

/*waarde

x(lj

;waarde ~ ( 2 1 ,

waargenomen

y

(103)

20.00,0.076,13.15

20.00,0.105,

3 . 5 0 3

20.00,0.134,

5 . 5 8

20.00,0.163,

8 . 1 7

Opstarten van het programma:

SEG

XPD

Resultaten in file XPD.OUT:

# # #

DESIGN AND ANALYSIS OF EXPERIMENTS

# # #

. . .

Echo van het beschreven model, met daarin opgenomen eer?

definitie

voor

de nummering van de interakties. Deze

nummering wordt verder bij het geven van de resultaten gebruikt.

Rev 2.1

N U M ~ E R

O F

VARIABLES:

2 N U M ~ E ~

OF ~ A R ~ M ~ T ~ ~ S :

7 NAIN

EFFECTS

:

VARIABLE HIGHEST ORDER

1

2

1 INTERACTIONS:

NUMEER VARIABLE

POWER

1

2

1

2

1

2

3

3 i

1

2

(104)

VARIABLE LAMBDA?

LAMBDA2

1 0.10OE

O 1

0.100E

O 1

2 O.?OOE O1

LAMBDA3

LAMBDA4

LAMEDAS

LAMBDA6

Gegeven worden resultaten van de berekeningen voor het

parameter schatten. Gegeven worden de matrix

(XT.Xj,

de matrix

**(XT.X)inverse, en de schatters**

voor

de parameters.

De betekenis van rij- en kolomindex bij de matrices kan

worden opgezocht bij de schatters voor de parameters.

# # #

# # # % # # # # # # #

fl

# # # # # # #

w

#

!!

44 # #

# # #

?ARANETER ESTIMATION

# # #

. . .

* * *

E X P E ~ I ~ E N T

EESIGN

IS ORT~OGONAL

* * *

NUMBER

O F

~ A R ~ M E T ~ R ~ :

N ~ ~ l ~ E R

O F

OBSERVATIONS

:

7

25 MATRIX (XT.X):

1

1 0.25000E 02

2 0.00000E

O0

3 0.00000E

O0

4 0.OÛÛO0E

ÛÛ

5 0.00000E

@O

6 O.OO090E

OO

7 0.00000E

O0

2

3

4

5 0.00000E

O0

0.00000E

O0

0.00000E

O0

0.OOOOOE

O0

0.50000E

O2

0.00000E

00 0.000OOE

O0

0.OOOOOE

O0

0.00000E

O0

0.70000E

O2

0.00000E

O0

0.OOOOOE

O0

O.OOÛOOE

O0

0.OOOOOE

OV

Q.5OVOVE

O2

O.OOOOOM

O0

0.00000E

O0

0.00000E

O0

0.00000E

o0 0.10000E

o 3

V.OQGOr3E

00 (2.0OOIOE

O0

0.OOOOOE

O0

0.00000E

O0

0.00000E

O0

0.OOOOOE

O0

0.OOOOOE

O0

O.OOO0OE

O0

MATRIX (XT.X)-1 (INVERSE):

I

2

3

4

5

1 0.40000E-01 0.000OOE

O0

0.OOOOOE

O0

0.00000E

O0

0.OOOOOE

O0

2 0.0OOOOE

O0

0.2OOOOE-CI 0.000OOE

O0

O.0000OE

O0

0.00000E

O0

3 0.00000E

O0

0.00000E

O0

0.14286E-01 0.00000E

O0

0.00000E

O0

(105)

H Id 13 M 3a

n

w N 2 i-3 N -a --L

0

H O

z

4 & (AJ w *.

.

M...

.

b3 4.4 21

n

.a w

-

.a -4 00 u2

z

w OD W

o

CIi 03 05 tD” 4 LO 4 Ul & ul

-

e

w

o

cn Lrl -a O OM O 00 WO PYMM MMMM

000 O000

O00

OO-LN i/

z

II xd II i-3 li P I:-JcnvlrpwN- H I1

x

/I

110000000

-

Ik...

*

..

iio~ooooo

*

lIo-00000

13 II OA00000 3 I/ 0NOO000 110~00000

x,

I!

mmmmmMtam-

iioc>ooooo

3.

h II 0N00000 II I/ n

110000000

z

C

11

*

.

:I

4008000

M

11-000000

cd

ll~000000

rn

llwooOOoO M llW000OOO

-

iI

MMmmMMm4..

il I I1

0000000

11

NOOOOOO

-.I~UIA

0000

O000 O000 0000 O000 O000

M

1’1

....

O000

0000

o000

....

O000 O000 O000

0000

MMMM OOQO OOQO

0000

....

O000 O000

OOQO

O000

0000

mmmm

O000

o000

O000

...

I

O000

OOO-.

O000

I...

I