Google
 

Trailing-Edge - PDP-10 Archives - decuslib10-09 - 43,50466/manov.chn
There are no other files named manov.chn in the archive.
O@+C #*4$&v #)4$'HL#|4$'Z+)"-\74+04"4
+0-\74+94#4
+9-\74+<4#|4
+8:Z+Dh,04Dh"v1:9&}$D"$D"$D"#$D"($D",$D"1$D"5$D":$D">$D"$D"$D"$$D"($D"-$D"1$ D"6 $ D": $ D"? $ D" $ D"  $ D"$ $ D") $ D"- $ D"2 $ D"6 $ D"; $ D"? $ D" $ D"  $ D"% $ D") $ D". $ D"2 $ D"7 $ D"; $ D"@ $ D" $ D"! $ D"% $ D"* $ D". $ D"3 $ D"7 $ D"< $ D"@ $ D" $ D"" $ D"& $ D"+ $ D"/ $ D"4 $ D"8 $ D"= $ D"A $ D" $ D"" $ D"' $ D"+ $ D"0 $ D"4 $ D"9 $ D"= $ D"B $ D" $ D"# $ D"' $ D", $ D"0 $ D"5 $ D"9 $ D"> $ D"B@@$O@+CL#)5$'L +@X@'K "'Lb +'T(1H1//' WESTERN MICHIGAN UNIVERSITY'//,	 ' MULTI-VARIATE ANALYSIS OF VARIANCE'/) +?X@'V "'YB$$ 
1:9's!$qD+E:Z+D#|2Dh$$(. H$ +@X@(< "(>b$#v#y +(D(8H0PROBLEM I4,I4, 10H VARIABLES I3, 8H FACTORS /) $t$D$ #y3d#}gO #v3f#gOG4$+ : Z+D Zh#* Zh#C Zh#\3:#v9(K +F4$(V : Z+D ((+B (( h"v F
@H
3:#v9(O+(a +?X@(X "(`B : Z+D : Z+D +D(.(

1:9(Z +D3:#v9(Y +(a(8(A6,A4)) #v D"u +F5$(l +@X@(e ") b : Z+D ((
 ((

3:#v9(f @@"u #x5$(t +?X@(o "(tB"u"u : Z+D #*1:9(q +(u(40I2)     "u."u D+H $2$+HgOA#x5$( +?X@({ "(tB : Z+D #*3:+H9(|  "u5D)@@"u +@X@) ")b"u"u +)
(1H0I2,9H CRITERIA I4, 43H COVARIATES  WITH THE FOLLOWING VARIABLES      )  #v3$+H++ +H( D+H : Z+D h#* D+I (( +I((+K (( +I((
+L3:+H9) +@X@) ") b : Z+D (
+L3:+H9)++)"(10(3XA6,A4)X)$.#vD+I+@X@)%#*4$)X:Z+DZh#CZh#\3:#v9)'L#z4$*9+@X@)+@: Z+J : Z+D : Z+D $b$+J &$+D..'3:#~9). +D3:#~9)- +J3:#y9),  +@X@)8@ : Z+J : Z+D $2$+J.
$+J. +D3:#v9)I +J3:+I9)H : Z+J : Z+D +J(.(

 +D1:9)P +J3:#v9)O  +@X@)W : Z+D +?X@)Z ")jBh"
+J+K : Z+D ( +D.!1:9)] : Z+D (.+D4 +D1:
9)aD:Z+Df+)l(A1,I1,29I2,5A4)     +8 D+K #|2D+K+)s : Z+D (.+D Z43:+K9)p +D +K F! +@X@)v ")|b +D"
\+D!y:Z+DTOR A1,I5,7H LEVELS  10X,5A4)     #~ +D2$!gO !0HgOG4$+"$ +D.! D!
 +D & F!2 +D !4D*$ +D & F!6 : Z+D (.+D !4D*!"$. D+I +@X@* "*b +D"
+I (.+D!+*(1H!9X,A1,I1,4H HAS I3,3H DF) +D( +D.  !. !. D !2 +D1:9*
4+Dv$!XD*'-\.;4+J4+D4*'44!4"Z+JJ:Z+DD:2Z+DJ$b$+J&$+D..'3:#~9*0J+D3:#~9*/ +J3:#y9*. L#w4$*J : Z+L $'. D+H +?X@*> "*BB +L Z+D 3:+H9*? +L +*D(80A1)     +L Z+D +=3Dh+*J3:+H9*D +L.:(1z@+*:++L#*D#z4$*sL#*4$*R-\1B4+L4+E4+G4+F4+G"#v.+L D"v #)4$'H +@X@*S` : Z+J : Z+D $2$+J.
$+J. +D3:#v9*d +J3:+I9*c : Z+J : Z+D +J(.(

]+D1:9*k++J3:#v9*jEV+@X@*rR:+Z+DN:XZ+J $b$#}&$.+D.@@	3:#~9*u+$b$#}+&$+D.+D.!(H	+D3:#~9*s=+@X@+@	:1Z+J : Z+D :6Z+D $b$+J &$+D..'3:#~9+ +D3:#~9++J3:#y9+I++.+@X@+.    
R               1    2    3    4    5    6    7    8    9   10   11   12   13   14   15   16   17   18   19   20   21   22   23   24   25   26   27   28   29   30   31   32   33   34   35   36   37   38   39   40   41   42   43   44   45   46   47   48   49   50    $..H D.O .K 	 D.P $ D.P@@.Q $3$.O+.96b.O0b7+,Q4,T4,x4-,4. $3D.I+,t .MX@,W ",Xb +,[(23H   DEVIATION CONTRASTS   ) : Z.Q $b$.I. .J.!( H $b$.I &$..I. .J."
.E J' : Z.R .Q2D+,m $b$.I &$..Q. .J.!* J'+,q $b$.I &$.R..Q. .J.@@' .R3:.I9,e .Q3:.I9,\ $b$.I..I .J.!( H+.9@@.R .MX@,z ",{b +,(20H   SPECIAL CONTRASTS )    @@.Q:.Q .MX@- "-	B : Z.R $b$.I &$..Q. .J.'3:.I9- +-
(16F5.0)  +.' .MX@-
 "-b.S.S : Z.R $b$.I &$..Q. .J.'3:.I9- +-(3X,2A1,10F12.5/(5X,10F12.5) ) &b$.I ($.Q. 
.J.
 /D.R .I2d.Q+, : Z.Q &b$.I ($ H.L. 
.J.
 /.R D/3:.I9- &b$.I .J. $'XD-*-\4J4.I4-*4.T4
.E+.9 .MX@-- "-	B : Z.Q $b$.I. .J.$3:.I9-.  .MX@-5 "-;b : Z.Q $b$.I. .J.$3:.I9-6 +-B(45H   ORTHOGONAL POLYNOMIAL CONTRASTS WITH SCALE /(5X 10F12.5) ) .MX@-C "-b  &b$.I .I. 
.J.
 /$ 
.J.
/%D D.T &b$.I .I. 
.J.
 /$ 
.J.
/%!*
 J.U : Z.Q".T &b$.I . 
.J.
/$.U D/$ $b$.I. .J.!( H3:.I9-R : Z.Q : Z.R &b$.I ($.Q 
.
 J.L.
 
