doepp reduced presentation5

7/24/2019 Doepp Reduced Presentation5

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1

DESIGN OF EXPERIMENTS


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Role of DOE in Process Improvement

DOE is a formal matematical meto! fors"stematicall" plannin# an! con!$ctin# scientific

st$!ies tat can#e e%perimental varia&les

to#eter in or!er to !etermine teir effect of a

#iven response'

DOE ma(es controlle! can#es to inp$t

varia&les in or!er to #ain ma%im$m amo$nts of

information on ca$se an! effect relationsips

)it a minim$m sample si*e'


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DOE is more efficient tat a stan!ar!

approac of can#in# ,one varia&le at a

time- in or!er to o&serve te varia&le.s

impact on a #iven response'

DOE #enerates information on te effect

vario$s factors ave on a response varia&lean! in some cases ma" &e a&le to !etermine

optimal settin#s for tose factors'


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DOE enco$ra#es ,&rainstormin#- activities

associate! )it !isc$ssin# (e" factors tat ma"

affect a #iven response an! allo)s te

e%perimenter to i!entif" te ,(e"- factors forf$t$re st$!ies'

DOE is rea!il" s$pporte! &" n$mero$s statisticalsoft)are pac(a#es availa&le on te mar(et'


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SI3 STEPS IN DOE

Fo$r elements associate! )it DOE4

1' Te !esi#n of te e%periment5

2' Te collection of te !ata5

+' Te statistical anal"sis of te !ata5 an!

/' Te concl$sions reace! an!recommen!ations ma!e as a res$lt of te

e%periment'


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TERMINO7OG8

Replication 9 repetition of a &asic

e%periment )ito$t can#in# an" factor

settin#s5 allo)s te e%perimenter to estimate

te e%perimental error :noise; in te s"stem$se! to !etermine )eter o&serve!

!ifferences in te !ata are ,real- or ,


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TERMINO7OG8

'Ran!omi*ation 9 a statistical tool $se! to minimi*epotential $ncontrolla&le &iases in te e%periment &"

ran!oml" assi#nin# material5 people5 or!er tat

e%perimental trials are con!$cte!5 or an" oterfactor not $n!er te control of te e%perimenter'

Res$lts in ,avera#in# o$t- te effects of te

e%traneo$s factors tat ma" &e present in or!er to

minimi*e te ris( of tese factors affectin# te

e%perimental res$lts'


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TERMINO7OG8

loc(in# 9 tecni?$e $se! to increase teprecision of an e%periment &" &rea(in# te

e%periment into omo#eneo$s se#ments

:&loc(s; in or!er to control an" potential

&loc( to &loc( varia&ilit" :m$ltiple lots of

ra) material5 several sifts5 several

macines5 several inspectors;' n" effects

on te e%perimental res$lts as a res$lt of te&loc(in# factor )ill &e i!entifie! an!

minimi*e!'


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TERMINO7OG8

3onfo$n!in# A concept tat &asicall" means tat

m$ltiple effects are tie! to#eter into one parenteffect an! cannot &e separate!' For e%ample5

1' T)o people flippin# t)o !ifferent coins )o$l!

res$lt in te effect of te person an! te effect of

te coin to &e confo$n!e!

2' s e%periments #et lar#e5 i#er or!er

interactions :!isc$sse! later; are confo$n!e! )it

lo)er or!er interactions or main effect'


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TERMINO7OG8

Factors 9 e%perimental factors orin!epen!ent varia&les :contin$o$s or

!iscrete; an investi#ator manip$lates to

capt$re an" can#es in te o$tp$t of te

process' Oter factors of concern are tose

tat are $ncontrolla&le an! tose )ic are

controlla&le &$t el! constant !$rin# te

e%perimental r$ns'


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TERMINO7OG8

Responses 9 !epen!ent varia&le meas$re!to !escri&e te o$tp$t of te process'

Treatment 3om&inations :r$n; 9e%perimental trial )ere all factors are set

at a specifie! level'


