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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "TWO-WAY ANOVA  (NO INTERAC
TION):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "with(stats):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "k:=3:  \+
m:=5:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "These are the 'true' pop
ulation paramaters (normally 'hidden' form us):" }{MPLTEXT 1 0 0 "" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "mu:=10:   alpha:=[-3,2,1]: \+
 beta:=[-2,3,-1,4,-4]:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Generat
ing data, based on the corresponding model:" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "X:=matrix(k,m):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "for i to k do for j to m do X[i,j]:
=mu+alpha[i]+beta[j]+random[normald[0,2]]() end do end do:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "i:='i':j:='j':" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 37 "The actual data analysis starts here:" }{MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalm(X);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7'$\"+P\"z;N(!\"*$\"+*zy
q/\"!\")$\"+LvgTQF*$\"+tKWHeF*$\"*RqV$**F*7'$\"+s*[_I\"F-$\"+\\#3G`\"F
-$\"+@9*y\"**F*$\"+xZ)oj\"F-$\"+'z/E5(F*7'$\"+igE/&*F*$\"+wnfl:F-$\"+<
ahC7F-$\"+$>9))=\"F-$\"+yZmifF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 40 "muH:=sum(sum(X[i,j],i=1..k),j=1..m)/m/k;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$muHG$\"+?x$4q*!\"*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "alphaH:=[seq(sum(X[i,j],j=1..m)/m - muH,i=1..k)];" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'alphaHG7%$!+Ena.S!\"*$\"+?b/`EF($\"
+?7]]8F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "betaH:=[seq(sum
(X[i,j],i=1..k)/k - muH,j=1..m)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%&betaHG7'$\"*(eS&o#!\"*$\"+!pTt6%F($!+!o'QK5F($\"++m?h;F($!+$=-Z,&F(
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "SSa:=m*sum(alphaH[i]^2,
i=1..k);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$SSaG$\"+BXaW7!\"(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "SSb:=k*sum(betaH[j]^2,j=1..m
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$SSbG$\"+G&=*z8!\"(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "SSt:=sum(sum(X[i,j]^2,i=1..k
),j=1..m)-sum(sum(X[i,j],j=1..m),i=1..k)^2/k/m;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$SStG$\"*&HZhG!\"'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "SSe:=SSt-SSa-SSb;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%$SSeG$\"***)4qB!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "MS
a:=SSa/(k-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$MSaG$\"+:EsAi!\")
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "MSb:=SSb/(m-1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$MSbG$\"+?jz\\M!\")" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "MSe:=SSe/(k-1)/(m-1);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%$MSeG$\"+QPiiH!\"*" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 12 "Ta:=MSa/MSe;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#
TaG$\"+b$4/5#!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "statev
alf[icdf,fratio[k-1,(k-1)*(m-1)]](.95);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#$\"+3,(*eW!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "1-s
tatevalf[cdf,fratio[k-1,(k-1)*(m-1)]](Ta);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"(4$\\l!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "Hi
ghly significant proof that the alphas are NOT equal to zero. " }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Tb:=MSb
/MSe;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#TbG$\"+t&RW;\"!\")" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "statevalf[icdf,fratio[m-1,(k
-1)*(m-1)]](.95);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+bL&y$Q!\"*" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "1-statevalf[cdf,fratio[m-1
,(k-1)*(m-1)]](Ta);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"(Q!eE!#5" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "Similarly, significant proof that
 the betas are NOT equal to zero." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 15 "Sigma estimate:" }{MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sqrt(MSe);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+$RF7s\"!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 
"TWO-WAY ANOVA (WITH INTERACTION)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT 
-1 80 "Warning, the protected names norm and trace have been redefined
 and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "k:=3:
  m:=5: n:=15:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "These are again
 the 'true' parameters: mu, alphas, betas and interaction terms:" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "ab:=ran
dmatrix(3,5)/30.: mu:=evalm([1$k]&*ab&*[1$m]/k/m); ab:=evalm(ab-mu):" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$!+********f!#5" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "alpha:=evalm(ab&*[1$m]/m);  ab:=eva
lm(ab-matrix(k,1,alpha)&*matrix(1,m,1)):" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%&alphaG-%'vectorG6#7%$!+LLL8:!\"*$!+mmmmC!#5$\"+++++KF." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "beta:=evalm([1$k]/k&*ab); ab
:=evalm(ab-matrix(k,1,1)&*matrix(1,m,beta));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%betaG-%'vectorG6#7'$\"+666\">#!\"*$\"+`bbbV!#5$!+mmm
'G#F+$\"+>AAA!)F.$!+AAAU6F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#abG-
%'matrixG6#7%7'$!)XWWW!\"*$!+$*))))))[!#5$\"*mmmm(F,$!+fbbb&)F/$\"*AAA
A'F,7'$!*xxxx&F,$!+@AAA:F,$!*nmmm%F,$\"+66667F,$\"+bbbb8F,7'F4$\"+6666
?F,$!*++++$F,$!+`bbbNF/$!+yxxx>F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
16 "Generating data:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "x:=array(1..k,1..m,1..n);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"xG-%&arrayG6&;\"\"\"\"\"$;F)\"\"&;F)\"#:7\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "for i to k do for j to m do
 for l to n do\nx[i,j,l]:=mu+alpha[i]+beta[j]+ab[i,j]+random[normald[0
,3]]() end do end do end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 25 "i:='i':  j:='j':  l:='l':" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
14 "Data analysis:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 56 "muH:=sum(sum(sum(x[i,j,l],i=1..k),j=1..m),l=1..n)/k/m
/n;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$muHG$!+L[0k')!#5" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "alphaH:=[seq(sum(sum(x[i,j,l],j=1..
