doepp reduced presentation5.ppt

8/19/2019 DOEpp Reduced PRESENTATION5.ppt

1/81

1

DESIGN OF EXPERIMENTS by

R. C. Baker

How to gain ! year" o# e$%erien&e inone "'ort week(


2/81

Ro)e o# DOE in Pro&e"" I*%ro+e*ent

, DOE i" a #or*a) *at'e*ati&a) *et'o- #or"y"te*ati&a))y %)anning an- &on-&ting "&ienti#i&

"t-ie" t'at &'ange e$%eri*enta) +ariab)e"

toget'er in or-er to -eter*ine t'eir e##e&t o# a

gi+en re"%on"e.

, DOE *ake" &ontro))e- &'ange" to in%t

+ariab)e" in or-er to gain *a$i** a*ont" o#

in#or*ation on &a"e an- e##e&t re)ation"'i%"

wit' a *ini** "a*%)e "i/e.


3/81

0


, DOE i" *ore e##i&ient t'at a "tan-ar-

a%%roa&' o# &'anging one +ariab)e at a

ti*e2 in or-er to ob"er+e t'e +ariab)e3"

i*%a&t on a gi+en re"%on"e.

, DOE generate" in#or*ation on t'e e##e&t

+ario" #a&tor" 'a+e on a re"%on"e +ariab)ean- in "o*e &a"e" *ay be ab)e to -eter*ine

o%ti*a) "etting" #or t'o"e #a&tor".


4/81

4


, DOE en&orage" brain"tor*ing2 a&ti+itie"

a""o&iate- wit' -i"&""ing key #a&tor" t'at *ay

a##e&t a gi+en re"%on"e an- a))ow" t'e

e$%eri*enter to i-enti#y t'e key2 #a&tor" #or#tre "t-ie".

, DOE i" rea-i)y "%%orte- by n*ero" "tati"ti&a)"o#tware %a&kage" a+ai)ab)e on t'e *arket.


5/81

5

B6SIC STEPS IN DOE

, For e)e*ent" a""o&iate- wit' DOE7

, 1. T'e -e"ign o# t'e e$%eri*ent8

, . T'e &o))e&tion o# t'e -ata8

, 0. T'e "tati"ti&a) ana)y"i" o# t'e -ata8 an-

, 4. T'e &on&)"ion" rea&'e- an-re&o**en-ation" *a-e a" a re")t o# t'e

e$%eri*ent.


6/81

9

TERMINO:OG;

, Re%)i&ation < re%etition o# a ba"i&

e$%eri*ent wit'ot &'anging any #a&tor

"etting"8 a))ow" t'e e$%eri*enter to e"ti*ate

t'e e$%eri*enta) error =noi"e> in t'e "y"te*"e- to -eter*ine w'et'er ob"er+e-

-i##eren&e" in t'e -ata are rea)2 or ?"t

noi"e28 a))ow" t'e e$%eri*enter to obtain*ore "tati"ti&a) %ower =abi)ity to i-enti#y

"*a)) e##e&t">


7/81

@

TERMINO:OG;

, .Ran-o*i/ation < a "tati"ti&a) too) "e- to *ini*i/e %otentia) n&ontro))ab)e bia"e" in t'e e$%eri*ent by

ran-o*)y a""igning *ateria)8 %eo%)e8 or-er t'at

e$%eri*enta) tria)" are &on-&te-8 or any ot'er#a&tor not n-er t'e &ontro) o# t'e e$%eri*enter.

Re")t" in a+eraging ot2 t'e e##e&t" o# t'e

e$traneo" #a&tor" t'at *ay be %re"ent in or-er to

*ini*i/e t'e ri"k o# t'e"e #a&tor" a##e&ting t'e

e$%eri*enta) re")t".


8/81

A

TERMINO:OG;

, B)o&king < te&'nie "e- to in&rea"e t'e %re&i"ion o# an e$%eri*ent by breaking t'e

e$%eri*ent into 'o*ogeneo" "eg*ent"

=b)o&k"> in or-er to &ontro) any %otentia)

b)o&k to b)o&k +ariabi)ity =*)ti%)e )ot" o#

raw *ateria)8 "e+era) "'i#t"8 "e+era)

*a&'ine"8 "e+era) in"%e&tor">. 6ny e##e&t"

on t'e e$%eri*enta) re")t" a" a re")t o# t'e b)o&king #a&tor wi)) be i-enti#ie- an-

*ini*i/e-.


