choosedef2(7,4,all:t) K

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Bernadette Parker
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1 i!"! a ` a c a ``` `aaa ``` aaa ``` `!ccc j'$k$ 1 C l ; B-?hm 4noqsr $h t=;2 4nXu ED4+* J D98 B v-,/. <; w ; 1 xx -;>= $-r <; 4Xu E'0. y&'z?h{ O Z$ 4noq}u *K #%$&')( $ +* '$&$-,/.&$103254"!"! &$ <;>=)7 ',?2A@B; (CD9 0FED43G&0!4!3G>H!"4! IJ- KML ( ON 0FE'43G&034!!G-ED"!4P IJQR ;>;%$ &+ N 6S TU$. L = $ htt// by Christoher Bingham Cmd> data <- read("","exml15.6") exml ) A data set from Oehlert (2000) \emh{a First Course in Design ) and Analysis of Exeriments}, New York W. H. Freeman. ) ) Table 15.6,. 398 ) Data for a 2^7 in standard order. Factors are size of image, ) shae of image, color of image, orientation of image, duration ) of image vertical location of image, and horizontal location ) of image. ) ABCD, ACEG, BCE, BCFG, ACF, CDEF, ABG, BDEG, ADE, ADFG, BDF, ) EFG, CDG, ABEF, and ABCDEFG are confounded with blocks. ) Columns are block, A, B, C, D, E, F, G, and resonse Read from file "TP1Stat5303DataOeCh15.dat" ~ 7&$k$ $ %$ ;3GZ / -2M $ %$ ; P3GZ / -;&r1 ;%$ H3GZ / ;)9$x 8'8 y ; ƒ ; (;&r $r2aed u 4 G-E <; tk r $h t=; $h >( < y$ ;){9 7? ;%$ ˆ-(&;&r.& choosedef2(7,4,allt) K ~ 7&$k$ 1u E k$ e 9$K Cmd> makecols(data,block,a,b,c,d,e,f,g,y,factorsrun(8)) Column 1 saved as factor block with levels Column 2 saved as factor a with 2 levels Column 3 saved as factor b with 2 levels Column 4 saved as factor c with 2 levels Column 5 saved as factor d with 2 levels Column 6 saved as factor e with 2 levels Column 7 saved as factor f with 2 levels Column 8 saved as factor g with 2 levels Column 9 saved as vector y 2

2 j'$k$ 1 -; A2R <;! <(>re <;>=, ; $hx$&d) <( 4!GZ >-253GZ / -;>r P3GZ / ;)9$x 8+G w; &K ~ 7 1 ; -; &K Cmd> anova("y=block + (a+b+c+d+e+f+g)^4") Model used is y=block + (a+b+c+d+e+f+g)^4 WARNING summaries are sequential DF SS MS CONSTANT block a b c d e f g a.b a.c a.d a.e a.f a.g b.c b.d b.e 1 5e-05 5e-05 b.f b.g c.d c.e c.f c.g d.e d.f d.g e.f e.g f.g a.b.c a.b.d a.b.e a.b.f a.b.g 0 0 undefined a.c.d a.c.e a.c.f 0 0 undefined a.c.g a.d.e 0 0 undefined a.d.f e e-06 a.d.g a.e.f a.e.g a.f.g b.c.d b.c.e 0 0 undefined b.c.f b.c.g b.d.e b.d.f 0 0 undefined b.d.g b.e.f b.e.g b.f.g c.d.e c.d.f c.d.g 0 0 undefined c.e.f c.e.g c.f.g d.e.f d.e.g d.f.g e.f.g 0 0 undefined a.b.c.d 0 0 undefined a.b.c.e a.b.c.f a.b.c.g a.b.d.e a.b.d.f a.b.d.g a.b.e.f 0 0 undefined a.b.e.g a.b.f.g a.c.d.e a.c.d.f a.c.d.g a.c.e.f a.c.e.g 0 0 undefined a.c.f.g a.d.e.f a.d.e.g a.d.f.g 0 0 undefined 4