m),l=1..n)/m/n-muH,i=1..k)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'alp
haHG7%$!+x_sc7!\"*$\"+&o?\"*3'!#5$\"+\"3K\"ykF+" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 62 "betaH:=[seq(sum(sum(x[i,j,l],i=1..k),l=1..n)/k
/n-muH,j=1..m)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&betaHG7'$\"+3&y
#>?!\"*$\"++[y!3\"!#5$!+(*\\wj@F($\"+8\"3j;\"F($!+3,!*H6F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "abH:=matrix(k,m,[seq(seq(sum(x[i,j,
l],l=1..n)/n-alphaH[i]-betaH[j]-muH,j=1..m),i=1..k)]);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%$abHG-%'matrixG6#7%7'$!+(okSg&!#5$!+F\\\"))R#F,$
!*d$R\"f'F,$!+dtvf\")F,$\"+Qw<#o\"!\"*7'$!+ZR'G$>F,$!+*e-(\\=F5$!+<k!y
&=F,$\"+Vt&zw(F,$\"+$*Q(>X\"F57'$\"+L'Gp`(F,$\"+#3%e*3#F5$\"+Ve%p^#F,$
\"*H+!=RF,$!+K::MJF5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "How well \+
does the previous set of estimates match the patterns of the 'true' va
lues?" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 
"SSt:=sum(sum(sum((x[i,j,l]-muH)^2,i=1..k),j=1..m),l=1..n);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$SStG$\"+(fH88$!\"'" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 33 "SSa:=sum(alphaH[i]^2,i=1..k)*m*n;" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%$SSaG$\"+7dMx<!\"(" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 32 "SSb:=sum(betaH[j]^2,j=1..m)*k*n;" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%$SSbG$\"+;vfL^!\"(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "SSab:=sum(sum(abH[i,j]^2,i=1..k),j=1..m)*n;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%%SSabG$\"+c+zMP!\"(" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 22 "SSe:=SSt-SSa-SSb-SSab;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$SSeG$\"+oivm?!\"'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "MSa:=SSa/(k-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
$MSaG$\"+g&Gn)))!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "MSb
:=SSb/(m-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$MSbG$\"+z$*R$G\"!\"
(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "MSab:=SSab/(k-1)/(m-1)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%MSabG$\"+qv[oY!\")" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "MSe:=SSe/k/m/(n-1);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%$MSeG$\"+9lpT)*!\"*" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 10 "sqrt(MSe);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+J
y9PJ!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Ta:=MSa/MSe;" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#TaG$\"+19nH!*!\"*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "statevalf[icdf,fratio[k-1,k*m*(n-1)
]](.95);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+2p()QI!\"*" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 61 "Statistically significant proof that the \+
alphas are NON-zero." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "Tb:=MSb/MSe;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Tb
G$\"+KG//8!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "statevalf
[icdf,fratio[m-1,k*m*(n-1)]](.95);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
$\"+m=k9C!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Ditto for betas,
" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Tab:
=MSab/MSe;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$TabG$\"+(4!eVZ!\"*" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "statevalf[icdf,fratio[(k-1
)*(m-1),k*m*(n-1)]](.95);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+e&*o#
)>!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "and also for the intera
ction terms." }{MPLTEXT 1 0 0 "" }}}}{MARK "67" 0 }{VIEWOPTS 1 1 0 1 
1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }