Cmd> data<-matread("hwprobs.dat","exmpl8.2") This is the data shown in Table 8.5, the copper and diet factors.
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- Georgiana Arnold
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1 Sa 5303 (Ohlr): Facoral Hanou 3 Cm> aa<-mara("hwprob.a","xmpl8.") Th h aa hown n Tabl 8.5, h coppr an facor. xmpl8. 3 ) Tabl of ramn man for h Lynch an Sran (990) ) aa. column ar cu normal an fcn, row ar ) km mlk pron, why, an can. Rpon ) ron lvl n lvr u. Cm> aa Th aa a marx gvng h rpon man for h x ramn group. Row ar an column ar coppr ramn. (,) (,) (3,)..53 Cm> rowplo(aa) Hr w mak an nracon plo wh a connc ln for ach row of h marx of man. Th ln ar no prfcly paralll, bu no wlly ffrn n lop Column Numbr
2 Sa 5303 (Ohlr): Facoral Hanou 3 Cm> colplo(aa) Now w mak an nracon plo wh a connc ln for ach column of man Row Numbr Cm> y<-vcor(aa) Pu h group man no a vcor for u n anova(). Cm> <-facor(,,3,,,3) Mak up an coppr facor ncang hr lvl. Cm> coppr<-facor(,,,,,) Cm> anova("y=coppr") Do h anova. No ha MacAnova on know ha ach of h valu h avrag of 5 un. Th SS from h compl aa ar 5 m a larg, an of cour w can ma rror n h full aa. Mol u y=coppr DF SS MS CONSTANT coppr coppr ERROR 0 0 unfn Cm> c<-cof(".coppr") G h coffcn for h.coppr nracon.
3 Sa 5303 (Ohlr): Facoral Hanou 3 3 Cm> colplo(c) Inracon plo wh nracon coffcn can how nracon mor clarly han plo wh group man, bu can b mor ffcul o jug f h z of h nracon ha prn manngful compar o h z of h man ffc. Hr w ha column rlavly hghr han column n row wo, bu h rvr ru n row 3. Howvr, lookng a h arlr plo w ha column hghr han column n vry row, bu h amoun ffr, an no by vry much compar o man ffc Row Numbr Cm> aa<-marx(vcor(584,489,453,66,606,6),3) Th ar h Nlon al chck boy wgh aa. Cm> aa Agan, ju group man. (,) (,) (3,) 453 6
4 Sa 5303 (Ohlr): Facoral Hanou 3 4 Cm> colplo(aa) Man by column. Hr w clar nracon. Th man n column ar farly ay acro row, bu h man n column cra acro row Row Numbr Cm> rowplo(aa) Th h am nformaon by row. I fn h ohr plo ar o nrpr Column Numbr
5 Sa 5303 (Ohlr): Facoral Hanou 3 5 Cm> aa<-mara("hwprob.a","xmpl8.5") Th h Hun an Laron lvr znc aa. xmpl ) Tabl of ramn man akn from fgur of Hun an ) laron 990. Column ar mal pron, mal znc, ) znc, an rpon (% znc rnon). Cm> makcol(aa,pro,mznc,znc,y) Pu h aa no vcor. Cm> nracplo<-macrora("morgn.mac","nracplo") Pck up a copy of morgn.mac from h cla ofwar wb pag, an hn ra n nracplo, a mor flxbl way o o nracon plo. Cm> nracplo(y,pro,mznc) W can a pry clar nracon bwn pron an mal znc, parcularly a h low lvl of pron y pro
6 Sa 5303 (Ohlr): Facoral Hanou 3 6 Cm> nracplo(y,pro,znc) No much nracon bwn pron an znc. 80 y pro Cm> nracplo(y,mznc,znc) No much nracon bwn mal znc an znc hr y mznc Cm> nracplo(y,pro,mznc,znc) Hr w look a pron on h horzonal ax, wh para ln for all h mal znc by znc combnaon. Th ln ar numbr wh h mznc changng fa, hn znc, hn a hr facor f ha bn u, an o on. Th ju rnforc h arlr mpron ha pron an mal znc nrac, bu nohng l.