3 a.e.f.g b.c.d.e b.c.d.f b.c.d.g b.c.e.f b.c.e.g b.c.f.g 0 0 undefined b.d.e.f b.d.e.g 0 0 undefined b.d.f.g b.e.f.g c.d.e.f 0 0 undefined c.d.e.g c.d.f.g c.e.f.g d.e.f.g ERROR ~ 7&$ $xkƒk$, ; )?hu l7&$ &+ y$r 3G>2v03G1 -;&r H!GZ <;)9$x 8D y ;!K 'e9$ 7&$ + w- <;>= D ƒ7&$ B >)=%$h $hx$&d,u$ -; >( k$ e K ~ $, a.b.g 2 a.c.f 2 a.d.e 2 b.c.e 2 b.d.f 2 c.d.g 2 e.f.g 2 a.b.c.d 2 a.b.e.f 2 a.c.e.g 2 a.d.f.g 2 b.c.f.g 2 b.d.e.g ';Zr I (;&r $8 t;%$-rns R7 %$ " r%$=k$>$h c.d.e.f h{ k$$r -,ƒk ~ 7&$h $ k$ EDP hu7&$ ED ;ˆ (>;>r%$-r $ xˆ$zd &K ~ 7&$ E' 2 U( tr17 %$.&$>$ ;17&$k$ Uk7&$ a.b.c.d. e.f.g, -r$ U - y=(a+b+c+d+e+f+g)^7 K!( B7 ;% ;GC ; (;&r $r r%$h <=; 1&( ' -; w>z 9$h $hx$&d) &K j'- U$ %$)2AED k$ ; (;>r $r O7. y&'z -;>r,/.z$ = $.&$Z' -( $ h = $. y&'z re x $$; $h >2 ;%e.&$&' -( $ huxk$,u$ ;) re x$k$ ; $h &K Cmd> yts <- yates(y) Cmd> chlot(rankits(yts),yts,xlab"normal scores",\ title"normal score lot of Yates effects") Cmd> chlot(halfnorm(abs(yts)),abs(yts),\ xlab"half normal scores",\ title"normal score lot of Yates effects") Normal score lot of Yates effects y 0.1 t s Normal scores Half normal scores lot of Yates effects Half normal scores x$&d) E'032AE'"!!25P4 -;>r E'4!H &$ ƒ9.&$ () w$ &K j'- r & ( tr $ ;) 7&$ ;%e 7 rk '7&$Z'z 7,/ <; $ C$&' A2v!2 6 2v!2 22 -;>r k$ $hx$&d) ED254!2vP!2 *32AEe0325!4 -;>r 03P IJ4<2542v4 2v4<254<254 2v4 NJ2 7&$. <== $ $hx$&d{ice'0n/ ƒ! y$ 8 7&$ (; ; (;>r $r,/ <; $hx$&d K 5 6