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TERMINO7OG8

Fi%e! Effects Mo!el A If te treatmentlevels are specificall" cosen &" tee%perimenter5 ten concl$sions reace!)ill onl" appl" to tose levels'

Ran!om Effects Mo!el 9 If te treatmentlevels are ran!oml" cosen from apop$lation of man" possi&le treatment

levels5 ten concl$sions reace! can &ee%ten!e! to all treatment levels in tepop$lation'


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P7NNING DOE

Ever"one involve! in te e%periment so$l!ave a clear i!ea in a!vance of e%actl" )at

is to &e st$!ie!5 te o&


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P7NNING DOE

Select a responseC!epen!ent varia&le:varia&les; tat )ill provi!e information

a&o$t te pro&lem $n!er st$!" an! te

propose! meas$rement meto! for tisresponse varia&le5 incl$!in# an

$n!erstan!in# of te meas$rement s"stem

varia&ilit"


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P7NNING DOE

Select te in!epen!ent varia&lesCfactors:?$antitative or ?$alitative; to &e

investi#ate! in te e%periment5 te n$m&er

of levels for eac factor5 an! te levels ofeac factor cosen eiter specificall" :fi%e!

effects mo!el; or ran!oml" :ran!om effects

mo!el;'


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P7NNING DOE

3oose an appropriate e%perimental !esi#n

:relativel" simple !esi#n an! anal"sis meto!s are

almost al)a"s &est; tat )ill allo) "o$r e%perimental

?$estions to &e ans)ere! once te !ata is collecte!

an! anal"*e!5 (eepin# in min! tra!eoffs &et)eenstatistical po)er an! economic efficienc"' t tis

point in time it is #enerall" $sef$l to sim$late te

st$!" &" #eneratin# an! anal"*in# artificial !ata to

ins$re tat e%perimental ?$estions can &e ans)ere!

as a res$lt of con!$ctin# "o$r e%periment


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P7NNING DOE

Perform te e%periment :collect !ata;pa"in# partic$lar attention s$c tin#s as

ran!omi*ation an! meas$rement s"stem

acc$rac"5 )ile maintainin# as $niform ane%perimental environment as possi&le'

o) te !ata are to &e collecte! is a critical

sta#e in DOE


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P7NNING DOE

nal"*e te !ata $sin# te appropriatestatistical mo!el ins$rin# tat attention is

pai! to cec(in# te mo!el acc$rac" &"

vali!atin# $n!erl"in# ass$mptionsassociate! )it te mo!el' e li&eral in te

$tili*ation of all tools5 incl$!in# #rapical

tecni?$es5 availa&le in te statisticalsoft)are pac(a#e to ins$re tat a ma%im$m

amo$nt of information is #enerate!


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P7NNING DOE

ase! on te res$lts of te anal"sis5 !ra)concl$sionsCinferences a&o$t te res$lts5

interpret te p"sical meanin# of tese

res$lts5 !etermine te practical si#nificanceof te fin!in#s5 an! ma(e recommen!ations

for a co$rse of action incl$!in# f$rter

e%periments


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2B

SIMP7E 3OMPRTIE EXPERIMENTS

Sin#le Mean "potesis Test

Difference in Means "potesis Test )it

E?$al ariances

Difference in Means "potesis Test )itne?$al ariances

Difference in ariances "potesis Test

Paire! Difference in Mean "potesis Test

One a" nal"sis of ariance


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3RITI37 ISSES SSO3ITED IT

SIMP7E 3OMPRTIE EXPERIMENTS

o) 7ar#e a Sample So$l! e Ta(eH

" Does te Sample Si*e Matter

n")a"H

at in! of Protection Do e ave

ssociate! )it Re


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fter a pro!$ction r$n of 12 o*' &ottles5concern is e%presse! a&o$t te possi&ilit" tat

te avera#e fill is too lo)'

o4 J 12

a4 KL 12

level of si#nificance J J 'B0 sample si*e J @

SPE3 FOR TE MEN4 12 '1


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Sample mean J 11'@

Sample stan!ar! !eviation J B'10

Sample si*e J @

3omp$te! t statistic J A2'B PAal$e J B'B>B0162

3ON37SION4 Since PAal$e L 'B05 "o$

fail to re


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Sin#le Mean "potesis Test Po)er 3$rve