7 Sa 5303 (Ohlr): Facoral Hanou y pro 4 4 Cm> aa<-mara("hwprob.a","xmpl8.0") Th ar h maz proung aa, an 8xx facoral. xmpl ) Daa ar mol on Tabl of ) Bruc Orman (986) "Maz Grmnaon an Slng ) Growh a Subopmal Tmpraur", MS Th, Unv Mnn ) Drmnaon of amyla acvy n prou maz unr ) varou conon ) Column h mpraur a whch h aay ak plac ) Lvl hrough 8 rprn 40, 35, 30, 5, 0, 5, 3, ) an 0 gr C ) Column h growh mpraur of h prou ) lvl 5 gr, lvl 3 gr ) Column 3 h vary of maz ) lvl B73, lvl Oh43 ) Column 4 h amyla pcfc acvy n nrnaonal un Cm> makcol(aa,amp,gmp,var,y) G column an mak facor. Cm> amp<-facor(amp) Cm> gmp<-facor(gmp) Cm> var<-facor(var)
8 Sa 5303 (Ohlr): Facoral Hanou 3 8 Cm> a<-vcor(40,35,30,5,0,5,3,0)[amp] Now w wan o u h fac ha analy mpraur quanav. So, g h acual mpraur no a vcor. Cm> a<-aˆ;a3<-aˆ3;a4<-aˆ4 W hav 7 f for analy mpraur, o xpr h a polynomal rm. Cm> a5<-aˆ5;a6<-aˆ6;a7<-aˆ7 Cm> anova("y=ampgmpvar",pval:t) Do h hr way anova. ampgmpvar a hor cu. rmrm xpan o rm + rm + rm.rm. You can ju kp arrng mor an mor rm oghr. amp, var, an gmp.var look gnfcan, h ohr rm l o. Bcau gmp.var gnfcan, I woul nclu gmp n my mol o manan hrarchy. Mol u y=ampgmpvar DF SS MS P-valu CONSTANT amp gmp amp.gmp var amp.var gmp.var amp.gmp. var ERROR Cm> rvyha() Chck h rual. Look lk om nonconan varanc. S u n z R Yha
9 Sa 5303 (Ohlr): Facoral Hanou 3 9 Cm> rvrank() Chck for normaly. Look pry goo. S u n z R Rank Cm> boxcoxvc("ampgmpvar",y) W ll ry Box-Cox o fx nonconan varanc. Howvr, I m no oo hopful, bcau h rao of h larg (499.8) o mall (97.) rpon only abou.5, an I on xpc h uual powr famly ranformaon o hav oo much ffc unl h rao bggr. Log look b, bu n ha much br han naural cal. componn: powr () (5) (9) (3) componn: SS () (5) (9) (3) Cm> 3.86(+nvF(.95,,64)/64) Th powr ju barly ou h 95% confnc nrval for ranformaon powr. () 4.0 Cm> ly<-log(y) L look a h log aa.
10 Sa 5303 (Ohlr): Facoral Hanou 3 0 Cm> anova("ly=ampgmpvar",pval:t) anova() on h log cal. Mol u ly=ampgmpvar DF SS MS P-valu CONSTANT amp gmp amp.gmp var amp.var gmp.var amp.gmp. var ERROR Cm> rvyha() Conan varanc may b a ll mprov on h log cal. S u n z R Yha
11 Sa 5303 (Ohlr): Facoral Hanou 3 Cm> rvrank() Normaly look a b wor hough. S u n z R Rank Th ffrnc bwn log aa an orgnal cal no all ha gra. Th log o hlp, bu h mprovmn no ha ramac. For h m bng, work wh h log aa. Cm> plo(ab(a,amp,man:t),ab(ly,amp,man:t)) Mak a plo of rpon man agan analy mpraur. Dfnly curv, mayb lghly aymmrc oo
12 Sa 5303 (Ohlr): Facoral Hanou 3 Cm> anova("ly=(a+a+a3+a4+a5+a6+a7)gmpvar",pval:t) Hr h anova ung polynomal rm for amp. I look lk w n cubc rm n amp, var, gmp, an h var by gmp nracon. No vnc of ax by var rm gnfcan. Th ax by gmp an ax by gmp by var rm ar mor problmac. A h mo w n h h fr hr rm of ach of h nracon. Combnng h lnar, quarac, an cubc par of h hr-way nracon ha a MS of abou.0367 (=.04/3), an a p-valu of abou.067. I woul probably lav ho hr rm ou, bu a clo call. Th hr ax by gmp rm hav a combn man quar of ( ny)/3 =.05; h ha a p-valu of.0; I woul kp h con orr rm. WARNING: ummar ar qunal DF SS MS P-valu CONSTANT a a a a a a a gmp a.gmp a.gmp a3.gmp a4.gmp a5.gmp a6.gmp a7.gmp var a.var a.var a3.var a4.var a5.var a6.var a7.var gmp.var a.gmp.var a.gmp.var a3.gmp.var a4.gmp.var a5.gmp.var a6.gmp.var a7.gmp.var ERROR