4 @;. <; x ;%e y ; 7&$h $ k$ 6 ' x$&d Ee0 u "!"SED"!"!"". E'"! u E!E'" ED"!"SE&. A P4 u " E'" ED" E'".! E'4!H u E!EE!E!E!EE&. A6 T 7Z$ ;7&$ 8 t=)7, h 1re t=e B ED2 <; 7&$ $hx$&d K T 7&$ ; 7&$ 4!;>r k-, x7z$ 8 t=)7 E'25 <; 7&$ $hx$&d -;>r ;&K 'e9$ 7 ED"!!2vP!4 -;>r ED4!H xk$h & ;>r9 ; (;>r $r? ;)x -;>r k$ k$h $ ;) re x$g $ ; $h.&$e% U$$ ;1. w&ez >25;%e{k$ %, $;) $hx$&d) &K -,/ -()9$ <;1 %$C ' -;%$ / 7&$ <;>re $h?h 7&$ ; (;>r $r $hx$&d) &K Cmd> confounded <- vector("abg", "acf", "ade", "bce", "bdf", "cdg", "efg", "abcd", "abef", "aceg", "adfg", "bcfg", "bdeg", "cdef","abcdefg"); conf <- re(0,15) Cmd> for(i,1,15){ tm <- match(vector("*a*","*b*","*c*","*d*","*e*","*f*","*g"),\ confounded[i],0,exactf) tm[tm!= 0] <- 1 conf[i] <- sum(tm*2^run(0,6));;} Cmd> rint(format"3.0f",conf) # confounded terms conf (1) ~ 7&$ <;! <(>r $ P!4!2AE'"! -;>r ED4!HK ~.&$, $ ; ;>=x( 2 ;%,/ Mƒ7> ;%,/ ye) 9$h $hx$&d), ( -, B{7&$ ; (;>r $r ;%$h &K ;%$ > 9 r B 19 k$ $ k7&$,.> K ~ 7&$ $.Z$ t=;%k$r ; 7&$ ye2 MISSING $ $ >; ;>=, $ = $h &K Cmd> yts[terms] <-? # set con Cmd> yts[grade(abs(yts),downt)][run(10)] WARNING missing values in argument(s) to abs() WARNING MISSING values in argument to grade() (1) (6) Cmd> chlot(rankits(yts),yts,xlab"normal scores",\ title"normal score lot of Yates effects") WARNING MISSING values in argument to rankits() Cmd> chlot(halfnorm(abs(yts)),abs(yts),\ xlab"half normal scores",\ title"half normal score lot of Yates effects") WARNING missing values in argument(s) to abs() WARNING MISSING values in argument to halfnorm() WARNING missing values in argument(s) to abs() Normal score lot of Yates effects E Main effect 0.15 y t s Normal scores Half normal score lot of Yates effects E Main effect Half normal scores l; 7&$,/ <; $hx$&d x ;>r () K 7 8

5 ``` ` B{ ye r $h t=; ' -;1.&$ 7&(>=)7 U &$ h <; -,/ y$e9$. y&'z r%$h <=;2 /7&$k$ y$ ;$,/ <; $hx$&d) 1 ;>r, $e ],U$h <;)9$x 8D w ; 1 k$ ; (;>r%$r B7. w&ez &K <;$k$ ; $.& (){7&$ ; (;>r $r $hx$&d)?$hx$&d < %$+ -, $h k-, -; -; &K X <;$k$ ; $.& (){7&$ (;C ; (;>r $r $hx$&d) ƒ-,u$h k-, -; -; B ~ 7&$. $ %, $ ;) )( D(k$ ( &( -,/ w$e9$ 8D98 ],/ y$h ' $ (17 - %$ ( ƒ% U 8D9 >2 -;>r B7 -;>r. y$ %$+ >2 k$h &$&D < %$+ K h( 7 - %$ ;. y&dz }hƒ O Z$.-2 3u>;. <;1 tk ~ 7Z$h $ >$ K ~ $ 7&$ &$8 ],U$ ;) }(; B) O7 <;1. wz'z k$ ' w$-r, $e ],U$h l;%$ hu7&$ 8D9 >2M A2M 17&$ K ~ k$ %,U$ ;){ - <=;&, $ ;) ; % U 9$ &K (1C ;>r -, t=; y$ %$+ 9 7&$ /7&+ y$ ye) 1 -;>r lx7z$ B ye) <; 7&$ /7&+ y$ we = $e{7&$ D, $ y$ %$+ Mhm K! $ 8e7 /7&+ y$ ye2 & (1x -;>r -, <=; y$ %$+?h{+k ~ 7&$ k$h >( B r $h t=; 7. -; $r k$,u$ ;)) &K 9 10

