F 1 2;1-P) F ;P) 1 2 =1/F ( 2 1 ;P) - lab.sdm.keio.ac.jp

1 11/8 6. F 2 A,B A n=11 B m=10 A cm B cm A N( 1, 12) B N( 2, 22) 12 22 1, 2 x11,x12,..,x1n N( 1, 12) x21,x22,..,x2m N( 2, 22) 222211// VVF= (n-1,m-1) F (1) F PPF ( , ;P)21F ( , ;1-P)=1/F ( , ;P)2121221212212121,211121)1()()2()2()2( )( + + + =xxxf F F 1, 2 P F( 1, 2;P) P=Pr{F F( 1, 2;P)} F( 1, 2;1-P)=1/ F( 2, 1;P) P=Pr{F F( 1, 2;1-P)}=Pr{1/F 1/F( 1, 2;1-P)} 1/F (m-1,n-1) P=Pr{1/F F( 2, 1;P)} 1/F( 1, 2;1-P)= F( 2, 1;P) F( 1, 2;1-P)= 1/F( 2, 1;P) 1) F(12,10; ) 2) F(12,10.

2 - 18 - 1) F(12,10; )= 2) F(12,10; )=1/F(10,12; )=1 (2) 2 n u1, u2,..u x= u12+ + u 2 n 2 xi N( , 2) ui=(xi- )/ = niix122)(1 n 2 x 2122)(1 Sxxnii= = n-1 2 2 n1 2 u1 n2 2 u2 x= (u1/n1)/(u2/n2) (n1,n2) F 2 S1/ 12 ( n-1), S2/ 22 ( m-1) 222211222211//)1(/)1(/ VVmSnS= (n-1,m-1) F V1/V2 (3) 1) H0 12 22 H1 12 22 2) = 3)

3 R F0 F(10,9; )=1/F(9,10; )=1 F0 F(10,9; )= 4) x11,x12,..,x1n x21,x 2,..,x2m F0 S1= (x1i-x1)2= - 19 -S2= (x2i-x2)2= V1=S1/(n-1)= V2=S2/(m-1)= F0=V1/V2= F0 (10,9) F 5) F0 H0 F0= F(10,9; )= H0 (4) 12/ 22=V1/V2= F( 1, 2;1- /2) (V1/ 12)/(V2/ 22) F( 1, 2.

4 /2) V1/V2 1/F( 1, 2; /2) 12/ 22 V1/V2 1/F( 1, 2;1- /2) V1/V2 1/F( 1, 2; /2) 12/ 22 V1/V2 F( 2, 1; /2) (10,9; ) 12/ 22 F(9,10; ) 12/ 22 t Student Welch 20% 5% A n=10 B m=9 A 78 80 79 83 82 85 78 74 76 84 B 81 84 82 88 86 83 78 84 89 A N( 1, 12) B N( 2, 22) 1 2 1) H0 12 22 H1 12 22 2) = 3) R F0 F(9,8; )=1/F(8,9; )=1 F0 F(9,8; )= 4) x11,x12.

5 ,x1n x21,x 2,..,x2m F0 S1= (x1i-x1)2= S2= (x2i-x2)2= V1=S1/(n-1)= - 20 - - 21 - V2=S2/(m-1)= F0=V1/V2= F0 (9,8) F 5) F0 H0 F0= F(9,8; )= 12 22