9/81

TERMINO:OG;

, Con#on-ing 6 &on&e%t t'at ba"i&a))y *ean" t'at

*)ti%)e e##e&t" are tie- toget'er into one %arente##e&t an- &annot be "e%arate-. For e$a*%)e8

, 1. Two %eo%)e #)i%%ing two -i##erent &oin" wo)-

re")t in t'e e##e&t o# t'e %er"on an- t'e e##e&t o#

t'e &oin to be &on#on-e-

, . 6" e$%eri*ent" get )arge8 'ig'er or-er

intera&tion" =-i"&""e- )ater> are &on#on-e- wit'

)ower or-er intera&tion" or *ain e##e&t.


10/81

1!

TERMINO:OG;

, Fa&tor" < e$%eri*enta) #a&tor" orin-e%en-ent +ariab)e" =&ontino" or

-i"&rete> an in+e"tigator *ani%)ate" to

&a%tre any &'ange" in t'e ot%t o# t'e

%ro&e"". Ot'er #a&tor" o# &on&ern are t'o"e

t'at are n&ontro))ab)e an- t'o"e w'i&' are

&ontro))ab)e bt 'e)- &on"tant -ring t'e

e$%eri*enta) rn".


11/81

11

TERMINO:OG;

, Re"%on"e" < -e%en-ent +ariab)e *ea"re-to -e"&ribe t'e ot%t o# t'e %ro&e"".

, Treat*ent Co*bination" =rn> <e$%eri*enta) tria) w'ere a)) #a&tor" are "et

at a "%e&i#ie- )e+e).


12/81

1

TERMINO:OG;

, Fi$e- E##e&t" Mo-e) I# t'e treat*ent)e+e)" are "%e&i#i&a))y &'o"en by t'ee$%eri*enter8 t'en &on&)"ion" rea&'e-wi)) on)y a%%)y to t'o"e )e+e)".

, Ran-o* E##e&t" Mo-e) < I# t'e treat*ent)e+e)" are ran-o*)y &'o"en #ro* a %o%)ation o# *any %o""ib)e treat*ent

)e+e)"8 t'en &on&)"ion" rea&'e- &an bee$ten-e- to a)) treat*ent )e+e)" in t'e %o%)ation.


13/81

10

P:6NNING 6 DOE

, E+eryone in+o)+e- in t'e e$%eri*ent "'o)-'a+e a &)ear i-ea in a-+an&e o# e$a&t)y w'at

i" to be "t-ie-8 t'e ob?e&ti+e" o# t'e

e$%eri*ent8 t'e e"tion" one 'o%e" toan"wer an- t'e re")t" anti&i%ate-


14/81

14

P:6NNING 6 DOE

, Se)e&t a re"%on"e-e%en-ent +ariab)e=+ariab)e"> t'at wi)) %ro+i-e in#or*ation

abot t'e %rob)e* n-er "t-y an- t'e

%ro%o"e- *ea"re*ent *et'o- #or t'i"re"%on"e +ariab)e8 in&)-ing an

n-er"tan-ing o# t'e *ea"re*ent "y"te*

+ariabi)ity


15/81

15

P:6NNING 6 DOE

, Se)e&t t'e in-e%en-ent +ariab)e"#a&tor"=antitati+e or a)itati+e> to be

in+e"tigate- in t'e e$%eri*ent8 t'e n*ber

o# )e+e)" #or ea&' #a&tor8 an- t'e )e+e)" o#ea&' #a&tor &'o"en eit'er "%e&i#i&a))y =#i$e-

e##e&t" *o-e)> or ran-o*)y =ran-o* e##e&t"

*o-e)>.


16/81

19

P:6NNING 6 DOE

, C'oo"e an a%%ro%riate e$%eri*enta) -e"ign

=re)ati+e)y "i*%)e -e"ign an- ana)y"i" *et'o-" are

a)*o"t a)way" be"t> t'at wi)) a))ow yor e$%eri*enta)

e"tion" to be an"were- on&e t'e -ata i" &o))e&te-

an- ana)y/e-8 kee%ing in *in- tra-eo##" between"tati"ti&a) %ower an- e&ono*i& e##i&ien&y. 6t t'i"

%oint in ti*e it i" genera))y "e#) to "i*)ate t'e

"t-y by generating an- ana)y/ing arti#i&ia) -ata to

in"re t'at e$%eri*enta) e"tion" &an be an"were-

a" a re")t o# &on-&ting yor e$%eri*ent


17/81

1@

P:6NNING 6 DOE

, Per#or* t'e e$%eri*ent =&o))e&t -ata> %aying %arti&)ar attention "&' t'ing" a"

ran-o*i/ation an- *ea"re*ent "y"te*

a&&ra&y8 w'i)e *aintaining a" ni#or* ane$%eri*enta) en+iron*ent a" %o""ib)e.