Po)er 3$rvealpa J B'B05 si#ma J B'10

Tr$e Mean

Po)er

11'> 11'@ 12 12'1 12'2B

B'2

B'/

B'6

B'>

1

Si l M i T P


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Sin#le Mean "potesis Test Po)er

3$rve A Different Sample Si*es


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DIFFEREN3E IN MENS A E7

RIN3ES

o4 1= 2

a4 1 2

level of si#nificance J J 'B0

sample si*es &ot J 10

ss$mption4 1J 2

Sample means J 11'> an! 12'1

Sample stan!ar! !eviations J B'1 an! B'2

Sample si*es J 10 an! 10


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DIFFEREN3E IN MENS A E7 RIN3ES

3an "o$ !etect tis !ifferenceH


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DIFFEREN3E IN MENS A E7

RIN3ES


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DIFFEREN3E IN MENS A $nE7

RIN3ES

Same as te ,E?$al ariance- case e%cept

te variances are not ass$me! e?$al'

o) !o "o$ (no) if it is reasona&le to

ass$me tat variances are e?$al OR

$ne?$alH


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DIFFEREN3E IN RIN3E

8POTESIS TEST

Same e%ample as Difference in Mean4

Sample stan!ar! !eviations J B'1 an! B'2

Sample si*es J 10 an! 10

N$ll "potesis4 ratio of variances J 1'B

lternative4 not e?$al

3omp$te! F statistic J B'20

PAal$e J B'B1/BB=1

Re


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DIFFEREN3E IN RIN3E

8POTESIS TEST

3an "o$ !etect tis !ifferenceH


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DIFFEREN3E IN RIN3E

8POTESIS TEST APOER 3RE


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PIRED DIFFEREN3E IN MENS

8POTESIS TEST

T)o !ifferent inspectors eac meas$re 1Bparts on te same piece of test e?$ipment'

N$ll "potesis4 DIFFEREN3E IN MENS

J B'B lternative4 not e?$al

3omp$te! t statistic J A1'22=B2

PAal$e J B'20B@//

Do not re


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PIRED DIFFEREN3E IN MENS

8POTESIS TEST A POER 3RE

Po)er 3$rve

alpa J B'B05 si#ma J +'>66

Difference in Means

Po)er

A0 A/ A+ A2 A1 B 1 2 + / 0

B

B'2

B'/

B'6

B'>

1


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ONE 8 N78SIS OF RIN3E

se! to test "potesis tat te means of

several pop$lations are e?$al'

E%ample4 Pro!$ction line as = fill nee!les an!"o$ )is to assess )eter or not te avera#e

fill is te same for all = nee!les'

E%periment4 sample 2B fills from eac of te @nee!les an! test at 0 level of si#n'

o4 1J 2 =3= 4 = 5 =6= 7

RES7TS4 N78SIS OF RIN3E


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RES7TS4 N78SIS OF RIN3E

T7E

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. ).%($" 1$!

SIN3E NEED7E MENS RE NOT 77


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SIN3E NEED7E MENS RE NOT 77

E75 I3 ONES RE DIFFERENTH

M$ltiple Ran#e Tests for = Nee!lesMet'o/ !0. percent SD

,ol2) ,ount Mean 3omogeneous 4roups

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

5( ) 11.(#" 6

5) ) 11.!#11 651 ) 11.!#)( 6

5" ) 11.!#($ 6

5$ ) 11.!!01 6

50 ) 11.!!0$ 6

5% ) 1).11 6

IS7 3OMPRISON OF =


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IS7 3OMPRISON OF =

NEED7ES

N1

N2

N+

N/

N0

N6

N=

o%Aan!AGis(er Plot

11'0 11'= 11'@ 12'1 12'+

3olQ1

3olQ2


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F3TORI7 :2(; DESIGNS

E%periments involvin# several factors : ( J

of factors; )ere it is necessar" to st$!"

te


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/B


Factors are ass$me! to &e fi%e! :fi%e!effects mo!el;

Desi#ns are completel" ran!omi*e!