.J.
 7D . .J.G$7 D73:.I9-] .Q3:.I9-\ &b$.I .J. $'XD-m-\5]4-m4.I4.I : Z.Q $b$.I. .J.!( H3:.I9-o@@.Q:.Q+.' .MX@-w "-b.S.S : Z.R $b$.I &$.Q.. .J.'3:.I9-y  .I2d.Q+-t+.9 $b$.I .J.!( H .MX@. ".b +.(25H   DIFFERENCE CONTRASTS   )     : Z.Q Z.L-\7v4.L!$"D.U $b$.I. .J.!( H  Z.R $b$.I &$.Q.. .J.@@'3:.I9. : Z.R $b$.I &$.Q.. .J. 
.U J'3:.Q9.!$.U &b$.I ($.Q..Q. 
.J.
 D/ .Q3:.I9.+.9 .P D.S .P D.S .P3D.Q+..6b.H0b7+.,4-4-u .I..K  D.S .Q..K  D.S:.Q .Q(..I .J. '.D.P6b.H0b7+.74-4-u+.AO@.K+.9+.A4 Z.G \.G  .H,!p,!p,!p, p, p, p,!p+,J .G .G\ .K,Ap/ ,Ap,Ap-|p 0CONTRAST  
O@1R@@#v@@1R : Z1S  Z1S $
$1S.@@ $
$.1S@@3:#v9.Y 1S3:#v9.X 1L5D.k $/#y D1T  1\X@$i ".f#y1T +.k('(2X,',I4,'I1,',I4,'X,10F6.0/(12X,10F6.0))')+/ $
$1LvD1T1PX@.n	".ob +.s( 21H0FORMAT OF DATA CARDS )   1OX@.t ".xB : Z1S 1\3:1T9.u +.z(20A4)     1PX@.{ ".b : Z1S 1\3:1T9.| +/(4X 20A4) L1M4$/A 1OX@/ "/B : Z1U 
\"/b3+/(17H0TRANSFORMATIONS4)?:Z1U $.h1PX@/ "/b 1U( D1N(


 +/ (16H SQRT  TRANS VAR   2X A6,A4)   +/? 1PX@/" "/&b 1U( D1N(


 +/*(16H LOGE  TRANS VAR   2X,A6,A4)   +/? 1PX@/, "/0b 1U( D1N(


 +/4(16H1ASINTRANS VAR   2X A6,A4)   +/? 1PX@/6 "/;b 1U


3+/?(5HUSERI1,10HTRANS5VARv32X#A6,A4):#v1U3:#v9/@@1U1M4$/L1OX@/DU"1\Q"ZB:UZ1S2O3:#y9/EB:Z1SS261S3:#v9/H +/VZ1QX@/NU"1\Q"ZB:UZ1S2O3:#y9/O : Z1S 26 1S3:#v9/R  : Z1S h265D/\3:#v9/V : Z1S h2O5D/\3:#y9/Y+0W:1R@@1V : Z1S h! D1V : Z1S 1S 2O (.1S3D4+/t3:1V9/` 1PX@/f "/kb1R : Z1W 2O3:#y9/h +/t(20X,11HOBSERVATION I10,47H OMITTED FROM ANALYSIS BECAUSEOF BAD CELL CODE        8I3)+/A 1V D1W"$.1S 1V 1S$ !. D1V 1V3$1W+/e 1S3:#y9/^ 1R4$0 : Z1U 1V3$h!Z+0 1V3Dh!Z+0-3:#v9/} $.#v D1U+0 #v3D#}+0M 1U Z1X #v.1U/ D1S $.1S D1X 1X 1S  "B F"B 1X 1S  !Z F!Z : Z1S $2$ 1X..1S  H $$ 1X..1S w Hw3:#v90 : Z1S $2$ 1X..1S 
$1S .D 3:1S90D 1S3:#v902+/A 1PX@0O "0Pb1R +0V(46H0ERROR IN DATA OR TOO MANY CELLS  OBSERVATION  I10)O@#) 1PX@0X "0Zb#v +0\(1H0,I3,6H CELLS  )  #v5D0^O@#)+1A@@1Z : Z1U h"BD1Z : Z1S!$ 1U3D"B+0j"1J 1U"B ($ 
1U.
 (w F1N-\7?41N @(w &2$ 1U.   
1U("B D 3:#v90a 1U3:#v90_@1Z @1LL1N4$1A  1\X@$i "0v#y +0y('(1H ,',I4,'I3,I10,4H OBS)') @@1[ $3$#v+0~ 1PX@0} "0~b +1(1H1 50X 30HMEANS AND STANDARD DEVIATIONS )   $.1[ D1[ $.1[ D1[ #v2$1[+1 #v D1[ $2$#v+1
 1PX@1 "0~b  1PX@1 "1b : Z1S "
3:#}91 1[ Z1S ((
 ((

P1S3:1[91 +1(1H0/P7H/FACTOR048X8HVARIABLE/ 1H4(2XA1),123X8(2XA6,A4)),:UZ1Uh"B@2@1\H1PX@1#2"1\Q"Zb\:;Z1SP$2$.1U1[ Z1S $$.1Uw3:1[917  1U3:#v91+1@(1H 28X 2HSD 5X 8F12.3)   #v2D1[+1+1G4 Z1J \1K  1K,!p,!p,!p,!p,!p+.V 1J 1K\ 1N/ ,Ap-|p 0
@@4T : Z4Y Zh4i3:4S92U@@4Y $ D4Z 4Z D4Y:4Z"4Y.4S4d3& &$4Y.4Y 4T. $'xXD2_-\7z42_ @4Z 4Y D4[ 4Z Z4[ &$4Y. 4T. $'xXD2f-\7z42f4Z4`2m 4[ D4[ &$4Y.4[ 4T. $'xXD2l-\7z42l @4Z 4[3:4S92a"4Y.4[4d3 : Z4\ &$.4[ 4T. 'x D4Z $$ 4[. 4T..4Y 
4T.
 
7x7J'x3$$.4Y44T.4Z4Hx3:4S92q 4[ 4i D4\ 4[ 4Y  4i F4i 4Y 4\ F4i &$4[.4[ 4T. $'xXD3-\7z434Y4`3 &$4[.4[ 4T. $'xXD3
4T.
 /x.4Y 
4T.
/x D4Z $$4Y. 4T. 4Z Hx 4Z Z4\ 4Z &$ 4Y. 
4T.
/x 
4[.
 
4T.
D7x"`7x3:4S93 4[3:4S93:4Y+2X : Z4Y@@4\:4\ 4Y/4\4d38 &$4\.4Y 4T. 'x D4Z 4Y D4[:4[ 4S/4[4$3' 4Z &$4Y.4[ 4T.'x ($4\ 
4[.
 
4T.
D7x"`7x+3. 4Y D4[:4[ 4S/4[4$3? $$4Y 4[. 4T."`'x+39 4Y3:4S93& 4S D4Y &$4Y.4Y 4T. 'x D4] 4]4Y D4U-\7z44U4Q4`47!$D4] $$4Y.4Y 4T. 4] Hx 4Y D4\:4\ 4S/4\4$3b 4] &$4\.4Y 4T.'x D4Z $$4\.4Y 4T. 4Z Hx@@4[:4[ 4Y/4[4d3N 4Z &$4Y.4[ 4T.'x ($4\ 
4[.
 