How t'e -ata are to be &o))e&te- i" a &riti&a)

"tage in DOE


18/81

1A

P:6NNING 6 DOE

, 6na)y/e t'e -ata "ing t'e a%%ro%riate"tati"ti&a) *o-e) in"ring t'at attention i"

%ai- to &'e&king t'e *o-e) a&&ra&y by

+a)i-ating n-er)ying a""*%tion"a""o&iate- wit' t'e *o-e). Be )ibera) in t'e

ti)i/ation o# a)) too)"8 in&)-ing gra%'i&a)

te&'nie"8 a+ai)ab)e in t'e "tati"ti&a)"o#tware %a&kage to in"re t'at a *a$i**

a*ont o# in#or*ation i" generate-


19/81

1

P:6NNING 6 DOE

, Ba"e- on t'e re")t" o# t'e ana)y"i"8 -raw&on&)"ion"in#eren&e" abot t'e re")t"8

inter%ret t'e %'y"i&a) *eaning o# t'e"e

re")t"8 -eter*ine t'e %ra&ti&a) "igni#i&an&eo# t'e #in-ing"8 an- *ake re&o**en-ation"

#or a &or"e o# a&tion in&)-ing #rt'er

e$%eri*ent"


20/81

!

SIMP:E COMP6R6TIE EXPERIMENTS

, Sing)e Mean Hy%ot'e"i" Te"t

, Di##eren&e in Mean" Hy%ot'e"i" Te"t wit'

Ea) arian&e"

, Di##eren&e in Mean" Hy%ot'e"i" Te"t wit'nea) arian&e"

, Di##eren&e in arian&e" Hy%ot'e"i" Te"t

, Paire- Di##eren&e in Mean Hy%ot'e"i" Te"t

, One ay 6na)y"i" o# arian&e


21/81

1

CRITIC6: ISSES 6SSOCI6TED ITH

SIMP:E COMP6R6TIE EXPERIMENTS

, How :arge a Sa*%)e S'o)- e Take

, 'y Doe" t'e Sa*%)e Si/e Matter

6nyway

, 'at Jin- o# Prote&tion Do e Ha+e

6""o&iate- wit' Re?e&ting Goo-2 St##

, 'at Jin- o# Prote&tion Do e Ha+e

6""o&iate- wit' 6&&e%ting Ba-2 St##


22/81

Sing)e Mean Hy%ot'e"i" Te"t

, 6#ter a %ro-&tion rn o# 1 o/. bott)e"8&on&ern i" e$%re""e- abot t'e %o""ibi)ity t'at

t'e a+erage #i)) i" too )ow.

, Ho7 µ K 1

, Ha7 µ L 1

, )e+e) o# "igni#i&an&e K α K .!5, "a*%)e "i/e K

, SPEC FOR THE ME6N7 1 .1


23/81

0

Sing)e Mean Hy%ot'e"i" Te"t

, Sa*%)e *ean K 11.

, Sa*%)e "tan-ar- -e+iation K !.15

, Sa*%)e "i/e K

, Co*%te- t "tati"ti& K .!, Pa)e K !.!A!519

, CONC:SION7 Sin&e Pa)e .!58 yo

#ai) to re?e&t 'y%ot'e"i" an- "'i% %ro-&t.


24/81

4

Sing)e Mean Hy%ot'e"i" Te"t Power Cr+e

Power Cr+ea)%'a K !.!58 "ig*a K !.15

Tre Mean

P o w e r

11.A 11. 1 1.1 1.!

!.

!.4

!.9

!.A

1

Si ) M H ' i T P


25/81

5

Sing)e Mean Hy%ot'e"i" Te"t Power

Cr+e Di##erent Sa*%)e Si/e"


26/81

9

DIFFERENCE IN ME6NS E6:

6RI6NCES

, Ho7 µ1 = µ2

, Ha7 µ1 µ2

, )e+e) o# "igni#i&an&e K α K .!5

, "a*%)e "i/e" bot' K 15

, 6""*%tion7 σ1 K σ2 ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗

, Sa*%)e *ean" K 11.A an- 1.1

, Sa*%)e "tan-ar- -e+iation" K !.1 an- !.

, Sa*%)e "i/e" K 15 an- 15


27/81

@

DIFFERENCE IN ME6NS E6: 6RI6NCES

Can yo -ete&t t'i" -i##eren&e


28/81

A

DIFFERENCE IN ME6NS E6:

6RI6NCES


29/81

DIFFERENCE IN ME6NS nE6:

6RI6NCES

, Sa*e a" t'e Ea) arian&e2 &a"e e$&e%t

t'e +arian&e" are not a""*e- ea).

, How -o yo know i# it i" rea"onab)e to

a""*e t'at +arian&e" are ea) OR

nea)


30/81

0!

DIFFERENCE IN 6RI6NCE

H;POTHESIS TEST

, Sa*e e$a*%)e a" Di##eren&e in Mean7

, Sa*%)e "tan-ar- -e+iation" K !.1 an- !.