:e%perimental trials are r$n in a ran!omor!er5 etc';

Te $s$al normalit" ass$mptions are

satisfie!'


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Partic$larl" $sef$l in te earl" sta#es ofe%perimental )or( )en "o$ are li(el" to

ave man" factors &ein# investi#ate! an!

"o$ )ant to minimi*e te n$m&er oftreatment com&inations :sample si*e; &$t5 at

te same time5 st$!" all ( factors in a

complete factorial arran#ement :te

e%periment collects !ata at all possi&le

com&inations of factor levels;'


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s ( #ets lar#e5 te sample si*e )illincrease e%ponentiall"' If e%periment is

replicate!5 te r$ns a#ain increases'

k # of runs2 4

3 8

4 16

5 32

6 64

7 128

8 256

9 512

10 1024


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F3TORI7 :2(; DESIGNS :( J 2;

T)o factors set at t)o levels :normall"

referre! to as lo) an! i#; )o$l! res$lt inte follo)in# !esi#n )ere eac level of

factor is paire! )it eac level of factor

'

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


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Estimatin# main effects associate! )it

can#in# te level of eac factor from lo)

to i#' Tis is te estimate! effect on te

response varia&le associate! )it can#in#

factor or from teir lo) to i# val$es'

2

;:

2

;: +1/2 yyyyEffectAFactor +

+

=

2

;:

2

;: 21/+ yyyyEffectBFactor +

+

=


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F3TORI7 :2(; DESIGNS :( J 2;4

GRPI37 OTPT Neiter factor nor Factor ave an effect

on te response varia&le'


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GRPI37 OTPT

Factor as an effect on te response

varia&le5 &$t Factor !oes not'


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GRPI37 OTPT

Factor an! Factor ave an effect on te

response varia&le'



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F3TORI7 :2 ; DESIGNS :( 2;4

GRPI37 OTPT

Factor as an effect on te response varia&le5 &$t onl" iffactor is set at te ,i#- level' Tis is called

interactionan! it &asicall" means tat te effect one factor

as on a response is !epen!ent on te level "o$ set oter

factors at' Interactions can &e ma


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EXMP7E4


micro&iolo#ist is intereste! in te effect

of t)o !ifferent c$lt$re me!i$ms me!i$m 1

:lo); an! me!i$m 2 :i#; an! t)o!ifferent times 1B o$rs :lo); an! 2B o$rs

:i#; on te #ro)t rate of a partic$lar

3F $#s'

EXMP7E4


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0B

EXMP7E4


Since t)o factors are of interest5 ( J25 an!)e )o$l! nee! te follo)in# fo$r r$ns

res$ltin# in

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

1 !o" !o" 17

2 %&'% !o" 15

3 !o" %&'% 38

4 %&'% %&'% 39

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

EXMP7E4


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EXMP7E4


Estimates for te me!i$m an! timeeffects are

Me!i$m effect J :10+@;C2 9 :1= +>;C2 J AB'0

Time effect J :+>+@;C2 9 :1= 10;C2 J22'0

EXMP7E4


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EXMP7E4


EXMP7E4


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EXMP7E4


statistical anal"sis $sin# te appropriatestatistical mo!el )o$l! res$lt in te

follo)in# information' Factor :me!i$m;

an! Factor :time;*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.

EXMP7E4


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EXMP7E4

3ON37SIONS

In statistical lan#$a#e5 one )o$l! concl$!etat factor :me!i$m; is not statisticall"

si#nificant at a 0 level of si#nificance

since te pAval$e is #reater tan 0 :B'B0;5

&$t factor :time; is statisticall" si#nificant

at a 0 level of si#nificance since tis pA

val$e is less tan 0'

EXMP7E4


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EXMP7E4

3ON37SIONS

In la"man terms5 tis means tat )e aveno evi!ence tat )o$l! allo) $s to

concl$!e tat te me!i$m $se! as an effect

on te #ro)t rate5 alto$# it ma" )ell

ave an effect :o$r concl$sion )as

incorrect;'


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EXMP7E4

3ON37SIONS !!itionall"5 )e ave evi!ence tat )o$l!

allo) $s to concl$!e tat time !oes ave an

effect on te #ro)t rate5 alto$# it ma")ell not ave an effect :o$r concl$sion )as

incorrect;'


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EXMP7E4

3ON37SIONS

In #eneral )e control te li(elioo! of

reacin# tese incorrect concl$sions &" te

selection of te level of si#nificance for tetest an! te amo$nt of !ata collecte!

:sample si*e;'

2( DESIGNS :( L 2;


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2(DESIGNS :( L 2;

s te n$m&er of factors increase5 te

n$m&er of r$ns nee!e! to complete a

complete factorial e%periment )ill increase

!ramaticall"' Te follo)in# 2( !esi#n

la"o$t !epict te n$m&er of r$ns nee!e! forval$es of ( from 2 to 0' For e%ample5 )en

( J 05 it )ill ta(e 20 J +2 e%perimental r$ns

for te complete factorial e%periment'


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Interactions for 2( Desi#ns :( J +;

Interactions &et)een vario$s factors can&e estimate! for !ifferent !esi#ns a&ove

&" m$ltipl"in# te appropriate col$mns

to#eter an! ten s$&tractin# te avera#eresponse for te lo)s from te avera#e

response for te i#s'


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6B

Interactions for 2( Desi#ns :( J +;

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


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2(DESIGNS :( L 2;

Once te effect for all factors an!

interactions are !etermine!5 "o$ are a&le to

!evelop a pre!iction mo!el to estimate teresponse for specific val$es of te factors'

In #eneral5 )e )ill !o tis )it statistical

soft)are5 &$t for tese !esi#ns5 "o$ can !oit &" an! calc$lations if "o$ )is'


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2(DESIGNS :( L 2;

For e%ample5 if tere are no si#nificant interactions

present5 "o$ can estimate a response &" te

follo)in# form$la' :for ?$antitative factors onl";

ONE F3TOR EXMP7E


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ONE F3TOR EXMP7E

Plot of Fitte! Mo!el

RS STD8

GR2DE

1B 12 1/ 16 1> 2B

00

60

=0

>0

@0

ONE F3TOR EXMP7E


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ONE F3TOR EXMP7E

Te o$tp$t so)s te res$lts of fittin# a#eneral linear mo!el to !escri&e te

relationsip &et)een GRDE an! RS

STD8' Te e?$ation of te fitte! #eneral

mo!el is

GRDE J 2@'+ +'1 :RS STD8;

Te fitte! orto#onal mo!el is

GRDE J =0 10 :S37ED RS;

T 7 l S i D i


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60

T)o 7evel Screenin# Desi#ns S$ppose tat "o$r &rainstormin# session

res$lte! in = factors tat vario$s peopletin( ,mi#t- ave an effect on a response' f$ll factorial !esi#n )o$l! re?$ire 2=J12> e%perimental r$ns )ito$t replication'

Te p$rpose of screenin# !esi#ns is tore!$ce :i!entif"; te n$m&er of factors!o)n to te ,ma


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Note tat

n" factor ! effect is no) confo$n!e! )it te a&interaction

n" factor e effect is no) confo$n!e! )it te ac

interaction

etc'

at is te !e interaction confo$n!e! )itHHHHHHHHa 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


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Pro&lems tat Interactions 3a$seU

Interactions 9 If interactions e%ist an! "o$ fail to

acco$nt for tis5 "o$ ma" reac erroneo$s

concl$sions' S$ppose tat "o$ plan an

e%periment )it fo$r r$ns an! tree factors

res$ltin# in te follo)in# !ata4



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Factor Effect J B

Factor Effect J B

In tis e%ample5 if "o$ )ere ass$min# tat

,smaller is &etter- ten it appears to ma(e

no !ifference )ere "o$ set factors an! 'If "o$ )ere to set factor at te lo) val$e

an! factor at te lo) val$e5 "o$r response

varia&le )o$l! &e lar#er tan !esire!' In tiscase tere is a factor interaction )it

factor '


