VI. Two-way tables and two-way ANOVA

24 Pages·2001·0.92 MB·English

Twtotw-aaoAwbn-N aldwOye aVV syAI .
Intr odAu.c tion
1. :sledo mnoisserge rro fnoitato ndnah-troh sf oweiveR mm =)...|y(
x ROTCA F + + x ROTCA F + + x :FACTOR + x x:
1 a 2 b 1 a 1 2
2. Analysis of variance srotca fyln ohti wsisylan anoisserge r:
3. :setoN
a. tnatropm ioo tt’ns inoitcnitsi dnoisserge r /AVONA
b. )?yhw (lartne cer aselba tAVON Adn astset- F,AVON AnI
c. 2-way ANOVA . .sa hAVON Ayaw- 3,srotca f 2sa h
d. Additive 2-way model: mm (y) = FACTOR ROTCA F +
a b
evitidda-noN : FACTOR ROTCA F + ROTCA F + ::ROTCAF
a b a b
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e. The noitacifissal cyaw-owt r o tuoya lyaw-owt :
ROW COLUMN FACTOR
FACTOR 1C 2C 3C 4C
1R Y Y Y Y
1 3 5 7
Y Y Y Y
2 4 6 8
2R Y Y Y Y
9 11 13 15
Y Y Y Y
10 12 14 16
3R Y Y Y Y
17 19 21 23
Y Y Y Y
18 20 22 24
Data File:
index ROW COLUMN Y
1 R1 C1 Y
1
2 R1 C1 Y
2
3 R1 C2 Y
3
4 R1 C2 Y
4
5 R1 C 3 Y
5
6 R1 C3 Y
6
...
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4. smre tngise dlatnemirepx etnatropmI
a. Experimental unit s itnemtaer teh thcih wo ttcejb oeh t:
applied
b. Treatment o tdeilpp as itah tnoitalupina mr onoitidno ceh t:
unitthse
c. Block stin ulatnemirepx eralimi sf onoitcello c a:
d. ngise dkcol bdezimodnaR o tstnemtaer tf osnoitazimodna r:
kcol bhca ero fyletarape sdetcudno cer astin u.repxe
5. mor fesir aya mnoitacifissal cyaw-ow t an iataD
a. )yralas= y,cud esry=lo c,xes=wo r:xE (ydut slanoitavresbo
b. stnemtaer t 2hti wtnemirepx edezimodnar
c. tnemtaer t 1hti w.repx ekcol bdezimodnar
)tnemtaer t =lo c,kcol b =wor(
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6. noitacilpeR
tuohti welba tyaw-2
setacilpe rhti welba tyaw-2
)lle cre p.sb o1 (setacilper
a. Balance snoitavresb of orebmu nema seh ter aereh tsnae m
)elba teh tf olle cre p.e.i (noitanibmo ctnemtaer trep
b. consideration special require replicates without tables 2-way
(Ch.14)
c. ).repxe kcolb dezimodnar( )1.1.31( srezarG deewaeS :xE
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seta c ., ihBsyl t egpyirleea wobtrwfaa-tr2tS
1. lla )b( ,noitcaretni )a( :tuoba eb yam tseretni fo )s(noitseuq :etoN
-ca fhto br oen of osleve lwe f a)c (,srotca fhto br oen of oslevel
snoitanibmo craeni lniatre c)d (r o,srot
2. tol pneh tledo mevitidda-no nyaw- 2ti f;elbisso pf i,tol p:erolpxE
yrassece nf imrofsnar t;seula vdetti fsusre vslaudiser
3. tset- Fn ahti wnoitcaretn iro ftseT
4. tuob ayliramir ps inoitseu qfI main effects noitcaretn ieh tpor d,
ere hysrevortno cemo s:etoN (tnacifingi sto ner ayeh tf ismret
)pihsnoitale recnacifingis/ezi selpma so teud
5. hti wtseretn if osnoitseu qcificep srewsnA
a. f osnoitanibmo craenil bb ’s
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b. segarev anmulo cr owo rf osnoitanibmo craenil
c. gnis usnoitaziretemara pesoh cylesi wn istneiciffeo c,RO
regression models (my preference)
6. ro f,yrassece nf i,seuqinhce tnosirapmo celpitlu mesU
gnipoon sata d)ii (r osnosirapmo celpitlu m)i(
melborP ataD srezarG deewaeS .C
1. n aereh ts I)b (,noitamrofsnar tro fdee nevlose R)a (:ygetartS
s I)c ()!to nyllufepoh (tnemtaer tdn akcol bneewte bnoitcaretni
fi 1( EGRAL rof srotacidni etaerC )d( ?tceffe tnemtaert a ereht
)tneser pf i1 (TEPMI Ldn a,)tneser pf i1 (LLAM S,)tneserp
2. f onoitropor p = p =esnopse r:ere hnoitamrofsnar ttuob aetoN
si ti fI .)1 dna 0 neewteb( htworger deewaes yb derevoc tolp
s’te L.])p-1(/p[go ls inoitamrofsnar tdoo g a,elbaterpretni
.)p-1(/ ps a”oita rnoitarenege rdeewaes “enifed
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syalpsi Dlacihpar Gelbisso P3
7 8
2 3
-2
5 6
1
2
-2
-1
lrr 3 4 lrr
2
-2
-3
1 2
2
-2 -5
1 2 3 4 5 6 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8
taert kcolb
;tnemtaer t.s vY taert ;kcol b.s vY
1 2 3 4 5 6
ro fyletarapes ro fedoc
each block treatment
2 F
f
L level
1
rLeogge neration
0
ratio, adjusted
laitraP
partial for treat l
for block effects
-1 o
r laudiseR
t
n
-2
o
c f
F
L f L f
-3
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RESAUNLOTVSA
D fS u mo fS M q e a nSFV P q a r l ( u F e )
block 7 76.23861 10.89123 35.96337 0.0000000
0000000 .6 02 5 5 t0 a. e 4 4r6 6t8 9 3. 92 12 3 95 9. 69
921902 1t0.a 90e 6r 53t1 4: 5.k131c 4 4o50.l3 30b2 .51
48203. 034635.4 18 4slaudise R