, Sa*%)e "i/e" K 15 an- 15

,

, N)) Hy%ot'e"i"7 ratio o# +arian&e" K 1.!

, 6)ternati+e7 not ea)

, Co*%te- F "tati"ti& K !.5

, Pa)e K !.!14!!@1

, Re?e&t t'e n)) 'y%ot'e"i" #or a)%'a K !.!5.


31/81

01


H;POTHESIS TEST

Can yo -ete&t t'i" -i##eren&e


32/81

0


H;POTHESIS TEST POER CRE


33/81

00

P6IRED DIFFERENCE IN ME6NS

H;POTHESIS TEST

, Two -i##erent in"%e&tor" ea&' *ea"re 1! %art" on t'e "a*e %ie&e o# te"t ei%*ent.

, N)) 'y%ot'e"i"7 DIFFERENCE IN ME6NS

K !.!, 6)ternati+e7 not ea)

, Co*%te- t "tati"ti& K 1.@!

, Pa)e K !.5!44

, Do not re?e&t t'e n)) 'y%ot'e"i" #or a)%'a K

!.!5.


34/81

04

P6IRED DIFFERENCE IN ME6NS

H;POTHESIS TEST POER CRE

Power Cr+e

a)%'a K !.!58 "ig*a K 0.A99

Di##eren&e in Mean"

P o w e r

5 4 0 1 ! 1 0 4 5

!

!.

!.4

!.9

!.A

1


35/81

05

ONE 6; 6N6:;SIS OF 6RI6NCE

, "e- to te"t 'y%ot'e"i" t'at t'e *ean" o#

"e+era) %o%)ation" are ea).

, E$a*%)e7 Pro-&tion )ine 'a" @ #i)) nee-)e" an-yo wi"' to a""e"" w'et'er or not t'e a+erage

#i)) i" t'e "a*e #or a)) @ nee-)e".

, E$%eri*ent7 "a*%)e ! #i))" #ro* ea&' o# t'e nee-)e" an- te"t at 5Q )e+e) o# "ign.

, Ho7 µ1 K µ2 = µ3= µ4 = µ5 = µ6 = µ7

RES:TS7 6N6:;SIS OF 6RI6NCE


36/81

09

RES:TS7 6N6:;SIS OF 6RI6NCE

T6B:E

Analysis of Variance

---------------------------------------------------------------------------

Source Sum of Squares Df Mean Square F-Ratio P-Val

---------------------------------------------------------------------------

Between groups 1.11! " .1#$$"% 1#."" .

it'in groups 1.$(1( 1$$ .!#)#$(---------------------------------------------------------------------------

*otal +,orr. ).%($" 1$!

SINCE NEED:E ME6NS 6RE NOT 6::


37/81

0@

SINCE NEED:E ME6NS 6RE NOT 6::

E6:8 HICH ONES 6RE DIFFERENT

, M)ti%)e Range Te"t" #or @ Nee-)e" Met'o/ !0. percent SD

,ol2) ,ount Mean 3omogeneous 4roups

--------------------------------------------------------------------------------

5( ) 11.(#" 6

5) ) 11.!#11 6 51 ) 11.!#)( 6

5" ) 11.!#($ 6

5$ ) 11.!!01 6

50 ) 11.!!0$ 6

5% ) 1).11 6

IS6: COMP6RISON OF @


38/81

0A

IS6: COMP6RISON OF @

NEED:ES

N1

N

N0

N4

N5

N9

N@

Bo$an-H'i"ker P)ot

11.5 11.@ 11. 1.1 1.0

Co)R1

C o )R


39/81

0

F6CTORI6: =k > DESIGNS

, E$%eri*ent" in+o)+ing "e+era) #a&tor" = k K

o# #a&tor"> w'ere it i" ne&e""ary to "t-y

t'e ?oint e##e&t o# t'e"e #a&tor" on a "%e&i#i&

re"%on"e.

, Ea&' o# t'e #a&tor" are "et at two )e+e)" =a

)ow2 )e+e) an- a 'ig'2 )e+e)> w'i&' *ay

be a)itati+e =*a&'ine 6*a&'ine B8 #an

on#an o##> or antitati+e =te*%eratreA!!te*%eratre !!8 )ine "%ee- 4!!! %er

'or)ine "%ee- 5!!! %er 'or>.


40/81

4!


, Fa&tor" are a""*e- to be #i$e- =#i$e-e##e&t" *o-e)>

, De"ign" are &o*%)ete)y ran-o*i/e-

=e$%eri*enta) tria)" are rn in a ran-o*or-er8 et&.>

, T'e "a) nor*a)ity a""*%tion" are

"ati"#ie-.


