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1 2006,, ,, 3 A vs B, B vs C, C vs A t[] t[] 2 5 6

2 LSD A vs B, B vs C, C vs A = = = (14.3) 10 3 A vs B, B vs C, C vs A 1 3 A vs B, B vs C, C vs A 1,, A vsb, P() B vsc, P() C vsa, P() () () () P() =P()+ P()+ P() P() P() P() P() =0.053 () () = (14.3) () 11 12

3 11 (multiple comparison procedure) 3 A vs B, B vs C, C vs A 3 = 1.67 (Bonferroni) P()+ P()+ P() = = P()+ P()+ P() = = P() = P()+ P()+ P() P() P() P() P() 0.05 P() = = P() P()+ P()+ P() (Holm)(Shaffer) 17 a priori comparison) a posteriori comparison) 18

4 1 4 3 A vs B C vs D (A and B) vs (C and D) ( A vs B A B = (+1) A +(-1) B +(0) C +(0) D C vs D D = (0) A +(0) B +(+1) C +(-1) D (A and B) vs (C and D) ( A + B )/2( + D )/2 = (1/2) A +(1/2) B +(-1/2) C +(-1/2) D (-1) (-1) = 0 11/2 + (-1)1/2 + 0(-1/2) + 0(-1/2) = 0 01/2 + 01/2 + 1(-1/2) + (-1)(-1/2) = 0 21, (Tukey) i j i j tij = ij x x 2 i 1 1 V E + ni n j j 24

5 (Tukey) q t ij 2 xi x q x j i x j tij = q 2 2 VE VE n n 25 Q xi x j Q = max i, j p 1 1 V E + ni n j Q e a 26 (Tukey) SPSS SPSS1 BonferroniTukey SPSSBonferroni (coherence) A = B = C A = B C = A B = C 30

6 1 (Tukey-Welsch) RyanRyanRyan, Einot, Gabriel and WelschR-E-G-WQ, F RyanRyan(1959, 1960) Einot, Gabriel(1975) Ryan Welsch(1977) (1990)p171Ryan Ryan 31 p A = B = C 3 3 {A,B,C} Q R-E-G-WQ R-E-G-WF Q 32 a-1 = a = (p= a, a1 p =1(1) p/a (2pa2) a p =0.05a=4 4 4 == == =1(10.05) 2/4 = k P( T c, T c, L T c ) P( T c ) , k i= 1 1T i c i T i c i k i i Q 35 44p=4 Q 4 Q Q = max i, j p x x i 1 1 V E + ni n j j 36

7 =4Q p=4{a,b,c,d} Q Tukey-Welsch max x i V E n i =4Q =4Q B vs C p q( p, φe; α p ) c p = max, c p 1 2 p=2 c p q = ( p φ ; α ), E p 2 p=4 4 q(p, E ; 4 ) /2 = ( ) /2 = 4 p = ( ) E E = n a = = ( ) 4 (1) = ( ) p-1 = 4-1 = 3 = ( ) q(p, E ; 3 ) /2 = ( ) /2 = ( ) c 2 = q(2, E ; 2 ) /2 = ( ) /2 =( ) 7 q(p, E ; 4 ) 3 p=4 4 4 = ( ) p=4 4 q(p, E ; 4 ) /2 = (3.861 ) /2 = p = (4 ) E E = n a = = 32-4 = (28 ) 4 (1) = (0.05 ) p-1 = 4-1 = 3 = (2.474 ) q(p, E ; 3 ) /2 = (3.499 ) /2 = (2.474 ) ( p=3, E =28, 3 = = q(2, E ; 2 ) /2 = (3.341 ) /2 =(2.362 ) ( p=2, E =28, 3 = q(p, E ; 4 ) 3 p=4 4 4 = ( ) =4Q = Q 4 p=3 Q