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6@


Interaction Plot

F3TOR

0

6

=

>

@

1B

RESPONSE

A1 1

F3TOR A1

1

Resol$tion of a Desi#n


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#

Resol$tion III Desi#ns 9 No main effects arealiase! )it an" oter main effect T some :orall; main effects are aliase! )it t)o )a"interactions

Resol$tion I Desi#ns 9 No main effects arealiase! )it an" oter main effect OR t)o factorinteraction5 T t)o factor interactions ma" &ealiase! )it oter t)o factor interactions

Resol$tion Desi#ns 9 No main effect OR t)o

factor interaction is aliase! )it an" oter maineffect or t)o factor interaction5 T t)o factorinteractions are aliase! )it tree factorinteractions'

i i


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3ommon Screenin# Desi#ns

Fractional Factorial Desi#ns 9 te totaln$m&er of e%perimental r$ns m$st &e a

po)er of 2 :/5 >5 165 +25 6/5 V;' If "o$

&elieve first or!er interactions are small

compare! to main effects5 ten "o$ co$l!

coose a resol$tion III !esi#n' W$st

remem&er tat if "o$ ave ma


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=2

3ommon Screenin# Desi#ns

Plac(ettA$rman Desi#ns 9 T)o level5resol$tion III !esi#ns $se! to st$!" $p to

nA1 factors in n e%perimental r$ns5 )ere

n is a m$ltiple of / : of r$ns )ill &e /5 >5

125 165 V;' Since n ma" &e ?$ite lar#e5

"o$ can st$!" a lar#e n$m&er of factors

)it mo!eratel" small sample si*es' :n J

1BB means "o$ can st$!" @@ factors )it1BB r$ns;

Oter Desi#n Iss$es


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=+

Oter Desi#n Iss$es

Ma" )ant to collect !ata at center points to

estimate nonAlinear responses

More tan t)o levels of a factor 9 no

pro&lem :m$ltiAlevel factorial;

at !o "o$ !o if "o$ )ant to &$il! a nonA

linear mo!el to ,optimi*e- te response'

:it a tar#et5 ma%imi*e5 or minimi*e; 9

calle! response s$rface mo!elin#


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=/

Response S$rface Desi#ns 9 o%Aen(en

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


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=0


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


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=6


3onto$rs of Estimate! Response S$rface

FactorQ3J6B'B

FactorQ

FactorQ1

arQ+

@+BB'B

@0BB'B@=BB'B

@@BB'B

1B1BB'B

1B+BB'B

1B0BB'B

1B=BB'B

1B@BB'B

111BB'B

11+BB'B

110BB'B

11=BB'B

1B 1/ 1> 22 26 +B

+B

+0

/B

/0

0B

00

6B

37SSROOM EXER3ISE


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==

37SSROOM EXER3ISE

STDENT INA37SS EXPERIMENT4

3ollect !ata for e%periment to !eterminefactor settin#s :t)o factors; to it a tar#et

response :spot on )all;'

Factor 9 ei#t of sa(er :lo) an! i#;

Factor 9 location of sa(er :close to

an! an! close to )all;

Desi#n e%periment 9 )o$l! s$##est

several replications

37SSROOM EXER3ISE


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=>

37SSROOM EXER3ISE

3on!$ct E%periment 9 st$!ent ol!s + foot

,pin te tail on te !on(e"- stic( an!attempts to it te tar#et' n o&server )ill

assist to mar( te it on te tar#et'

3ollect !ata 9 st$!ents ta(e !ata ome for)ee( an! come &ac( )it )at "o$ )o$l!

recommen! ND )"'

8O TE77 TE 37SS O TO P78TE GME TO ,IN-'

37SSROOM EXER3ISE


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=@

37SSROOM EXER3ISE

37SSROOM EXER3ISE


80/81

>B

37SSROOM EXER3ISE

-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


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3onto$r Plots for Mean an! St!' Dev'

doepp reduced presentation5

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