41/81

41


, Parti&)ar)y "e#) in t'e ear)y "tage" o#e$%eri*enta) work w'en yo are )ike)y to

'a+e *any #a&tor" being in+e"tigate- an-

yo want to *ini*i/e t'e n*ber o#treat*ent &o*bination" ="a*%)e "i/e> bt8 at

t'e "a*e ti*e8 "t-y a)) k #a&tor" in a

&o*%)ete #a&toria) arrange*ent =t'e

e$%eri*ent &o))e&t" -ata at a)) %o""ib)e

&o*bination" o# #a&tor )e+e)">.


42/81

4


, 6" k get" )arge8 t'e "a*%)e "i/e wi))in&rea"e e$%onentia))y. I# e$%eri*ent i"

re%)i&ate-8 t'e rn" again in&rea"e".

k # of runs2 4

3 8

4 16

5 32

6 64

7 128

8 256

9 512

10 1024


43/81

40

F6CTORI6: =k > DESIGNS =k K >

, Two #a&tor" "et at two )e+e)" =nor*a))y

re#erre- to a" )ow an- 'ig'> wo)- re")t int'e #o))owing -e"ign w'ere ea&' )e+e) o#

#a&tor 6 i" %aire- wit' ea&' )e+e) o# #a&tor

B.

RUN Factor A Factor B RESPNSE RUN Factor A Factor B RESPNSE

1 !o" !o" #1 1 $1 $1 #1

2 %&'% !o" #2 2 (1 $1 #2

3 !o" %&'% #3 3 $1 (1 #3

4 %&'% %&'% #4 4 (1 (1 #4

)*n*ra!&+*, S*tt&n s rt%o ona! S*tt&n s


44/81

44


, E"ti*ating *ain e##e&t" a""o&iate- wit'

&'anging t'e )e+e) o# ea&' #a&tor #ro* )ow

to 'ig'. T'i" i" t'e e"ti*ate- e##e&t on t'e

re"%on"e +ariab)e a""o&iate- wit' &'anging

#a&tor 6 or B #ro* t'eir )ow to 'ig' +a)e".

>=

>= 014 y y y y Effect A Factor +

−+

=

>=

>= 140 y y y y Effect B Factor +

−+

=


45/81

45

F6CTORI6: =k > DESIGNS =k K >7

GR6PHIC6: OTPT, Neit'er #a&tor 6 nor Fa&tor B 'a+e an e##e&t

on t'e re"%on"e +ariab)e.


46/81

49


GR6PHIC6: OTPT

, Fa&tor 6 'a" an e##e&t on t'e re"%on"e

+ariab)e8 bt Fa&tor B -oe" not.


47/81

4@


GR6PHIC6: OTPT

, Fa&tor 6 an- Fa&tor B 'a+e an e##e&t on t'e

re"%on"e +ariab)e.



48/81

4A

F6CTORI6: = > DESIGNS =k >7

GR6PHIC6: OTPT

,Fa&tor B 'a" an e##e&t on t'e re"%on"e +ariab)e8 bt on)y i##a&tor 6 i" "et at t'e Hig'2 )e+e). T'i" i" called

interaction an- it ba"i&a))y *ean" t'at t'e e##e&t one #a&tor

'a" on a re"%on"e i" -e%en-ent on t'e )e+e) yo "et ot'er

#a&tor" at. Intera&tion" &an be *a?or %rob)e*" in a DOE i#

yo #ai) to a&&ont #or t'e intera&tion w'en -e"igning yore$%eri*ent.


49/81

4

EX6MP:E7


, 6 *i&robio)ogi"t i" intere"te- in t'e e##e&t

o# two -i##erent &)tre *e-i*" *e-i* 1

=)ow> an- *e-i* ='ig'>U an- two-i##erent ti*e" 1! 'or" =)ow> an- ! 'or"

='ig'>U on t'e growt' rate o# a %arti&)ar

CF Bg"U.

EX6MP:E7


50/81

5!

EX6MP:E7


, Sin&e two #a&tor" are o# intere"t8 k K8 an-we wo)- nee- t'e #o))owing #or rn"

re")ting in

RUN -*,&u. /&.* )ro"t% Rat*

1 !o" !o" 17

2 %&'% !o" 15

3 !o" %&'% 38

4 %&'% %&'% 39

)*n*ra!&+*, S*tt&n's

EX6MP:E7


51/81

51

EX6MP:E7


, E"ti*ate" #or t'e *e-i* anti*ee##e&t" are

, Me-i* e##e&t K =150>U < =1@ 0A>U K !.5

, Ti*e e##e&t K =0A0>U < =1@ 15>U K.5

EX6MP:E7


52/81

5

EX6MP:E7


EX6MP:E7


53/81

50

EX6MP:E7


, 6 "tati"ti&a) ana)y"i" "ing t'e a%%ro%riate"tati"ti&a) *o-e) wo)- re")t in t'e

#o))owing in#or*ation. Fa&tor 6 =*e-i*>

an- Fa&tor B =ti*e>*ype 777 Sums of Squares

------------------------------------------------------------------------------------

Source Sum of Squares Df Mean Square F-Ratio P-Value

------------------------------------------------------------------------------------

FA,*8R A .)0 1 .)0 .11 .(!0)

FA,*8R B 0".)0 1 0".)0 ))0. .%)%

Resiual ).)0 1 ).)0------------------------------------------------------------------------------------

*otal +correcte 0#.(0 $

All F-ratios are 9ase on t'e resiual mean square error.

