Analysis of Variance
Chapter 10 Analysis of Variance
Scilab code Exa 10.3a Dependence of mileage on gas used
1 Xij = [220 251 226 246 260; 244 235 232 242 225; 252
2 Xi = zeros (3 ,1) ;
6 for j =1:5
18 Xdotdot= sum ( Xi ) m ;
19 new = ( Xi - X d o t d o t ) 2;
20 SSb = n sum ( new ) ;
25 disp ( TS , ” V a l u e of the test statistic is”);
26 pvalue=1- cdff ( ”PQ” , TS , m -1 , (( n m ) - m ) ) ;
27 disp ( pvalue , ” The p−v a l u e is”)
28 if ( pvalue > 0 . 0 5 )
29 disp (”Since t h e p−v a l u e is greaterthan.05, the
null hypothesis t h a t t h e mean m i l e a g e is t h e same
for all3brandsof gasoline
Scilab code Exa 10.3b Dependence of mileage on gas used
1 X i j o l d = [220 251 226 246 260; 244 235 232 242 225;
2 Xij = X i j o l d - 220;
3 m =3;
4 n =5;
5 Xidot= zeros (3 ,1) ;
11 Xidot=Xidotn;
12 Xdotdot= sum (Xidot)m;
13 SSb =0;
14 for
i =1: m
15 SSb = SSb + ( X i d o t ( i ) - X d o t d o t ) 2;
16 end
17 SSb = SSb n ;
18 X i j s q u a r e d = Xij .2;
23 disp ( TS , ” V a l u e of the test statistic is”);
Scilab code Exa 10.3c Difference in GPA
1 Xij = [3.2 3.4 3.3 3.5; 3.4 3.0 3.7 3.3; 2.8 2.6 3.0
2 Xi = zeros (3 ,1) ;
6 for j =1:4
18 Xdotdot= sum ( Xi ) m ;
25 disp ( TS , ” V a l u e of the test statistic is”);
26 pvalue=1- cdff ( ”PQ” , TS , m -1 , (( n m ) - m ) ) ;
27 disp ( pvalue , ” The p−v a l u e is”)
28 C=3.95; f r o m t a b l e A5
29 W=C sqrt ( SSW ( 9 4 ) ) ;
30 disp (W);
31 disp ( Xi (1) - Xi (2) + W , ” and ” , Xi (1) - Xi (2) -W , ” Mean1 −
Mean2 l i e s between” );
32 disp ( Xi (1) - Xi (3) + W , ” and ” , Xi (1) - Xi (3) -W , ” Mean1 −
Mean3 l i e s between” );
33 disp ( Xi (2) - Xi (3) + W , ” and ” , Xi (2) - Xi (3) -W , ” Mean2 −
Mean3 l i e s between” );
Scilab code Exa 10.4b Estimating Parameters
1 X =[75 73 60 70 86; 78 71 64 72 90; 80 69 62 70 85;
2 Xidot= zeros (4 ,1) ;
3 for
i =1:4
4 for j =1:5
5 Xidot(i)=Xidot(i)+X(i,j);
9 Xjdot= zeros (5 ,1) ;
10 for j =1:5
11 for
i =1:4
12 Xjdot(j)=Xjdot(j)+X(i,j);
16 Xdotdot= sum ( X i d o t ) 4;
17 d i s p ( X d o t d o t )
18 meanhat=Xdotdot;
19 alphahat=Xidot-meanhat;
20 betahat=Xjdot-meanhat;
21 disp ( meanhat , ” The e s t i m a t o r of t h e mean i s ” ) ;
22 disp ( ” The a l p h a s
a r e −” )
23 disp (alphahat)
24 disp ( ” The b e t a s
a r e −” )
25 disp (betahat)
Scilab code Exa 10.5a Species collected
4 Xidot= zeros (8 ,1) ;
5 for
i =1:8
6 for j =1:6
7 Xidot(i)=Xidot(i)+X(i,j);
11 Xjdot= zeros (6 ,1) ;
12 for j =1:6
13 for
i =1:8
14 Xjdot(j)=Xjdot(j)+X(i,j);
18 Xdotdot= sum ( X i d o t ) 8;
19 new = ( X i d o t - X d o t d o t ) 2;
20 SSr = n sum ( new ) ;
21 new1 = ( X j d o t - X d o t d o t ) 2;
22 SSc = m sum ( new1 ) ;
23 SSe = 0;
24 for
i =1: m
25 for j =1: n
32 pvaluec=1- cdff ( ”PQ” , TS1 , m -1 , N ) ;
33 pvaluer=1- cdff ( ”PQ” , TS2 , n -1 , N ) ;
34 d i s p ( p v a l u e r , pvaluec);
35 d i s p ( TS1 , TS2 ) ;
36 disp ( TS1 , ” The v a l u e of t h e F− s t a t i s t i c for testing
that there
i s no row effect is”);
37 disp ( pvaluec , ” The p−v a l u e for testing that there is