) F ( r eP u l q a nSFV a q e fS Mmo u fSD
k c 3 o4l 8b6 3 .302 31 98 .1 06 187302 .67
7 9 9 8 00. 4456893 .t 9 a 21 e2 r3 t9 95 . 69
Resi d u a28l 9 3 s . 7 6 608 . 4 3 5 8 6 4

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3. ...dluo cen o,rehtru ftceff etnemtaer teh terolpx eoT
a. es udna (leve lreht oyrev eo tleve ltnemtaer tyrev eerapmoC
si siht tub ;)tnemtsujda nosirapmoc elpitlum remarK-yekuT
ew (stnemtaer teh tf oerutcurt sralucitra peh to tevitisnesni
,hsi fegra lgnidulcn if ostceff ecificep seh tsserdd ao thsiw
.. .r o,)stepmi lgnidulcn idn ahsi fllam sgnidulcni
b. gnidulcni fo tceffe eht gnitneserper snoitanibmoc raenil mroF
large fish, etc. (see Section 13.3.4), or...
c. 3 eht fo ecnesba/ecneserp eht rof selbairav rotacidni etaerC
:ti fdn asrezar gf osdnik
+tepmil.dn i +llams.dn i +egral.dn i +KCOLB
ind.large ·· ind.small+ ind.limpet ·· tepmil.dni
egral.dn i:etoN( ·· )?yh W.egral.dn i =llams.dni
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“large” = 1 if treatment level is
5 or 6; and 0 otherwise
Value Std. Error t value Pr(>|t|)
(Intercept) 0.1805 0.1497 1.2055 0.2314
block1 0.2300 0.1222 1.8814 0.0634
block2 0.6249 0.0706 8.8539 0.0000
block3 0.5315 0.0499 10.6494 0.0000
block4 -0.0341 0.0387 -0.8810 0.3808
block5 0.1121 0.0316 3.5530 0.0006
block6 -0.0508 0.0267 -1.9060 0.0601
block7 -0.0104 0.0231 -0.4520 0.6524
large -0.5078 0.2117 -2.3982 0.0187
small -0.4941 0.2117 -2.3338 0.0220
limpet -1.8925 0.2117 -8.9382 0.0000
large:limpet -0.2125 0.2994 -0.7097 0.4799
small:limpet 0.2017 0.2994 0.6738 0.5023
tnacifingis-no nf onoitele demit-a-ta-enO
pet stxe netairporpp an as ismre tnoitcaretni
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