EX6MP:E7


54/81

54

EX6MP:E7

CONC:SIONS

, In "tati"ti&a) )angage8 one wo)- &on&)-et'at #a&tor 6 =*e-i*> i" not "tati"ti&a))y

"igni#i&ant at a 5Q )e+e) o# "igni#i&an&e

"in&e t'e %+a)e i" greater t'an 5Q =!.!5>8

bt #a&tor B =ti*e> i" "tati"ti&a))y "igni#i&ant

at a 5 Q )e+e) o# "igni#i&an&e "in&e t'i" %

+a)e i" )e"" t'an 5Q.

EX6MP:E7


55/81

55

EX6MP:E7

CONC:SIONS

, In )ay*an ter*"8 t'i" *ean" t'at we 'a+eno e+i-en&e t'at wo)- a))ow " to

&on&)-e t'at t'e *e-i* "e- 'a" an e##e&t

on t'e growt' rate8 a)t'og' it *ay we))

'a+e an e##e&t =or &on&)"ion wa"

in&orre&t>.


56/81

59

EX6MP:E7

CONC:SIONS, 6--itiona))y8 we 'a+e e+i-en&e t'at wo)-

a))ow " to &on&)-e t'at ti*e -oe" 'a+e an

e##e&t on t'e growt' rate8 a)t'og' it *aywe)) not 'a+e an e##e&t =or &on&)"ion wa"

in&orre&t>.


57/81

5@

EX6MP:E7

CONC:SIONS

, In genera) we &ontro) t'e )ike)i'oo- o#

rea&'ing t'e"e in&orre&t &on&)"ion" by t'e

"e)e&tion o# t'e )e+e) o# "igni#i&an&e #or t'ete"t an- t'e a*ont o# -ata &o))e&te-

="a*%)e "i/e>.

k DESIGNS =k >


58/81

5A

k DESIGNS =k >

, 6" t'e n*ber o# #a&tor" in&rea"e8 t'e

n*ber o# rn" nee-e- to &o*%)ete a

&o*%)ete #a&toria) e$%eri*ent wi)) in&rea"e

-ra*ati&a))y. T'e #o))owing k -e"ign

)ayot -e%i&t t'e n*ber o# rn" nee-e- #or+a)e" o# k #ro* to 5. For e$a*%)e8 w'en

k K 58 it wi)) take 5 K 0 e$%eri*enta) rn"

#or t'e &o*%)ete #a&toria) e$%eri*ent.


59/81

5

Intera&tion" #or k De"ign" =k K 0>

, Intera&tion" between +ario" #a&tor" &an be e"ti*ate- #or -i##erent -e"ign" abo+e

by *)ti%)ying t'e a%%ro%riate &o)*n"

toget'er an- t'en "btra&ting t'e a+eragere"%on"e #or t'e )ow" #ro* t'e a+erage

re"%on"e #or t'e 'ig'".


60/81

9!

Intera&tion" #or k De"ign" =k K 0>

a b c ab ac bc abc

$1 $1 $1 1 1 1 $1

(1 $1 $1 $1 $1 1 1

$1 (1 $1 $1 1 $1 1

(1 (1 $1 1 $1 $1 $1

$1 $1 (0 1 $1 $1 1

(1 $1 (1 $1 1 $1 $1$1 (1 (1 $1 $1 1 $1

(1 (1 (1 1 1 1 1


61/81

91

k DESIGNS =k >

, On&e t'e e##e&t #or a)) #a&tor" an-

intera&tion" are -eter*ine-8 yo are ab)e to

-e+e)o% a %re-i&tion *o-e) to e"ti*ate t'ere"%on"e #or "%e&i#i& +a)e" o# t'e #a&tor".

In genera)8 we wi)) -o t'i" wit' "tati"ti&a)

"o#tware8 bt #or t'e"e -e"ign"8 yo &an -oit by 'an- &a)&)ation" i# yo wi"'.


