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. (,) 0.7.8 (,) 0.93.87 (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..4. 3.8 3.6.4. 0.8..4.6.8 Column Numbr
Sa 5303 (Ohlr): Facoral Hanou 3 Cm> colplo(aa) Now w mak an nracon plo wh a connc ln for ach column of man..4..8.6.4. 0.8.5.5 3 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 4.789 4.789.8556 0.978 coppr 0.677 0.677.coppr 0.070933 0.035467 ERROR 0 0 unfn Cm> c<-cof(".coppr") G h coffcn for h.coppr nracon.
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. 0.5 0. 0.05 0-0.05-0. -0.5.5.5 3 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. (,) 584 66 (,) 489 606 (3,) 453 6
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. 60 600 580 560 540 50 500 480 460.5.5 3 Row Numbr Cm> rowplo(aa) Th h am nformaon by row. I fn h ohr plo ar o nrpr. 60 600 580 3 560 540 50 500 480 460 3..4.6.8 Column Numbr
Sa 5303 (Ohlr): Facoral Hanou 3 5 Cm> aa<-mara("hwprob.a","xmpl8.5") Th h Hun an Laron lvr znc aa. xmpl8.5 6 4 ) 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. 80 75 70 y 65 60 55 50.5.5 3 3.5 4 pro
Sa 5303 (Ohlr): Facoral Hanou 3 6 Cm> nracplo(y,pro,znc) No much nracon bwn pron an znc. 80 y 75 70 65 60 55 50.5.5 3 3.5 4 pro Cm> nracplo(y,mznc,znc) No much nracon bwn mal znc an znc hr. 85 80 75 y 70 65 60 55..4.6.8 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.
Sa 5303 (Ohlr): Facoral Hanou 3 7 85 3 3 3 y 80 75 70 65 60 55 50 45 3 4 4.5.5 3 3.5 4 pro 4 4 Cm> aa<-mara("hwprob.a","xmpl8.0") Th ar h maz proung aa, an 8xx facoral. xmpl8.0 96 4 ) 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)
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.06+07.06+07 0 amp 7 3.78+05 4.683+04 0 gmp 55 55 0.846 amp.gmp 7 758 03 0.538 var 6.38+04 6.38+04 0 amp.var 7 74 67.7 0.9666 gmp.var.065+04.065+04 0.000305 amp.gmp. var 7 657 893.9 0.4 ERROR 64 4.09+04 64. Cm> rvyha() Chck h rual. Look lk om nonconan varanc. S u n z R.5 0.5 0-0.5 - -.5-00 50 300 350 400 450 Yha
Sa 5303 (Ohlr): Facoral Hanou 3 9 Cm> rvrank() Chck for normaly. Look pry goo. S u n z R.5 0.5 0-0.5 - -.5 - - - 0 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 () - -0.75-0.5-0.5 (5) 0 0.5 0.5 0.75 (9).5.5.75 (3) componn: SS () 4.4+04 4.07+04 3.93+04 3.879+04 (5) 3.86+04 3.874+04 3.9+04 3.998+04 (9) 4.09+04 4.56+04 4.44+04 4.668+04 (3) 4.94+04 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.
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 336 336 0 amp 7 3.06 0.4309 0 gmp 0.00438 0.00438 0.374 amp.gmp 7 0.0806 0.058 0.0539 var 0.5896 0.5896 0 amp.var 7 0.0758 0.00394 0.6544 gmp.var 0.08599 0.08599 0.000863 amp.gmp. var 7 0.04764 0.006806 0.96 ERROR 64 0.3497 0.005464 Cm> rvyha() Conan varanc may b a ll mprov on h log cal. S u n z R.5 0.5 0-0.5 - -.5-5.4 5.5 5.6 5.7 5.8 5.9 6 6. Yha
Sa 5303 (Ohlr): Facoral Hanou 3 Cm> rvrank() Normaly look a b wor hough. S u n z R.5 0.5 0-0.5 - -.5 - - - 0 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. 6 5.9 5.8 5.7 5.6 0 5 0 5 30 35 40