4T.
D7x"`7x+3X@@4[:4[ 4Y/4[4d3i 4] &$4Y 4[. 
4T.
D/x"`/x+3b>4Y 4Y5d3A $ D4Z 4Z D4Y:4Z"4Y.4S4d4" &$4Y.4Y 4T. 'x D4] 4Z Z4\ &$.4Y 4T. 'x ($4Y. 
4T.
/xD4] &$.4Y 4T. 'x D4] &$. 4T. 'x ($4Y. 
4T.
/x D4^ $. D4^ 4S/4^4$4 4^ Z4[ &$.4Y 4T. 'x ($4\. 
4T.
/xD4] &$.4\ 4T. 'x ($4Y. 
4T.
/xD4^3:4S94 $$4\.4Y 4T. 4] Hx $$4Y.4\ 4T. 4^ Hx 4\3:4S93s $$4Y.4Y 4T. 4] Hx+3l 4S D4\>4\ 4\4d4I 4\ 4_ D4_ 4\/4_4D4# : Z4[ &$4\. 4T. 'x D4Z $$4\. 4T. *$
4_.
 
4T.
 7x Hx $$4_. 4T. 4Z Hx3:4S94)+4#O@4T 4WX@49 "4>b%4U4 : Z4_ 4i3:4Y94; +4I(14H0IN THE ABOVE 2A4,A2,13H MATRIX, ROW I3, 48H IS PROBABLY A LINEAR COMBINATION OF ROWS        24I3)   +4N4 Z4R \4R  4S,!p, p,!p, p+2S 4R 4R\ 4U/ ,Ap-|pT=8(
"$.5e D5f : Z5f@@5g  Z5g &$5f. 5d. 'xD5g3:5d94w 5g D5h-\7?45g @5g &$5f.5f 5d. 'x D5h 5h5$5"`5g 5g5h &$5f.5f 5d. D'x 5g5h5h D5i 5f 5i F5l 5f3$5f+5# 5f Z5i@@5g 5f Z5g &$5f. 5d. 'x ($5i. 
5d.
/D5g3:5d95 5g5i D5h 5f Z5g 5h &$5f. 5d.'x ($5i 
.
 
5d.
D7"`73:5d9555i3:5f95 D5j &$5j.5j 5d. 'x 5j 5l D5h 5h &$5j 5j. 
5d.
/x$"D/x 5d3D5j+5; $.5j D5j 5j Z5g 5h &$5j . 
5d.
D/x"`/x3:5d955"$.5j D5k 5k4D5\ : Z5g $$5j. 5d.@@x3:5k95> : Z5k 5j/ D5l@@5g 5l Z5g &$5l. 5d. 'x ($5j. 
5d.
/xD5g3:5d95F 5g 5l5l D5h 5l Z5g 5h &$5l. 5d.'x ($5j 
.
 
5d.
D7x"`7x3:5d95Q 5k3:5k95C 5f3:5e95%+5a4 Z5b \5c  5c, p,!p,!p+4s 5b 5c-|p : Z6  .6  Dh6!3:695w : Z6  $ .63$+6 $ .6. D6!6b6!0b7+646464646
 6 .6 $XD6-\7?46 @+6 6 .6 $XD6-\7Y46 @+6 6 .6 $XD6-\746 @+6 6XD6 6XD6-\6a46 464646! 6 3:695{+64 Z6 \6  6,!p, p, p+5v 6 6\ 6-|p 6j.6k  D6m 6j.6k  D6m6b6m0b7+6@46`46`46`46E46H46L46P46W46\!$6m 6j.6j D+6`!$6m D6l-\7Y46l 6j.6j @+6`!$6m 6m 6j.6j F+6`!$6m!&6m F6l-\7Y46l@ 6j.6j @+6`!$6m 6m F6l-\7Y46l 6j.6j @+6`-\7?46m @6l-\746l 6j.6j @+6e4 Z6h \6i  6i,!p, p, p, p+6: 6h 6i\ 6k/ ,Ap-|p 6w D6x+6s4 D6u Z6v \6v  6w,!p+6n 6u 6v 6v 6x-|p $$7
 D7
 7
X@6|.7X@$i3"7b : Z7
96} +7(20A4)    +74 Z7	 \7	  7
,!p,p,cp+6x7	77	\77-|pCNM`1,>&c#p2b7+7"pp+;74@77@7,><7,7?,^p7B7,><7,7$,^,~77ap"`,~+P%07V@,~9~j0x7ASINOF,ARGc>c1.0+IN7MAGNITUDECR+7D.7M"+7E.7M"TB#p@,~4B7L+P%0
7M#p+7A  ,~>attempt to take SQRT of negative argC2|t(1,>&c p4@7i @7X,> <7q,7Y,^7W,~{e^bC2|p1,>&c p5`7]4@7i+P%07r#p3@7l+7k)r. !@7p! n@7p(|h"7l 7m B7p 7m7n7n7p7p7o,~+D%0
7j 7o,~  ,~ 0_i/X3 6P'M 5( bB W
R:`@x7XATTEMPT'TO:TAKEZLOG)OF'NEGATIVEARGM2|1,>&cp+7yM3!d`,~C1,>&c#p,~S01,>&c#p+"7,~U,~@@'O "v5D&u $ D'O-\+4'O #)4$'F 'MX@&x@ : Z'P : Z'O $2$'P.
2$#v+' 'MX@' "'b +'(1H1,30X,20HREDUCED MODEL MATRIX  ) $.'Q D'R $.'R D'Q $
3$#v+'& 'MX@'% "'b  #w2$'Q+'( #w D'Q 'MX@'* "'1b : Z'O "
1:9'+;'RRZ'P'P3:'Q9'. +'7(1H0/7H0FACTOR40X,10HPARAMETER2/1HQ8(2X,A1),2X,10I10)'J:KZ'Pr'MX@':K"'RQ"b:Z'O$2$.'P
-\,(4'v4'x $.&$ D'z $ D'z : Z'{ .'y@@ : Z'{ $ '{.'y$D 'x3$'z+'f 'z.'x  '{.'y.D:'z1:9'_ '{3:'z9'\ $3D'z+'n:'z 'z Z'{ .'y@@1:9'l+'s4 Z'v \'w  'w,!p, p, p+'W 'v 'w\ 'y/ ,Ap-|p	 : Z($ h!Z D($ : Z(% ($ D(% $/.#y D(& (% (&& ! D($ $.(% ($ (&$ !/ D ((3:#y9'!$ D(& : Z(% h(( D(' .("  D(' .(#  D(( &b$(( ($('.('. 'D(&3:#y9(
 $$(".($ (& F< ($3:#v9'|:("+(4 Z(  \(!  (!,!p, p, p+'| (  (!\ (#/ ,Ap-|p $ D(i $ D(i : Z(j : Z(j Zh(q3:(j9(0 : Z(j $ Dh(u $ Dh(} $ Dh(y3:#y9(3:(i (i & FZ : Z(j h(q D(k (k Dh(m"$ (k.! (i$DZ (k & F(u (k & F(} (k ! F(y3:(j9(: (i (.Z D( &$(i $oXD(I-\'o4(j4(m4(I (hXD(L-\(4(i4(}4(L-\)/4(}4(u4(y4#y4(kL(k4$(J : Z(j $.#y/ D(l $.(j/ D(l (l (l3D(q+(^ (l:(q (l Z(m"(l. (l.(q Dh(q3:(j9(Z+(2 (j3:(j9(Q (j3:#y9(/+(d4 Z(f \(g  (g, p+(, (f (g\ (h-|p : Z) ) .)3D+)3:)9)@@)+) $3$)+)
 $ D)+)"$	3$)+)+)4 Z) \)  ),!p,!p,!p, p,!p+) ) )\ )/ ,Ap,Ap-|p@@): : Z); $/.)9 D); );.)8  );.)9/5D)%3:)99)O@):+). );.)8:")9.);4D). $.); D)< )< Z); .)8 .)8 ' F3:)99)*+)44 Z)6 \)7  )7, p, p, p,!p,!p+) )6 )7\ ):,Ap-|p $ D)[ : Z)\ .)Y  D)\!$@ D)] : Z)] )\&)] D)^ )]$)^/D)\"`)\ )[.)Z )Z  	 F )^4D)L )[.)Z )^.)Z ' F )]7 .$(} D)]:)[1:9)B )\1:9)>+)V4 Z)X \)X  )Y, p, p, p+)< )X )X-|p : Z, , Dhv@@hZ1:29) #{5$)d $1 Dw : Z,@@hr1:9)e $ D, $
 D,-$o4,4,4q $ D) $ D#w : Z,
 h!$D#w Zh,@@h, $ Dh, 3:#y9)o-\(4,4,!4, #w4$* ,X@)x ")yb +)(1H0/50H0COMPLETE FACTORIAL WITH NO MISSING CELLS         )  #w3D#v+*
 ,X@* "*b +*
(52H0ERROR IN DATA. TOO FEW CELLS FOR COMPLETE FACTORIAL )  ++~ $ D[ $3D#v+*-\(a4, $ #y,,@ D#)++ $ D#) , Dw++@@#w ,X@* "*b +*(1H0/26H0SPECIAL ORDER OF EFFECTS      ) #{4$*% ,X@* "*b +*$(54H NO CONSTANT TERM IN THIS MODEL UNLESS SPECIFIED BELOW) +*' ,
3D+*' $ D#w@@,
@$ D,[ $.#w@D#)@$.#w D,@@,'. D, ,X@*4 "*9b , Z, 3:,9*5 , +*:(1H 80A1)  : Z,:, , $XD*>-\)4*>4,4,4"
 D,"$.,4$+c5d*F , D,
+&$,.,3"5D,+,$D,"$., D,6b,0b7+*L4*R4*U4*t4+J4+c4*r4+R4+L4+Z4*k4+IX$-D,4,4$*f+*",4$*f.,(.,g!0DgO &2&,gO (2H,gOGG4$+c , , F, ,(., !$D,
 D,++: ,, D, , ,F,1$ ,(.,.!. , D,"$ ,., ,(.,. ! D, , , F,  ,3:#y9+-\(4,4,!4,-\)/4,!4,4,4#y4,L,4$+= : Z,@@h,3:#y9+D@@, $2D,++^>#)+, #{4$+c $2D,++^:,+*t"$., #) Dv $2D,++Q #) & Fv++^ $2$,gO &2F,gOG4$+X , #) Fr #) &1 Fv++^O@, $3D,++^ , Dw@@,++J ,1:(9*; ,.:(1z@+*1 $( D, ,X@+d "+fb, ++i(10H ERROR COL   I4,6H ABOVE) ++~>,++c &$#) $oXD+m-\)R4+m4[4"
9+q ++~(12H0THE EFFECT  18A1, 62H MAKES THE DEGREES OF FREEDOM MORE THAN THE NUMBER OF CELLS     )    O@#)+,4 Z, \,  ,,!p+)^ , ,-|p

W    C6Md 1,>&c,,0,~[&r1,>&c,,0,~[&r1,>&c,,0@,~C6Md1,>&c,,0`,~,>e|Pw+,22ap p*|,2a|+,6 ph" ab~+,2,^,~Kc@ p p+,CKcK  ,,C @,~KcJ  ,,C @,~KcI  ,,C @,~KcH4B,S5@,F5",O+D%0
,EU),~4",U,>$D,S5`,LaB+,LL@,S+,L$+",P(BdB$+",P5b,K ,^,~,,D6 ,S+,O"`/ +,O  ,~aB#`0@3@,T,~  ,~ $.#v D) )X@&u@ : Z)	 : Z)	 $$)	.w3:#v9&w )	3:#v9&v : Z)	 : Z)	 $$)	.

 )	1:9' )	3:#v9'  )X@'
@@)
 : Z)
 h"BD)
 $h"BXD'-\+F4' @) : Z)	 $2D)
+'@@h)v )
 "B &$.)
wDh)v ) &$ )
.D w3:#v9' : Z)	 ) &$ )
.D <3:#w9' )
3:#v9'Q4#v4#w44#v4)D $3D#w+'> : Z)	@@) : Z)	 &$)	. <D)3:)	9'* )	 )D )2$)+'5 )X@'3 "'6b)	  )	3:#w9'(+'>(7H0COLUMN  I4, 47H OF REDUCED MODEL MATRIX IS PROBABLY REDUNDANT    ) #~ D)	 $.)	 D)
 : Z)	 $.#v/ D)
 : Z)
 $.#v/ D)
+'J>)	 $.#~ D)
>)
 $$)	.)
 ($)
.)w F< )
3:#v9'D )	3:#v9'A )	 D)
 D) : Z)	 #w D)
 &$)	.)
 w D)@@) )
 )D4D'\!$ )
)D D) )
2$#w+'f $.)
 D) ) Z)	 &$.)
 < &$)	.wD)"`)3:#w9'` )D) $$)	.)
 ) Fw>)
 )
5D'U )	3:#v9'T $2D#wgOM#x4$(X : Z)
 h)D D) &$. < Dh)D $$. ) F<3:#w9'p-\+)4#w4Q : Z)
  Z)	@@)  Z)	 &$ )
.  <.)	<D)3:#w9'| $$)	.)
 ) F< )	3:#w9'z &$)
 )
. $ <XD(	-\+F4(	 @ < )
3:#w9'y"$.#w D) : Z)
 $. D)	 )	 Z)	 &$)
.)
 < &$ . < 
)
.
 (< H(<3:#w9( )
3:)9( "(b +(*('1CORRELATIONS OF CONTRASTS WITH STANDARD DEVIATIONS OF C','ONTRASTS DIVIDED BY STANDARD DEVIATIONS OF ',	'VARIABLES ON DIAGONAL')    @@) $.) D) $3D)gO &
2&#wgOA5$(4 )X@(3 "(4b +(5(1H1) $.) D)-\+64)4#w @) )X@(: "(>b ) Z)	 "v3:)9(; +(A(1H0/9H0CONTRAST  10A12)  ) Z)
 Z)-\+64)4) @) )X@(F "(Mbh"v ) Z)	 $$)
.<3:)9(G )
 3:#w9(A+(O(A7,5X 10F12.3) #w2d)+(+ : Z)
 &$. < D) $$. h)D F< ) Dh)D3:#w9(Q )
 : Z)	 : Z)
 $2$)	. ($)	.)
  < F #~2d)
+(c )	 D)
:)	:)
3:#v9(\ )	3:#v9([ : Z)	 h)v)
 Dh
3  Z)	@@) #v3D#w+(t $.#w D) ) Z)
$&2$)	.$.&2$)	.D)3:#v9(n/$w D"v+)4 Z) \)+&r ) )-|pp1:
"$.*a D*d : Z*d@@*e  Z*e &$*d. *`. 'kD*e3:*a9* *e D*f-\+F4*e @*e &$*d.*d *`. 'k D*f *f5$*"`*e *e*f &$*d.*d *`. D'k *e*f*f D*g *d *g F*h *d.*c"*e F *d3$*d+*< *d Z*g@@*e *d Z*e &$*d. *`. 'k ($*g. 
*`.
/D*e3:*a9*( *e*g D*f *d Z*e *f &$*d. *`.'k ($*g 
.
 