62/81

9

k DESIGNS =k >

, For e$a*%)e8 i# t'ere are no "igni#i&ant intera&tion"

%re"ent8 yo &an e"ti*ate a re"%on"e by t'e

#o))owing #or*)a. =#or antitati+e #a&tor" on)y>

ONE F6CTOR EX6MP:E


63/81

90

ONE F6CTOR EX6MP:E

P)ot o# Fitte- Mo-e)

HRS STGD;

G R 6 D E

1! 1 14 19 1A !

55

95

@5

A5

C5

ONE F6CTOR EX6MP:E


64/81

94

ONE F6CTOR EX6MP:E

, T'e ot%t "'ow" t'e re")t" o# #itting agenera) )inear *o-e) to -e"&ribe t'e

re)ation"'i% between GR6DE an- HRS

STD;. T'e eation o# t'e #itte- genera)

*o-e) i"

, GR6DE K .0 0.1 =HRS STD;>

, T'e #itte- ort'ogona) *o-e) i"

, GR6DE K @5 15 =SC6:ED HRS>

T : ) S i D i


65/81

95

Two :e+e) S&reening De"ign" , S%%o"e t'at yor brain"tor*ing "e""ion

re")te- in @ #a&tor" t'at +ario" %eo%)et'ink *ig't2 'a+e an e##e&t on a re"%on"e.6 #)) #a&toria) -e"ign wo)- reire @ K1A e$%eri*enta) rn" wit'ot re%)i&ation.

T'e %r%o"e o# "&reening -e"ign" i" tore-&e =i-enti#y> t'e n*ber o# #a&tor"-own to t'e *a?or2 ro)e %)ayer" wit' a

*ini*a) n*ber o# e$%eri*enta) rn". Oneway to -o t'i" i" to "e t'e 0 #)) #a&toria)-e"ign an- "e intera&tion &o)*n" #or#a&tor".

N t t' t


66/81

99

Note t'at

6ny #a&tor - e##e&t i" now &on#on-e- wit' t'e abintera&tion

6ny #a&tor e e##e&t i" now &on#on-e- wit' t'e a&

intera&tion

et&.

'at i" t'e -e intera&tion &on#on-e- wit'a b c d = ab e = ac f = bc g = abc

$1 $1 $1 1 1 1 $1

(1 $1 $1 $1 $1 1 1

$1 (1 $1 $1 1 $1 1

(1 (1 $1 1 $1 $1 $1

$1 $1 (0 1 $1 $1 1

(1 $1 (1 $1 1 $1 $1

$1 (1 (1 $1 $1 1 $1

(1 (1 (1 1 1 1 1


67/81

9@

Prob)e*" t'at Intera&tion" Ca"e(

, Intera&tion" < I# intera&tion" e$i"t an- yo #ai) to

a&&ont #or t'i"8 yo *ay rea&' erroneo"

&on&)"ion". S%%o"e t'at yo %)an an

e$%eri*ent wit' #or rn" an- t'ree #a&tor"

re")ting in t'e #o))owing -ata7



68/81

9A


, Fa&tor 6 E##e&t K !

, Fa&tor B E##e&t K !

, In t'i" e$a*%)e8 i# yo were a""*ing t'at

"*a))er i" better2 t'en it a%%ear" to *ake

no -i##eren&e w'ere yo "et #a&tor" 6 an- B.I# yo were to "et #a&tor 6 at t'e )ow +a)e

an- #a&tor B at t'e )ow +a)e8 yor re"%on"e

+ariab)e wo)- be )arger t'an -e"ire-. In t'i"&a"e t'ere i" a #a&tor 6 intera&tion wit'

#a&tor B.


69/81

9


Intera&tion P)ot

F6CTOR 6

5

9

@

A

1!

R E S P O N S E

1 1

F6CTOR B1

1

Re"o)tion o# a De"ign


70/81

@!

g

, Re"o)tion III De"ign" < No *ain e##e&t" area)ia"e- wit' any ot'er *ain e##e&t BT "o*e =ora))> *ain e##e&t" are a)ia"e- wit' two wayintera&tion"

, Re"o)tion I De"ign" < No *ain e##e&t" area)ia"e- wit' any ot'er *ain e##e&t OR two #a&torintera&tion8 BT two #a&tor intera&tion" *ay bea)ia"e- wit' ot'er two #a&tor intera&tion"

, Re"o)tion De"ign" < No *ain e##e&t OR two

#a&tor intera&tion i" a)ia"e- wit' any ot'er *aine##e&t or two #a&tor intera&tion8 BT two #a&torintera&tion" are a)ia"e- wit' t'ree #a&torintera&tion".

i i


71/81

@1

Co**on S&reening De"ign"

, Fra&tiona) Fa&toria) De"ign" < t'e tota)n*ber o# e$%eri*enta) rn" *"t be a

%ower o# =48 A8 198 08 948 V>. I# yo

be)ie+e #ir"t or-er intera&tion" are "*a))

&o*%are- to *ain e##e&t"8 t'en yo &o)-

&'oo"e a re"o)tion III -e"ign. W"t

re*e*ber t'at i# yo 'a+e *a?or

intera&tion"8 it &an *e"" % yor "&reeninge$%eri*ent.

C S i i


72/81

@

Co**on S&reening De"ign"

, P)a&kettBr*an De"ign" < Two )e+e)8re"o)tion III -e"ign" "e- to "t-y % to

n1 #a&tor" in n e$%eri*enta) rn"8 w'ere

n i" a *)ti%)e o# 4 = o# rn" wi)) be 48 A8

18 198 V>. Sin&e n *ay be ite )arge8

yo &an "t-y a )arge n*ber o# #a&tor"

wit' *o-erate)y "*a)) "a*%)e "i/e". =n K

1!! *ean" yo &an "t-y #a&tor" wit'1!! rn">

Ot'er De"ign I""e"


73/81

@0

Ot'er De"ign I""e"

, May want to &o))e&t -ata at &enter %oint" to

e"ti*ate non)inear re"%on"e"

, More t'an two )e+e)" o# a #a&tor < no

%rob)e* =*)ti)e+e) #a&toria)>

, 'at -o yo -o i# yo want to bi)- a non

)inear *o-e) to o%ti*i/e2 t'e re"%on"e.

='it a target8 *a$i*i/e8 or *ini*i/e> <

&a))e- re"%on"e "r#a&e *o-e)ing


74/81

@4

Re"%on"e Sr#a&e De"ign" < Bo$Be'nken

RUN F1 F2 F3 100

1 10 45 60 11825

2 30 45 40 8781

3 20 30 40 8413

4 10 30 50 9216

5 20 45 50 9288

6 30 60 50 8261

7 20 45 50 9329

8 30 45 60 10855

9 20 45 50 9205

10 20 60 40 8538

11 10 45 40 9718

12 30 30 50 11308

13 20 60 60 10316

14 10 60 50 12056

15 20 30 60 10378


75/81

@5


Regression coeffs. for Var_3

----------------------------------------------------------------------

constant = 2312.5

A:Factor_A = 36.575

B:Factor_B = 200.067C:Factor_C = 3.85

AA = .0875

AB = -.81167

AC = -0.0825

BB = 0.117222

BC = -0.311667

CC = 1.10875


76/81

@9


Contor" o# E"ti*ate- Re"%on"e Sr#a&e

Fa&torCK9!.!

Fa&tor6

F a & t o rR B

ar0

0!!.!

5!!.!@!!.!

!!.!

1!1!!.!

1!0!!.!

1!5!!.!

1!@!!.!

1!!!.!

111!!.!

110!!.!

115!!.!

11@!!.!

1! 14 1A 9 0!

0!

05

4!

45

5!

55

9!

C:6SSROOM EXERCISE


77/81

@@

C:6SSROOM EXERCISE

, STDENT INC:6SS EXPERIMENT7

Co))e&t -ata #or e$%eri*ent to -eter*ine

#a&tor "etting" =two #a&tor"> to 'it a target

re"%on"e ="%ot on wa))>.

, Fa&tor 6 < 'eig't o# "'aker =)ow an- 'ig'>

, Fa&tor B < )o&ation o# "'aker =&)o"e to

'an- an- &)o"e to wa))>

, De"ign e$%eri*ent < wo)- "gge"t

"e+era) re%)i&ation"

C:6SSROOM EXERCISE


78/81

@A

C:6SSROOM EXERCISE

, Con-&t E$%eri*ent < "t-ent 'o)-" 0 #oot

%in t'e tai) on t'e -onkey2 "ti&k an-atte*%t" to 'it t'e target. 6n ob"er+er wi))

a""i"t to *ark t'e 'it on t'e target.

, Co))e&t -ata < "t-ent" take -ata 'o*e #orweek an- &o*e ba&k wit' w'at yo wo)-

re&o**en- 6ND w'y.

, ;O TE:: THE C:6SS HO TO P:6;THE G6ME TO IN2.

C:6SSROOM EXERCISE


79/81

@

C:6SSROOM EXERCISE

C:6SSROOM EXERCISE


80/81

A!

C:6SSROOM EXERCISE

-ARER

S/

ER/A

PE1S/ BS 2N BS 3R BS 4/ BS -EAN

S/ANAR

EA/N

$2750 $4500 $4750 $5000 $4250 1021

$12500 $6750 $4625 $4000 $6969 3871

3000 3250 3875 6250 4094 1484

4625 11250 12625 14000 10625 4155

-ARER

S/

: ER/A PE ;AS SE / ;A


81/81

Contor P)ot" #or Mean an- St-. De+.

doepp reduced presentation5.ppt

Documents