6 ! $ D, w$ -; $ &$8 t,u$ ;){9 -,/ k$ u y$ %$+?h B D= $ I y- <;>=N -;>r. u P $C O 8$ ; 7&$ y$+ tr1 U 'k ; ; u k$ ' k$ ;%e x 8D e 9 x = $.&$e% U$$ ; 9 Z, y$&$h?hu C y$+ trk ' 7&$ y$+ tr re < tr $r <;)9 7Z-, = $;%$ ( 8 B 19 7 '7 B =%$,U$e7&r t=;%$r x -;>r -, BDK ~ 7&$ ; ;>r 25 k$ -;>r k$ C ;>r -, t=;%$r9 7&$ 1I B &(. we) N/ <;. y&'z u 7Z+ w$ ye K E 4 P 0 H * 'e9$ 7&$k$? ;%$ y$ %$+ Mhm ;>r -,?G y$e9$ $ h y$ %$+ <; $ 8'7 hu7&$ ; ;%$ 7Z+ w$ ye) 1I. w&ez NJK A;%e7&${ =)8 +( B(x R$ D,/ y$ ~ 7&$ k$h & ; $ w$h <r?h ) &K ~ 7&$ /7&+ w$ G w{ -;>r B)G ye 8D9 k$ RP ye)?h ) >2 E ; $ZD9$r B7 (;>=( >2AE ;%e2 -;>r 4 k$h -;) K RP ke9$&d -;)) ~ 7&$ <;, y ;1.& (){7&$ P w?h ), t=)7 =( tr $ '7&h <;>=? ;)x ) &K % $ D,/ y$ & (, t=)7 -;){9 -,/ k$ k$h -;){ -;&r ;%; k$h -;)1( <;>=? ;))G x U$+ t=)7) 1I G-ED2 G-ED2]E'2]E&NJK '$$r ye) U$k$ t=;%$r9 E'0 ;) t=(% ( k$ ;1 C y$+ tr2s7&$ 7Z+ w$ ye) >25P /7&+ y$ ye) &$ $>$r ye K 8'7 7Z+ w$ ye - >(.Dre tr $r <;)9 ( -,/ 8D k$ 9 /7 '7 7&$ ({ ke9$&g -;)ƒk$ %,U$ ;)) U$k$ x -;&r -, t=;%$rk 11 12

7 @BU& ( re tr; {7 %$ 7&$ ke9$&d -;) B{7 r " $hx$&d2 & ( U ( tr7 %$,Ur $+ X z&$ u K u $$r &$ $hx$&d u x -;>r -,. y&'z $hx$&dƒ7&$ z. y&'z Bx7 $$r &$ tk 17&$ { B7 >8 B -; $ u x -;>r -, O ye >(.> we $xk O7 8 -; $ K ~ 7&$h $ $xk k$ re x$k$ ;) ; $ 8'7 B{ we -;>r 7&$ B wk ( ( tr -; Z$ B ( <;>=. y&'z, $ -; u u ~ 7 -;>r) r ;%$ 8D9, -r $+ B7 $x8 K '$&' -( $,U$ -; k$ r $8 < %$r Jk-,. y&'z 9e &2S7 k$ -; -; B- &K T/7 U ( tr j $ re =)x D, ƒ7 r $ <=; yz z&$ M 1 1 A 4 3 (WPE) (SPE) ~ 7&$ r $ ;%-, <; 9 ƒ9$h <;>=1 ( <r.&$ 7&$ 7&+ y$ ye $x I T L Nm,U$ -; >( k$k!(){7&$k$ $& ;>r 8D9 7&$,Ur $+ 8D( u T/7 U ( tr j $ re =)x D, 7 r%$h <=; yz Bz&$ (WPE) 12 A 4 3 M 1 1 AB 9 (SPE) B