*`.
D7"`73:*a9*2 *g3:*d9*& *d3:*a9*
 : Z*d : Z*h@@*e  Z*e &$*h. *`. 'k ($*d. 
*b.
/fD*e3:*a9*A *e *h*h D*f *h Z*e *f &$*h. *`.'k ($*d 
.
 
*b.
D7f"`7f3:*a9*L *h3:*a9*? *d3:*b9*>+*]4 Z*_ \*_  *`, p,!p,!p, p,!p, p+*
 *_ *_-|p +/ D+1 &$+1.+1 +0. 'k D+1!$D+1 $$+1.+1 +0. +1 Hk +1 D+2:+2 +/3$+2++ +1 &$+2.+1 +0.'k D+2 $$+2.+1 +0. +2 Hk@@+3:+3 +13d+3++ +2 &$+1.+3 +0.'k ($+2 
+3.
 
+0.
D7k"`7k++@@+3:+3 +13d+3++' +1 &$+1 +3. 
+0.
D/k"`/k++ >+1 +15D+++,4 Z+. \+.  +/,!p, p++ +. +.-|pC6Md 1,>&c,+>,~[&r1,>&c,+>,~[&r1,>&c,+>@,~C6Md1,>&c,+>`,~,>e|Pw++A2ap p*|+@a|++E ph" ab~++@,^,~gG@1,>&c7cp++Q (Bdb++L.+T"++M.+T"TB#p@,~4B+S+P%0
+U#p++H+,~>attempt9to&takeSQRT#of$negative arg (4X@&s $.#v D(5 #x4$'+' $4$' (4X@&y (4X@&z@ : Z(6 : Z(5 $
](63:(59'	(7(4X@'O@$-\.o3#)4$($5$2D(5+'|(3X@'"'bL+'(52H0THEREHAS$BEENAGDIVISIONxBYZERO0IN)THIS ANALYSISu D)(>$$5d($(3X@'!6"'"bX+'*(1H1/' WESTERN(MICHIGANUNIVERSITY'//,	'MULTI-VARIATE"ANALYSISOF VARIANCE'/)(8(2X@',6"'/B$$(( #v3$(7+($ (( (6((
3:(79'{ (7( D(8:$ $&$t D(9 $t$(9 $/ F(9 (3X@( "(b(9(9"u"u : Z(5 (
3:(89( +("(8H0PROBLEM I4, 11H REANALYSIS I4, 19H WITH THE FOLLOWINGI4,13H CRITERIA AND I4, 11H COVARIATES /1X10(3X A6,A4) )   #wH#z4$&w+(/ (3X@(& "('b +(+(35H TOO MANY VARIATES AND COVARIATES  )O@#)+($+(/4 Z(0 \(1+&r (0 (1-|p
+"u."u.D)c :3Z)c+h#* D)d )d3d#vgO )d0FgOG4$)R )d #C D)d 3D)d+)P h#\ D)e )d Dh#\ )d )e F#\ )d Z#C )e )d F#C Z)e-\<E4)d4)e @)f"$.)f D)f )f4D(d : Z)g &
)i )e(.( )d(.(

 )d(.()i
1:9)) : Z)g &2$)e.  D)g $2$)e. (2$)d.   F $2$)d. )g F3:#v9)6 : Z)g &$)e. w D)g $$)e. ($)d.  w Fw $$)d. )g Fw3:#v9)A )e 
3 D)g )e )d  
3 F
3 )d )g F
3 )c3:)c9(<+)]O@#) )aX@)T ")Ub)d +)Z(9H0VARIABLE I4, 15H DOES NOT EXIST    )+)Q+)]4 Z)^ \)_+(: )^ )_-|p
 $.#v D/@@/ "u."u D/ $."u D/@@/@@/ $2D"ugOD$5$)v /X@)u ")vb +)}(7H1SOURCE 27X 2HSS 7X 2HDF 10X 2HMS 14X 1HF10X 11HP LESS THAN       )@@/ "u D/ "v D/-\:|4.r4//4
.s $ D/+*" $ D/-\:|4.r4//4
.u "u D/ "v D/ $ D/+*" $ D/-\:|4.r4//4
.w "u D/ "v."v D/ $ D/+*" $3D/+.9:/ / r4D* / D/ / r D/-\:|4.y4//4
.y / "v D/0 "u D/ / Z D/ $ D/ / ( D/"$./ /.Z D/	 : Z/	 /3Dhv+*&3:#)9*"+.5 $3$"u+*8:/ / // F/ / // F/ / /0 F/  / / F/0 "u1DgO &3F/gOA5$*8 /X@*4` : Z/	 $
$3:/9*5 ""u.D/ "u2d/+.c $2D/gOG$4$*H /X@*?@ : Z/
$: Z/	 $
.+3:#v9*A /
3:/9*@ O@$ /X@*H : Z/
$.Z/	6b/0b7+*L4*N4*Q4*T4*Y &
$8 D/+*` &
./	.+ D/+*` &
$8 &
./	+ D/+*`@@/ / Z/
 &2$/
.  &2$/	.D/3:/	9*[ $
$/	./
 / F $$/	./
\/	F/9*J /
3:/9*I`/ @/ "u4D+& &
$"u."u $$XD*n-\/q4"u4*n4/
 /
4D+ "u.D/
 /X@*r "*wb$//4 /
( D.(


 ++(1H0/1H03A4, 53H HAS A POSSIBLE LINEAR DEPENDENCY INVOLVING VARIABLE  A6,A4,51H AND PRECEEDING COVARIATES FOR THE CURRENT ORDRING    )  &
$"u "u. $ $XD+ $$XD+-\:^4"u4"u4+4+ : Z/
  Z/	@@/ / Z/
 &
$ /
.  ./	D/3:/9+ $
$/
./	 / F"/ &
$/	 /
.D  /	3:"u9+
3:"u9+
 &
$"u "u. $ $XD+" $$XD+#-\0w4"u4"u4+"4+#O@/-\:|4.r4/4
.{L$4$+, $3D"u+++-\24/&4	74/4.t4.}+.5-\<U4/!$ D/
 $3D"u++~ : Z/
 &
$. $XD+4-\<04.t4+4 @.-\<U4. @h	 /
h	u&$.uD/
 $. D/
 /
 Z/	 h	 /
	 (
$./
   $$/
.uF+@ /
3:/=./X@+J"+Lb$//4"u++X(1H1 3A4,75H CORRELATIONS OF CRITERIA WITH STANDARD DEVIATIONS ON DIAGONAL ADJUSTED FOR I3,11H COVARIATES   ) @@/
 ((

3:/` ++j(1H0/10H0VARIABLE  11X,10(A6,A4,1X) )    / Z/
 Z.-\<E4.4/zb /
((
 /
((

 / Z/	 $$./
/9+t /
3:"u9+k++}(1H  A6,A4,8X, 10F11.3)   "u2d/
  Z/	 $$/
. (
$./
H:uF, /
3:"u9+ $2D"u+, $/ D/ /X@, ",b$//4$// +,(1H03A4,          11X F15.3, I6, F15.3) +,.-\/q4"u4$4/
 /
4D, /X@, ",b$//4 /
( D.(