13 Sa 5303 (Ohlr): Facoral Hanou 3 3 Cm> anova("ly=(a+a+a3)gmp+vargmp+amp.gmp.var",pval:t) Hr w hav pull h gnfcan rm ou an hn lump all ohr mol f no h amp.gmp.var rm. No urprzngly, h lfovr rm no gnfcan. No ha w houl no g our coffcn from h mol. WARNING: ummar ar qunal DF SS MS P-valu CONSTANT a a a gmp a.gmp a.gmp a3.gmp var gmp.var gmp.var. amp ERROR Cm> anova("ly=(a+a+a3)gmp+vargmp") Hr h ruc mol wh only h gnfcan rm. U coffcn from h mol. WARNING: ummar ar qunal DF SS MS P-valu CONSTANT a a a gmp a.gmp a.gmp a3.gmp var gmp.var ERROR Cm> cof() Coffcn. componn: CONSTANT () 5.04 componn: a () componn: a () componn: a3 () componn: gmp () componn: a.gmp (,) componn: a.gmp (,)
14 Sa 5303 (Ohlr): Facoral Hanou 3 4 componn: a3.gmp (,) componn: var () componn: gmp.var (,) (,) Cm> conra("gmp",vcor(-,)) Th largr han xpc coffcn for gmp promp m o look a a conra n gmp. Compar h o h SS for gmp abov. Wha ha happn ha whn avragng acro all lvl of amp, hr no much ffrnc. Howvr, gvn ha w ar fng only cubc polynomal o amp, w n o hav ffrn nrcp for h wo lvl of gmp for h polynomal o f. componn: ma () componn: () 0.03 componn: () Cm> cof("a")+cof("a.gmp") W hav a coffcn for a an an a.gmp rm. Th gv an ovrall a coffcn an ffrnc for h a coffcn bwn h gmp group. W coul combn h o wha h a coffcn ar n h wo gmp group. (,) Cm> anova("ly=a.gmp+a.gmp+a3.gmp+vargmp") Y, anohr mol, h combnng a an a.gmp no on rm. DF SS MS CONSTANT a.gmp gmp.a gmp.a var gmp gmp.var ERROR Cm> cof("a.gmp") Sam a compu bfor. (,)
15 Sa 5303 (Ohlr): Facoral Hanou 3 5 Cm> aa<-mara("hwprob.a","xmpl8.8") Th ar h CPU pag faul aa. xmpl ) pag faul aa. column ar algorhm, qunc, z, ) allocaon, an numbr of faul Cm> makcol(aa,alg,q,z,alloc,faul) G vcor an mak facor. Cm> alg<-facor(alg);q<-facor(q) Cm> z<-facor(z);alloc<-facor(alloc) Cm> lfaul<-log(faul) W ak log bcau h aa ju look mulplcav. Thng m o ncra by facor rahr han conan amoun. Cm> anova("lfaul=(alloc+z+q+alg)ˆ3",pval:t) Hr h anova. Th powr form for a rm n a mol ak all man ffc, facor nracon (f), an 3f. W u h 4 facor nracon a rror. I look lk all combnaon of allocaon, z, an qunc ar gnfcan. Algorhm an alg.allocaon ar alo gnfcan, bu only conrbu a ll b of h mol SS. Mol u lfaul=(alloc+z+q+alg)ˆ3 DF SS MS P-valu CONSTANT alloc z q alg alloc.z alloc.q alloc.alg z.q z.alg q.alg alloc.z. q alloc.z. alg alloc.q.alg z.q.alg ERROR
16 Sa 5303 (Ohlr): Facoral Hanou 3 6 Cm> rvyha() W mgh hav ovrranform a b, bu rual on look oo ba. S u n z R Yha Cm> cof("alg") Hr ar h coffcn for alg. I look lk algorhm prouc xp(.5) =.54 m a many faul a algorhm. () Cm> cof("alloc.alg") Lookng a h nracon, w ha alg o rlavly wor on allocaon 3 (mall) han on h ohr allocaon. I ll br han alg on alloc 3, ju by no a much a on h ohr allocaon. (,) (,) (3,) Cm> boxcoxvc("(alloc+z+q+alg)ˆ3",faul) A ll Box-Cox how ha log wa h rgh ranformaon. componn: powr () (5) (9) (3) componn: SS () (5) (9) (3)
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