8 f ~ 7&$ r $ ;%-, <; 9 ƒ9$h <;>=1 1 = ; 7&$ 7&+ y$ ye $x I T L Nm,U$ -; >( k$.&$&' -( $ 7 17&$ y$ re <;>= $+ <=e. y$ x -;>r -, k$,.&$+ y- K ], 8 x7z$ r $ ;-, <; 9ƒk$ ;>= -;>r1a 17&$ B ye $xkƒij!l N, $ ; >( k$k = ; B 17&$ y$ re <;>= $+ t=e. y$ x -;>r -, 9$,.&$+ y- -;>r1a+k YYYY [[[ [ fff ~ $ j'$k$ 1 -; $ D,/ y$. $r ; r), -9$$+ y$ -;>r x8 y$ ƒ7&$ &$8 ], $ ; (>r) <;>= ke9$&d -;)) B7 ) $$r ( $h &K R{7&$ 7&+ y$ ye w$ %$h 2 $h C'8.&$r 1 6!2 B7. y&'z &K ~ 7&$k$ ; k$ ; & ( ' -; q 7 - %$ -;! y$ r $ 8D2M ; 7?$ &$G ], $ ;)2 %$x -,{, ;2S7&$ 7Z+ w$ ye) 7&$-,? $+ < %$h U$k$ =)k ( &$r ; >( &$. y&'z?hƒ B Z$ u P!2 B7 7&$ /7&+ y$ w 8D9 y$ %$+ t=;%$r <;1-6 K Cmd> data <- read("","sandt") sandt 64 4 format ) Slit lot data from Steele & Torrie ) Exeriment to study effects of 4 rotectants on ) oats grown from 4 seed sources. ) Seed source was whole lot factor, arranged in 4 randomized ) blocks (relicates). Protectant was slit lot factor, ) all 4 levels in each whole lot ) Col. 1 Block number (1-4) ) Col. 2 Seed lot (1-4) ) Col. 3 Protectant (1-4) ) Col. 4 Yield (resonse) Read from file "TP1Stat5303Dislayssandt.dat" Cmd> makecols(data,block,seed,rotectant,y) Cmd> block <- factor(block);seed <- factor(seed) Cmd> rotectant <- factor(rotectant) Cmd> anova("y=blocks+seed + E(blocks.seed) + rotectant + seed.rotectant",fstatt) Model used is y=blocks+seed + E(blocks.seed) + rotectant + seed.rotectant DF SS MS F P-value CONSTANT e e blocks seed ERROR rotectant seed. rotectant ERROR ~ 7&$ $$r ( $,/ ; $hx$&d 7 <=)7 B t=; ' -;) 1x7Z$ <;)9$x 8D y ; hƒ $$r. ke9$&d -;) K 15

9 j'$k$ 7&$ C 1( $ U %$x ( $h( $ (k$ h Q 8eA;% ( /x } 9$, <; E(...) I 7&$k$ E(blocks.seed) N 2 anova() k9$ k78$ $, < ; D,U$r ERROR1 -;&r 7&$ /7&+ y$ we $xkk ~ 7&$ C <; M$x 9$, ; D,U$-r ;>r 7Z$ % ye $xkƒ9$,ƒk (17 r,uk$ 7 ; ;$ E(...) 2 $%, m( ]r.8$ ERROR1 2 ERROR2 2 ERROR3 2 K K K K ~ 7&$ r $ ;%-, <; 9 $ 8'7 7&$ ;%$ ERRORx,U$ ; > &( >9$-K j'$k$ 17Z$ D,U$ B7Z () E() Cmd> anova("y=blocks*seed + rotectant + seed.rotectant",\ fstatt) Model used is y=blocks*seed + rotectant + seed.rotectant DF SS MS F P-value CONSTANT e e e-44 blocks e-12 seed e-12 blocks.seed rotectant seed.rotectant ERROR ~ 7&$! k$ 7&$ D,U$K ~ 7&$ G blocks -;&r >9$ r ˆ$9$; I ;&r <; xk$&dxn 25 <; $ seed x7z$ ( $ /7 U$ z-;- 9.Z$ 7&$ B{ we $xk{ r $ ;%-, ; 9K 17

by Christopher Bingham

by Christopher Bingham a D D E!"! #%$&')( $* '$&$,+.-&$0/!12"!"!2 4657 85&$9 ;:=