 +,+(1H0/1H03A4, 53H HAS A POSSIBLE LINEAR DEPENDENCY INVOLVING VARIABLE  A6,A4,49H AND  PRECEDING VARIATES FOR THE CURRENT ORDERNG   )    -\24/&4	74/4.t4.} : Z/@@/
 Z/1$3D"u+,4G$.#)/XD//4$- / v D/ /2D/+.  / ( D/"$./ /.Z D/	 &$/ $oXD,>-\2=4,>4/&4"
$: Z/	 $
.+3:#v9,F /
3:/9,E O@$ /X@,M : Z/
$ Z/	 /5D,S &
. + D/+,Z@@/ / Z/
 &2$/
.  &2$/	.D/3:/	9,U "u5D,^ $
$/
./	 / F+,c / &$/	./

$/
./	 D /	3:/9,O /
3:/9,N "u4D- &
$"u."u $XD,j-\34"u4,j4/
 &
$"u."u $XD,q "u $XD,q-\314"u4"u4,q4,q : Z/
  Z/	@@/ / Z/
 &
$/
.  &
$/	.D/3:/9,u"/ &
$/
 /	.  *$
/
.
/	( /	3:"u9,s /
3:"u9,rF/1Z+D/ $3D"u+./4$-4/X@-	4"-b$/&4	S+-A4,1X,3A4) @@/L$4$-R /X@- "-b"u +-"(46H0SUMS OF PRODUCTS FOR HYPOTHESIS ADJUSTED FOR I3,1X,11HCOVARIATES   )  @@/
 ((

3:/* +-4(1H0/10H0VARIABLE  11X,10(A6,A4,1X) )    / Z/
 Z.-\<E4.4/Db /
((

 /
((
 / Z/	 $
$./
3:/9-> /
3:"u9-5+-G(1H-KA6,A4,8X,10E11.3)	"u2d/5$-R /X@-O "-b$//4$/4 -\6
4/4/4	4/@@$L/4$.@@/(
 ((

3:/^ +-n(1H0/29H0RAW REGRESSION COEFFICIENTS   /30X 8HVARIATES  /11H COVARIATES   9X 8(4X A6,A4) ) / Z/	 /X@-p "-{b /	((
 /	((

 / Z/
 $
$/	.3:/9-n+-~(1H/A6,A4,8X,/8F14.3).}"u2d// /4$. /X@.
 ".b$/&4	//// +.(1H 18A1, 5X, F15.3, I6,3F15.3)    +.  /X@. ".b$/4//// +.(1H 3A4,11X, F15.3, I6,3F15.3)@@/+,4 /
4D.4 "u.D/
 /X@.# ".'b /
( D.(


 +.4(1H0/43H0LOSS OF ACCURACY IN ABOVE DUE TO VARIABLE  A6,A4,51H AND  PRECEDING COVARIATES FOR THE CURRENT ORDERING   )     /3:#)9,/6b/0b7+.74*4*
4*4* $2D"u+.c-\24/&4	74/4/04/ $4$.c "u4D.c@@/ $./ D/ $./ D.-\<E4.4/ @/ /X@.G ".Mb / Z/	 / / / 3:/9.H +.T(1H0/28H0RAW REGRESSION COEFFICIENTS/11H0COVARIATES  8X,8(2X 3A4) )    : Z/	 /X@.W "-{b /	((
 /	((

 / Z/
 $
$/	.3:/9.\ /	 3:/9.U /2d/+.@+.q $ D/
 $2D"u+.f@@/
 /X@.h ".jb/
$//4 +.n(I1,15HTOO FEW DF IN     3A4) +.5+.q4 Z.~ \.~+)j .~ .~-|pWITHIN CELLS   RESIDUAL       WITHIN+RESID   ERROR     REGRESSION     p1:
@@/z"$./y D/{ /{4$/U : Z/| &
$. /z. 's D/| $3D+/E : Z/} &
$/|. /z. 'rD/|"`/|3:/|9/@ &
$/|./| /z. 's4d/M /| &
$/|./| /z.'s2$/w+/O /| D/z@@/|-\<U4/| @/| $
$/|./| /z. /| Hs /y2D/|+/V+/u /| Z/} &
$./| /z. ' D/~ $3D/|+/e : Z/} &
$/|. /z. 'r (
$/}. 
/z.
/D/~"`/~3:/|9/] /|5D/i $
$/}./| /z.@@+/m /~/| &
$/}./| /z. D' /}3:/{9/V /|3:/y9/9+/u4 Z/x \/x  /y,!p, p,!p+/6 /x /x\ /z,Ap-|pp1: : Z0S"$. D0T  Z0T 0T4d0 : Z0U &
$0S . 
0R.
 /s *
$
.
0T 
0R.
7s 
0T.
 0R.D?s"`?s3:0T90 &
$0S 0T. 
0R.
 /s 
0S.
 0R.?s D/s &
$0S.0S 0R. 's5D0 $
$0S.0T 0R.@@s 0T3:0Q90 : Z0T"$. D0U 0U4d0, : Z0U &
$0S. 0R. 's (
$.0T 
0R.
/s *
$
0T 
0S.
 0R.D?s"`?s3:0U90! 0T/0T4$09 0T Z0U &
$0T . 
0R.
 /s *
$
0S.
 
0R.
7s 
0S.
 0R.D?s"`?s3:0T90/ &
$0T 0S. 
0R.
 /s ,
$
0S.
0S 0R.?s D/s &
$0S.0S 0R. 's5D0G $
$0T.0S 0R.@@s 0T3:0S90 0S3:0Q9/+0N4 Z0P \0P  0Q,!p, p, p+/~ 0P 0P-|p : Z1 0~ D1 &
$1.1 1. 's D1@@1 &
$1.1 0. 's4D0c!$ &
$1.1 0.'s D1"1.0~4d0o $.1 D1 1 Z1 &
$ 1. 
0.
 /s.1 
1.
/sD1"`13:0~90g 1D1 $
$1.1 1. 1 Hs>1 15d0X 13:090V+0{4 Z0} \0}  0~,!p,!p, p, p+0V 0} 0}-|p $."u D2  "u."u D2  "u0DgO &2F2gOG4$1 2X@1
$ 2.  H3:2 91@@2! $3$"u+1 2X@1 "1b"u +1(    23H0ESTIMATES ADJUSTED FOR I3,11H COVARIATES  )    $.2! D2" $.2" D2!-\<E4"u42! @2! $2$"ugO &2F2"gOA &2&2"gO (2(#wgOAG5$1/ 2X@1. "1/b"u +15(23H1ESTIMATES ADJUSTED FOR I3,11H COVARIATES  )   2X@16 "1=b 2" Z2! ((
 ((

