1 5 2017 5 8 4 : website: email: http://www3.u-toyama.ac.jp/kkarato/ kkarato@eco.u-toyama.ac.jp 1 2 1.1............................. 2 1.2 IF.................................... 3 1.3............................... 4 2 6 2.1............................. 6 2.2................................. 9
1 2 1 1.1 1 20XX 2 63 3 31 45 4 23 1 2 3 4 63 74 20 157 11 31 3 45 74 105 23 202 1 data 03.xls sheet(1) data 03.xls sheet(1) 2 1. n 1 2. m 1 3. O 11 O 12, O 21, O 22, n 2, m 2 2 O 11 = 3 O 12 = 4 n 1 = 7 O21 = 1 O 22 = 2 n 2 = 3 m 1 = 4 m 2 = 6 N = 10
1 3 O 12 = n 1 O 11 O 21 = m 1 O 11 n 2 = N n 1 m 2 = N m 1 O 22 = n 2 O 21 ( O 22 = m 2 O 12 ) X {x 1, x 2, } Y {y 1, y 2 } 2 2 4 K L (K 1) (L 1) (K 1) (L 1) 1.2 IF 1 0 2 x 1 1 0 2 y 1 IF IF = if(, ) = if( 3 + 2 = 5, 1 0 ) 3 + 2 = 5 = 1 = if( 3 + 2 = 3, " " " " ) 3 + 2 = 3 = 2 x 1 x 1 = { 1, 0, 1 0 data 03.xls sheet(1) F4 = IF ( C4 = "", 1, 0 ) 2 y 1 1 0 G4
1 4 = IF ( D4 = "", 1, 0 ) x 1 n 1 y 1 m 1 1 0 2 = IF ( F4 + G4 = 2, 1, 0 ) x 1 = 1 y 1 = 1 1 2 x 1i + y 1i = 2 1 0 H O 11 1 data 03.xls sheet(2) T 46 39 21 106 13 6 15 34 59 45 36 140 1.3 Excel IF 2 data 03.xls sheet(2) OK 1 2
1 5 1 2 2 data 03.xls sheet(3) 20 30 1 2 3 4 5
2 6 3 data 03.xls sheet(5) 2005 2 2.1 N m p 1, p 2,, p m H 0 : p 1 = p 10, p 2 = p 20,, p m = p m0 O 1, O 2,, O m E 1 = Np 10, E 2 = Np 20,, E m = Np m0 m (O j E j ) 2 Q = m 1 χ 2 (1) E j j=1 3 data 03.xls sheet(6) A 360 25-29 A [ ] [%] 220 62 99 31 41 7 360 100. A 5%
2 7 3 A A H 0 : p 1 = 0.62, p 2 = 0.31, p 3 = 0.07 p 1, p 2, p 3 A 3 A O 1 = 220 ( 1 ) O 2 = 99 ( 2 ) O 3 = 41 ( 3 ) N = 220 + 99 + 41 = 360[ ] A E 1 = 360 0.62 = 223.2 ( 1 ) E 2 = 360 0.31 = 111.6 ( 2 ) E 3 = 360 0.07 = 25.2 ( 3 ) (1) m = 3 3 1 = 2 χ 2 5% χ 2 0.05,2 = 5.991 Q > 5.991 Q A : Q = : 0.05 : m = 3 : m 1 = 2 (220 223.2)2 223.2 : C Q = 5.991464547 + (99 111.6)2 111.6 + (41 25.2)2 25.2 = 11.37480799 A A χ 2 : CHIINV = chiinv(, )
2 8 3 CHITEST p 4 2 χ 2 : 5% f(x) 0.0 0.1 0.2 0.3 0.4 0.5 chiinv(0.05,2)=5.991 0.05 0 5 10 15 x χ 2 p (1): CHIDIST = chidist(, ) Q = 11.37480799 p 0.003388378 0.338% 0.05
2 9 χ 2 p (2): CHITEST = chitest(, ) CHITEST p p Q = chiinv(p, ) 4 p = chidist(q, ) Q = chiinv(p, ) data 03.xls sheet(7). 5% : Q = 5.128235775 : 0.05 : m = 7 : m 1 = 6 : C Q = 12.59158724 p 0.527474409 0.05 2.2 K L (K 1)(L 1) χ 2
2 10 4 data 03.xls sheet(8) N = 25 5 10 6 4. 5% 4 2 2 (, ) (, ) ( ) ( ) ( ) 11 12 O11 O = 12 5 10 = 21 22 O 21 O 22 6 4 N = 5 + 10 + 6 + 4 = 25[ ] (2) {E ij } ( ) 11 12 = 21 22 Pr(, ) = Pr() Pr() = 15 25 11 25 = 0.264 Pr(, ) = Pr() Pr() = 15 25 14 25 = 0.336 Pr(, ) = Pr() Pr() = 10 25 11 25 = 0.176 Pr(, ) = Pr() Pr() = 10 25 14 25 = 0.224 ( ) Pr(, ) N Pr(, ) N = Pr(, ) N Pr(, ) N ( 6.6 ) 8.4 4.4 5.6 (3) K L ( ij ij ) 2 Q = (K 1)(L 1) χ 2 (4) ij i=1 j=1 K L (O ij E ij ) 2 Q = i=1 j=1 K L K = 2, L = 2 (2 1) (2 1) = 1 χ 2 5% 3.841 Q > 3.841 Q Q O ij
2 11 : Q = : 0.05 (5 6.6)2 6.6 + (10 8.4)2 8.4 + (6 4.4)2 4.4 + (4 5.6)2 5.6 = 1.731601732 : K = 2 : L = 2 : (K 1)(L 1) = 1 : C Q = 3.841459149 C Q χ 2 0.05,1 = chiinv(0.05,1) p = chidist(, ) Pr(1.731601732 < χ 2 ) = 0.188206555 18.82% 5% = chitest(, ) p 5 data 03.xls sheet(4) 5%