8 p=3 {A,B,C} Q = ( ) ( or ) {A,B,D} Q = ( ) ( or ) {A,C,D} Q = ( ) ( or ) {B,C,D} Q = ( ) ( or ) 3 = ( ) p=3 {A,B,C} Q = {A,B,D} Q = {A,C,D} Q = {B,C,D} Q = = p=2 {A,C,D} {A,C,D}A vs C, C vs D, D vs A {A,B,C} {A,B} Q = ( ) ( or ) {B,C} Q = ( ) ( or ) {C,A} Q = ( ) ( or ) {A,B,D} {A,B} {B,D} Q = ( ) ( or ) {D,A} Q = ( ) ( or ) {A,C,D} {A,C} {C,D} Q = ( ) ( or ) {D,A} {B,C,D} {B,C} {C,D} {D,B} c 2 = ( ) 45 {A,B,C} {A,B} Q = ( ) {B,C} Q = ( ) {C,A} Q = ( ) {A,B,D} {A,B} {B,D} Q = ( ) {D,A} Q = ( ) {A,C,D} {A,C} {C,D} Q = ( ) {D,A} {B,C,D} {B,C} {C,D} {D,B} c 2 = Newman-Keuls Duncan Newman-Keuls p = Duncan p =1 p (Tukey) Newman-KeulsTukey p p = (1990) 48

9 3 (Ryan)S30 2 a p α p = a ( p 1) α α = a( p 1) 2 49 Peritz Tukey-WelschNewman-Keuls (1997) SPSS SPSSR-E- G-WF 50 (contrast) A vs B A B = (+1) A +(-1) B +(0) C +(0) D vs D = (0) A +(0) B +(+1) C +(-1) D ( and vs and ) ( A + B )/2( + D )/2 = (1/2) A +(1/2) B +(-1/2) C +(-1/2) D 10 0S21 51 (Scheffe) 1997) 52 (Dunnett) 1997) 53 54

10 A < B < C < D (A (1997) (1997)SPSS LSD Dunncan 4 Newman-KeulsStudent-Newman-Keuls LSDANOVA 3(1997p31) LSD (1) LSDANOVA A = B = C = D ANOVA5 5 1 = P(E(A,B,C,D) and [G(A,B) or G(B,C) or or G(C,D)]) =P(E(A,B,C,D))P [G(A,B) or G(B,C) or or G(C,D)]) = = ( 0.925% ) 57 4LSD (2) A = B = C D 1 ANOVA100 1 = P(E(A,B,C,D) and [G(A,B) or G(B,C) or or G(C,D)]) =P(E(A,B,C,D))P [G(A,B) or G(B,C) or or G(C,D)]) 1 P [G(A,B) or G(B,C) or G(C,A)]) = = ( 14.3% ) 58 4LSD (3) (1)(2) A = B = C D 4 LSD 3LSD (1) A = B = C 4 1 = P(E(A,B,C) and [G(A,B) or G(B,C) or G(C,A)]) =P(E(A,B,C))P [G(A,B) or G(B,C) or G(C,A)]) = = (0.715%) 59 60

11 3LSD (2) A = B c 1 = P(E(A,B,C) and [G(A,B) or G(B,C) or G(C,A)]) =P(E(A,B,C))P [G(A,B) or G(B,C)]) = 0.05 (5%) E(A,B,C,D):ANOVA G(A,B)AB 3LSD (3) 3 1 (0.05) (1) Tabachnick & Fidell, ) Tukey 75 DunnettC 75 DunnettT3 Tukey-Kramer(Tukey ) 75 DunnettC 75 DunnettT3 (2) Fidell, ) R-E-G-WQRyan, Einot, Gabriel and Welsch Gabriel HochbergGT2 Games-Howell (2004) 2004) Student-Newman-Keuls Dunncan Waller- Dunncan LSD Bonferroni TamhaneT2 Scheffe Dunnett 65 66

12 2 Dunnett Tukey R-E-G-WQRyan, Einot, Gabriel and Welsch 75 DunnettC 75 DunnettT3 Tukey-Kramer (SPSSTukey) Gabriel HochbergGT2 75 DunnettC Games-Howell 75 DunnettT SPSS LSDBonferroniSidak3 LSDLSD Bonferroni Sidak p86 71 Sidak Bonferroni Bonferroni Bonferroni Sidak h i α = 1 (1 α) i 1/ h 72

13 SPSS HochbergGT2 Tukey Tukey Gabriel HochbergGT2 Gabriel SPSS Waller-Duncan T 2004pp52-53) SPSS (1997) (1990) (2005) (2004) SPSSBASE Tabachnick, B. G., & Fidell, L. S. (2001) Computer-Assisted Research Design and Analysis. Allyn & Bacon. Fidell, L. S. (2000) Discovering Statistics: using SPSS for Windows. SAGE Publications. (2004)

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