3:2!917 +1C(1H0     45X 8HCRITERIA / 9H CONTRAST 11X 8(4XA6,A4))   : Z2" $2D"u+1S .2  D2 "u1DgO 23FgOA5$1S 2X@1N@ : Z2! $
$.2"3:291O 2"X: Z2#23DhvgO+&2&hvgOG4$2:h( D2#"$.2#.hZ D2$$2#4D2 &$ $oXD1a"2XD1a-\2=41a41a4"  Z2' 2$A$5$1x h
3 D2&"2& &$.2%w &
$.2& 2!.2D"`3:2 91u 2!3:"u91m 2X@2 "2b2% 2" Z2' .23:2!92 +2
(1H I6,12X 8F14.3)   2%3:2$91k 2#3:#)91T 2"3:291D "u2d2!+1+24 Z2 \2  2, p, p,!p, p,!p+1 2 2\ 2/ ,Ap-|p
W$ $ D2F : Z2G .2D  D2G!$@ D2H : Z2H 2G&2H D2I 2H$2I/D2G"`2G 2F.2E 2E  	 F 2I4D27 2F.2E 2I.2E ' F 2H7 .$(} D2H:2F1:92- 2G1:92)+2A4 Z2C \2C  2D, p, p, p+2' 2C 2C-|p@@3
 D3 34$2i : Z3 &
$. 3 $3D+2Y : Z3 &
$.33D3"`33:392S &
$3.343a 3 &
$3.323
+2b-34D3 @3 $
$3.3 3s 3
2D3+2i+3 3 Z3 &
$3. 3 $3D3+2x : Z3 &
$ 3. 
3
 /f.3 
3
/gD3"`33:392p 35D2| $
$3.3+3 33 &
$3.3 33:392j 33:3
92M+34 Z3 \3  3
,!p,|p,!p+2I33\3 : Z3; : Z3< &
$3;. 3:. 's D3<"$. D3= 3=4d3" : Z3= &
$.3< 3:. 's (
$3;. 
3:.
/sD3<"`3<3:3=93 3< &
$3<.3< 3:.'s D3< &
$3<.3< 3:. 's5D3*@@3< $
$3;.3< 3:. 3< Hs 3<3:3993 3;3:3993+364 Z37 \38  38,!p,!p, p, p+3 37 38-|p 6 D6 $."u D6 "u."u D6-\<E4"u46 @6`"u @6`6 @6-\<U46 @6`6 @6 6 D6 66 D6 66 D6 : Z6 &
$. 6 Dh
 6 &
$. &$.
3:"u93M-\0J4"u44$-\94"u44	P4946  6 4D3_ 6X@3^ "3_b +3d(40H0LOSS OF ACCURACY IN EIGENVALUE PROBLEM   )   -\:14"u4"u4$49!$ 6	O D	h $3D6+3s"$.6 D6  : Z6 6/ D6! h	P5$3p@@h	P!$ 6!	O	i D	h3:6 93m 6X@3u "3vb +4(81H0TESTS OF SIGNIFICANCE USING WILKS LAMBDA CRITERION AND CANONICAL CORRELATIONS       /15H TEST OF ROOTS 13X 1HF 9X 5HFHYP 7X 5HDFERR 4X 11HP LESS THAN   5X 1HR) @@6! : Z6!$ D6" 66 D6"!$3D6"+4 6$  6 6"& F6-\<U46 @6"!$6"666 6H6"D D6# 6#6 D6!$6"" h	h 
,<m H6#!$6#66# D6$-\;44646#46$ @6$-\<04646$ @6%!$h	O h	O F6-\<U46 @6% 6X@4+ "4/b66$66#6%6% +43(I3,8H THROUGH I3,5X,5F12.3)   63$6%+45:6!"6D6 $."u.6 6(/` @6&"6&D6 63:694 6! D6& $ D6' 6!5D4@ $ D6& $2$6!+4C $ D6& 6X@4D "4Ib66 : Z63:6&94F +4Z(1H0/1H0 27X 19HUNIVARIATE F TESTS 14X 47HSTANDARDIZED DISCRIMINANT FUNCTION COEFFICIENTS   /9H VARIABLE 11X 2HF( I2,1H, I5,1H) 4X 7HMEAN SQ 4X 11HP LESS THAN   I7,7I8)   : Z6 $h
XD4^-\;4464644^@6$-\<04646$b@6':Z6!6.6  &
 6((

 6
 6
6' : Z6! 	h3:6&94p  63:"u94[+4x(1H A6,A4, 7X, 3F12.3, 5X,  8F8.3)  6!4D6	 64D5+ 6X@4| "4b 6' Z63:6&94} +5(1H0/21H0DISCRIMINANT SCORES   /9H CONTRAST 47X  8I8)  "$.6.6 D6(@@6( 6 Z6 : Z6! &$.6 w D6) "u4D5 6 Z6) &$ 6.  w.6!D6)"`6)3:695 6! 6) F
 6!3:"u95	:6( 6' Z6!@@6) : Z6) h
&.+D6)3:"u95 66)+6!D	h 6!3:6&95.6X@5# "5)b6(6' Z6!(	h3:6&95$  63:6(95+5+(I7, 52X  8F8.3)    L#*4$5 6X@5. "51b 6' Z63:6&95/ +5:(1H0/52H0CORRELATIONS BETWEEN VARIABLES AND COMPOSITE SCORES/9H VARIABLE 47X  8I8)    : Z6 $. D6* 6' Z6!@@6) : Z6* &$.6 
 6((

$6'.Z6!	h3:6&95XX63:"u95;+5(1HA6,A4,48X,  8F8.3)   6!3D6&+6	 $.6& D6' $.6' D6-\<E46!46 @6& 6X@5g "5kb 6' Z63:6&95h +5t(1H0/1H0 60X 47HSTANDARDIZED DISCRIMINANT FUNCTION COEFFICIENTS / 9H VARIABLE 47X 8I8)     6!2$6&+5w 6! D6& : Z6 6' Z6! 6.6  &
 6((

 6' Z6! 	h3:6&96  63:"u95w+4y+64 Z6 \6  6,!p,!p, p,!p+3> 6 6\ 6/ ,Ap-|pSLf 0p1:
 9 D9_@@9 9_4D9"$.9_ D9`"$.9_ D9`@@9a@@9a : Z9b  Z9b &
$9b. 9. 'sD9a3:9_963 &
$9b.9b 9. 'sD9a &
$9b.9b 9. 'sDD9a"`9a 9b3:9_962 9aD9a 9  D9- 9`4$7/4D7$ : Z9c &
$. 9. 's D9c@@9d  Z9b &
$9c. 9. 'tD9d3:9`96L $
$9c.9c49.@@s9d4d79c9cD9d!$D9d 9c5$6Z"9 @9f 9c 9f F9v $
$9c.9c 9. 9f Hs 9e9f D9e 9d9e"D9c 9c Z9b 9e &
$9c. 9.'t D9f 9f Dh9w $
$9c. 9. 9f Ht3:9`96j@@9f 9c Z9b@@9g 9c Z9b &
$.9b 9.  h9vD9g3:9b96w $.9b D9g 9`/9g4$7 9g Z9b &
$9b. 9.  h9vD9g3:9`97 9b 9g F9 9g 9b9vD9f 9b3:9`96u 9c Z9b 9fh9vh9"Dh93:9`97 9c Z9b h9 D9h h9v D9h  Z9b 9hh9v 9hh9D &
$9b . 
9.
D("`(3:9`97 9b3:9`97 9c 9c F9 9c9c 9c D9E 9c (
$9c.9c 
9.
 ( F9- 9c3:9`96G &
$9_.9_ 9. 'f D9c 9_ 9c F9 9c9c 9_ D9E 9_ (
$9_.9_ 
9.
/s9F9,99@@9E:9Z9b7:Z9b7$9 D9i@@9g $ D9i+8	 9jD9g!$ D9j"9j9- D9k 9k D9k 9k9k9F D9l-\<U49l @9l : Z9b 9j D9m 9l5D7L@@9m@@9n!$ D9j+7g 9b 99l D9m 9b 9E9l D9n 9k9l D9j 9b.9i D9n 92d9n+7U 9 D9n : Z9b 9j &
9.
/r 
9m
/D9f9m &
9.
/r 
9j
/"D/9$ 9f Hr3:9n97V"9j 9b9- D9o 9k9o9n D9o 9k9o 9b D9, 9o9o D9k 9j9o 9m9m 9b 9 D9k 9b2D9i+7y 9k9m 9b D9 9k9n9k 9b D9E+8 9k9k 9b9F D9l-\<U49l @9l 9l9m 9b D9 9l9n 9b D9E 9b3:9i97G 9i 9k F9-:9i 9 9i3$9E+8 9g 9i9- 9i.9 D 9i@@9 9i@@9E>9i 9i4D8( 9 9i2$9E+8 9i 9- D9p 9pD D9p 9i 9,D D9q 9p9q D9q"9p9q D9r 9r9r 9i9E D9-\<U49 @9f 9f9q D9q"9f9q D9p 9p9p D9-\>49 @9 9p9q F9-\>499 @9r 9r4$8' 9p D9j+7> 9q D9j+7> 9g9- 9 D : Z9b Zh9, Zh9 Zh9E3:998+ 9 D9i+8= : Z9b .9 3d+8< .9  D9f .9  F .9 9f F h9E D9r h9F Dh9E 9r Dh9F3:9i980>9i 9i5D8/ 9`4D8Y : Z9s h9E D9s 9s 9, D9t 3D9t+8W h9 D9t 9t 9t F9 9t 9t F9, : Z9b &
9t.
 
