005 n X i i 1 5 i 1 5 i 1 X i 3 X i 40 n i1 i i n X i 40 1
005 95
005 testing statistical hypothesis - A B A B 5 ()()() ()()() 3
005 ( ) null hypothesis 5 pp0.01p1 4
005 (1) 1 4 6 () N i 1 ( X i X ) N X i i X N N N -1 5
005 1 68.3 95.5 99.7 t 0 ( ) - ( ) {( -1)( ) + ( B -1)( )} 1 1 {( ) + ( ) - } A df 6
005 t 0 ( ) - ( ) ( ) ( ) ( ) ( ) df + ( ) ( ) + ( ) ( -1) ( ) ( -1) p<0.05 ( ) ( ) F 0 df df B F0 B F0 1.0.5 5.5 df 1 1df 0.05.5 00.05 00.05 df 00.05 7
005 0.0100.05 0.00100.01 00.0010.1 5 0. 1 179.9SD7.155170.SD7.38 9.7cm 3.19 0.0048 1 8
005 9
005 10
005 SPSSSPSS http://www.spss.co.jp/index.html SSRI http://software.ssri.co.jp/ 11
005 FreeJSTAT FreeJSTAT http://www.vector.co.jp/soft/win95/business/se35119.html 1
005 [mode]mo [median] Mdn Me N() N +1 Me N() Me N N + 1 [arithmetic mean]m X [geometric mean]g GM 1, X, 3 n 1 N G ( X X X [dispersion] [range] ()qr [semi-interquartile range] Q Q 1 Q Q 3 Q1 Q3 [mean deviationmean variation]( x i ) MD, MV 1 MD N N i 1 X i X [standard deviation] SD s u 13
005 SD N i 1 ( X X ) i N [coefficient of variation]sd X 100 V CV SD CV 100 X 14
005 (Z F ) -- (Mann-Whitney) (Wilcoxon) (Kruskal-Wallis)(Friedman) 1-1 t 0 ( ) - ( ) {( -1)( ) + ( B -1)( )} 1 1 {( ) + ( ) - } A df 1- t 0 ( ) - ( ) ( ) ( ) ( ) ( ) df + ( ) ( ) + ( ) ( -1) ( ) ( -1) 15
005 t 0 df 1 F 0 ( ) ( ) df ( 1 )( ) A B () U A U B A A + 1 ( A) B+ - A B B + 1 ( A) B+ - B UA UB U Z 0 ( A) B 1 U - A B A + B1 Z0 5% 1.961%.580.1 3.9. 0 U - 16
005 A B a b a+ b c d c+ d a+ c b+ d () χ n( a d - b c - n/) ( a + b) c + d ( a + c)( b + d) Zi Zi 0 Zi R z R n( n + 1) / 4] 1/ n( n + 1)(n + 1) / 4 z 5% 1.961%.580.1 3.9. A B A + 17
005 k i ()Ri () N n i N ( N + 1) R i N H k1 H k 1 Ri N( N + 1) i 1 ni 3( N + 1) ni () C H H/C 1 T C 1 N( N 1) ( t t) T t [] k k (k1) χ 1 k-1 ( f T ) N 4 / ij i f ij T i 18
005 k (k1) χ r 1 k nk( k + 1) j 1 ( R ) j 3n( k + 1) R j j N k k k 19
005 H 0 : µ µ 1 H : µ µ 1 1 1 H 0 : µ µ µ 3 1 3 H : µ µ 1 1 H1 : µ 1 µ 3 H : µ µ 1 13 3. (Ryan) (Tukey) (Duncan) (Scheffe) (LSD) 0
005 3 x + 5 y y 5x + 3x 8 xy xy x y x y x y (x, y ) (x, y) (x3, y3)(x,y ) x y () () ()() 1
005 (x)(y) (x)(y) x x y () () () XY (XY) (X) Y A B X Y {N X N ( XY X Y X ) }{N Y ( Y ) }
005 r 0.9136 (r) ()0 t 0 r N df N- 1 r 0 df r t0 9.511df180.1% 3
005. 4
005 or. 5
005 A B 3. 6
005 ] i j (Expectation) E ij N i. N N... j Eij i j Ni. i Nj. j. N.. i 1 j 1 O E M K ( ij ij ) df ( M 1)( K 1) Oij i j Observation Eij i j Expectation M K E ij 3 511 5% 9.4881 13.770.1 18.467. 7
005 MK 5 1. Fisher. 5 3. 5. 8
005 χ n( ad bc) ( a + b)( a + c)( b + d)( c + d) df ( -1)( -1) 1 5 n n( ad bc ) χ ( a + b)( a + c)( b + d)( c + d) df ( -1)( -1) 1. 9
005 Fisher s exact test 0 (a) 1 14 C 1 7 C 13 17 C 5 (17!) (10!) (14!) (13!) (7!) (1!) (5!) (!) (8!) (b) 14 C 13 7 C 13 17 C 4 (17!) (10!) (14!) (13!) (7!) (13!) (4!) (1!) (9!) (c) 0 3 14 C 14 7 C 13 17 C 3 (17!) (10!) (14!) (13!) (7!) (14!) (3!) (0!) (10!). 30
005 B C df ( B C χ B + C ) ( -1)( -1) 1. 31