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 (.0354+.09+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 336 336 0 a 0.8754 0.8754 0 a.09.09 0 a3 0.0499 0.0499 0.0078 a4 0.00839 0.00839 0.4736 a5.337-06.337-06 0.9876 a6 0.00343 0.00343 0.435 a7 0.00784 0.00784 0.4779 gmp 0.00438 0.00438 0.374 a.gmp 0.03543 0.03543 0.033 a.gmp 8.904-05 8.904-05 0.8988 a3.gmp 0.09 0.09 0.04 a4.gmp 0.006 0.006 0.903 a5.gmp 0.006886 0.006886 0.658 a6.gmp 0.0009846 0.0009846 0.676 a7.gmp 0.00347 0.00347 0.545 var 0.5896 0.5896 0 a.var 0.00099 0.00099 0.6554 a.var 0.0877 0.0877 0.0684 a3.var 0.0079 0.0079 0.53 a4.var 0.0008668 0.0008668 0.697 a5.var 0.003733 0.003733 0.45 a6.var 4.3-06 4.3-06 0.9777 a7.var 0.0009307 0.0009307 0.68 gmp.var 0.08599 0.08599 0.000863 a.gmp.var.406-06.406-06 0.987 a.gmp.var 0.000839 0.000839 0.804 a3.gmp.var 0.04069 0.04069 0.00895 a4.gmp.var 3.99-05 3.99-05 0.939 a5.gmp.var 0.005807 0.005807 0.3064 a6.gmp.var 3.37-06 3.37-06 0.9803 a7.gmp.var 0.000854 0.000854 0.6988 ERROR 64 0.3497 0.005464
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 336 336 0 a 0.8754 0.8754 0 a.09.09 0 a3 0.0499 0.0499 0.0078 gmp 0.00438 0.00438 0.374 a.gmp 0.03543 0.03543 0.033 a.gmp 8.904-05 8.904-05 0.8988 a3.gmp 0.09 0.09 0.04 var 0.5896 0.5896 0 gmp.var 0.08599 0.08599 0.000863 gmp.var. amp 0.007 0.004577 0.6695 ERROR 64 0.3497 0.005464 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 336 336 0 a 0.8754 0.8754 0 a.09.09 0 a3 0.0499 0.0499 0.005764 gmp 0.00438 0.00438 0.363 a.gmp 0.03543 0.03543 0.0094 a.gmp 8.904-05 8.904-05 0.8966 a3.gmp 0.09 0.09 0.0065 var 0.5896 0.5896 0 gmp.var 0.08599 0.08599 0.00009 ERROR 86 0.4504 0.00537 Cm> cof() Coffcn. componn: CONSTANT () 5.04 componn: a () 0.04378 componn: a () 0.0005904 componn: a3 () -3.73-05 componn: gmp () -0.336 0.336 componn: a.gmp (,) 0.04665-0.04665 componn: a.gmp (,) -0.00976 0.00976
Sa 5303 (Ohlr): Facoral Hanou 3 4 componn: a3.gmp (,).64-05 -.64-05 componn: var () 0.07837-0.07837 componn: gmp.var (,) 0.0993-0.0993 (,) -0.0993 0.0993 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 () 0.673 componn: () 0.03 componn: () 0.764 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. (,) 0.09043-0.00864 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 336 336 a.gmp 0.8937 0.4469 gmp.a.09.055 gmp.a3 0.049 0.04 var 0.5896 0.5896 gmp 0.03 0.03 gmp.var 0.08599 0.08599 ERROR 86 0.4504 0.00537 Cm> cof("a.gmp") Sam a compu bfor. (,) 0.09043-0.00864
Sa 5303 (Ohlr): Facoral Hanou 3 5 Cm> aa<-mara("hwprob.a","xmpl8.8") Th ar h CPU pag faul aa. xmpl8.8 54 5 ) 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 99 99 0 alloc 9.7 46.35 0 z 4.69 0.85 8.95-4 q 4.64.3 7.3-3 alg.50.50.84-09 alloc.z 4 0.5043 0.6.689-05 alloc.q 4 9.5.378.63-0 alloc.alg 0.06004 0.0300 0.005736 z.q 4 0.89 0.07.5-06 z.alg 0.0 0.0 0.06579 q.alg 0.0764 0.00888 0.0 alloc.z. q 8.05 0.35 6.76-06 alloc.z. alg 4 0.00400 0.00 0.8365 alloc.q.alg 4 0.060 0.00650 0.49 z.q.alg 4 0.0456 0.00364 0.3548 ERROR 8 0.08 0.0085
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.5 0.5 0-0.5 - -.5-4 5 6 7 8 9 Yha Cm> cof("alg") Hr ar h coffcn for alg. I look lk algorhm prouc xp(.5) =.54 m a many faul a algorhm. () -0.5 0.5 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. (,) -0.0487 0.0487 (,) -0.06 0.06 (3,) 0.0473-0.0473 Cm> boxcoxvc("(alloc+z+q+alg)ˆ3",faul) A ll Box-Cox how ha log wa h rgh ranformaon. componn: powr () - -0.75-0.5-0.5 (5) 0 0.5 0.5 0.75 (9).5.5.75 (3) componn: SS () 4.009+05 9.848+04 3.867+04.99+04 (5).059+04.50+04 6.366+04.648+05 (9).0+06 3.8+06.5+07 6.63+07 (3) 3.45+08