9.
97rHr9$ 9f Hr3:998I 9s3:9`98@@@9u@@9u : Z9v 9` D9v>9v 9v4d8q@@9g 9v Z9b &
$9v. 
9.
/sD9g3:9`98_ 9gD9g 9v Z9b 9g &
$9v. 9.'s (
.
 
9.
D7s"`7s3:9`98h+8\:9v.9D9u 9v.9 D9u 9v3:998Z 9aD D9-\>49 @9f 9a9u D9-\>499f9f4@8:9 9aD D9f 9a9u D9-\>499f9f4@9 $.D9+94 Z9 \9  9,!p, p, p, p,!p+6+ 9 9\ 9,Ap-|p 0rqm : Z:; :8 D:; &
$:;.:; :9. 's4D:!$ &
$:;.:; :9.'s D:<":;.:84d:) $.:; D:= := Z:= &
$.:; :9. 's (
::.
/rD:<"`:<3::89:!:<D:<:$: :;3::99:+:54 Z:7 \:7  :8,!p,!p, p, p+: :7 :7-|p : Z:h : Z:h &
$.:h :g. 's D:i"$. D:i :i4d:O : Z:j &
$:h. :f. 's (
$.:h 
:g.
/sD:i"`:i3::i9:G :i &
$:h.:h :f.'s D:i &
$:h.:h :f. 's5D:W@@:i $
$:h.:h :g. :i Hs :h3::e9:? :h3::f9:>+:b4 Z:d \:d  :e,!p,!p, p, p+:> :d :d-|p-\;w4;4
; ":qb : Z; .;3:;9:m +:r(20A5)    -\;t4;4
; ":yB : Z; .;3:;9:v +:{(20A4)    +;4 Z; \;  ;,!p, p, p+:j ; ;\ ;-|pTST   ;E D;H ;F D;H ;F D;I@@;I!$3$;I+; $ D;I!$D;I ;H D;J ;H D;H ;J D;H!$	;H!& F;J!$	;H!& F;K!$};J ;I 
;=,<m!&;K D;G-\>4;G @;K ;I ;=,<p;K;J D;G-\<U4;G ;K F;K!$3$;H+;) ;H;H ;K;>&F;K ;>;K;?;K;?;K;@;K$ D;K!$;K D;G $2D;I+;3";@D;G"`;G+;94  ;AQ * ;D Z;D \;E  ;E,!p,!p,!p+;!0;AX0*0 ;D ;E ;G-|pu*U* *U*4=8(s8Y6EW=>VSY a 0!*;k**,^,~*x,> <;k*<;m  pZ@;a@@;a@@;b <"`|+;UPw,~ "p h a`~+;Zh  ``~+;[$<"!;\d<#/"+;UP,~@@@ @@0@x@@@`edX91,>&c,>Zp @;a\`;` <;a,,^,~SMI 1,>&c,;N <$ B;a+<_MI 1,>&c,;N <& B;a+<I5R1,>&c,;N <' B;a*\<7ApX"<( B;a/& pd"~l" B;a*\</& pd"~l"$ B;a*\</& pd"~l"
 B;a*\<Sp*\</&Xp B;j@@;j <) B;a*\</& pd"~l" B;aRF;` <;a,+;LEV4i91,>&c+<S,i@1,>&c+<_,i@1,>&c+<K>21,>&c+<K>401,>&c+<[<I71,>&c
&<) w @)@. 
"5B<
&</,~`.
.4SEQIN^<#SEQOUT^<%RANDOM^<&SEQINOUT;j
%0 THE FOLLOWING ROUTINE IS NOT IMPLEMENTED IN FOROTS: 
C6 1,>&c,<;,~[B1,>&c,<;,~[B1,>&c,<;@,~C61,>&c,<;`,~,>e|Pw+<=3!p p*|<=a|+<A ph" ab~+<=,^,~C6Md 1,>&c,<M,~[&r1,>&c,<M,~[&r1,>&c,<M@,~C6Md1,>&c,<M`,~,>e|Pw+<P2ap p*|<Oa|+<T ph" ab~+<O,^,~gG@1,>&c7cp+<` (Bdb+<[.<c"+<\.<c"TB#p@,~4B<b+P%0
<d#p+<W  ,~>attempt to take SQRT of negative argKc3@ p p+<sKc3K  ,<s 
,~Kc3J  ,<s ,~Kc3I  ,<s ,~Kc3H4B=	5@<w5"=	+D%0
<vU ,~,>,># $)D/$@,>4d=X $(F) + =5F=5"<"` ,=+=#  ,> <=,=c,^@,> <=
,=>,^5&=",^,^,^,~! ,~xxKc#@ p p+=Kc#K  ,= @,~Kc#J  ,= @,~Kc#I  ,= @,~Kc#H4B=;5@=5"=%+D%0
=U ,~ D=;!$ @=: B=:5"="#`+ =7,="!"B,~+ =&(BdB+ =&5B=!  =;,~ +7`=:+=.`d +D%0=*+D%0
=*U `d @6 =:+=% =:`B"`+=%/=<id +=1+D%0=*#=:,> <==,=c,^ @`=:@,> <==,=>,^+=+U",="=:+ =&+=! ,~xKc1,>&c p3"=Z+=D3b=Y+=F+D%0
=CU ,~+D%0=E  ,~ D=Z F=[@@=[%"j"%=X)/;`:XD=T5f=MaF+=M.&@(|h&f=[ =W=X =W =[=VD=Y@ =Z =[,~!t0_'"S'qf!um.	.#Y% !vyO^	RXC2|t(1,>&c p4@=s @=b,> <=|,=c,^=b,~{e^bC2|p1,>&c p5`=g4@=s+P%0=|#p3@=v+=u)r. !@=z! n@=z(|h"=w =w B={ =x=x=y={=z=y,~+D%0
=t =z,~  ,~ 0_i/X3 6P'M 5( bB W
R `@x=bATTEMPT TO TAKE LOG OF NEGATIVE ARGC1,>&c#p,~S01,>&c#p+">,~U ,~