6 One-way layout 3 (oneway layout) k k y y y y n n y y K yn y y n n y y K yn k y k y k yknk n k yk yk K y nk (grand mean) (SST) (SStr: ) (SSE= SST-SStr), ( 39 ) ( )(rato) F- (normalty assumpton), Medan, Kruskal-Walls ( ) [00 ] http://wolfpackhannamackr Nonparametrc 73
6 ( : Analyss of Varance: ANOVA) t n t -n (unt) (CRD: Completely Randomzed Desgn) (A, B, C) 4 CRD, 5,, 7,, 0, 3 CRD ( :block) (randomzed) Randomzed Block Desgn B A C B C A B A [00 ] http://wolfpackhannamackr Nonparametrc 74
3 m (ppm) 0 Lake Observaton 0 3 3 4 5 3 4 6 8 7 5 3 4 5 3 4 6 5 8 9 6 0 30 y = u + + e = µ + e τ =,, K k j =,, K, n : ( y y) = ( y y ) + ( y y) Y( ) : y y) = ( y y ) + ( ( y y) SST = SSE + SStr 3 ~ Normal(0, σ ) e : Hartley s test 0 : t : H σ = σ = K = σ max( s ) : Fmax = ~ F ( :, ) mn( s ) (Homoscadcty)dl (Heteroscadcty) σ = ku y * = y σ = ku y * = log( y) [00 ] http://wolfpackhannamackr Nonparametrc 75
( ) Source DF SS MS Treatment t- = y SStr ( y) MStr = SStr /( t ) MStr F = Error n-t SSE = SST SStr MSE = SSE /( n t) MSE Total n- = ( y y) SST ~ F( t, n t) (Post-hoc test) (multple comparson) F- H 0 : u = u = = ut (parwse: : H 0 : u = u 3 ) (contrast: : H 0 : u u + u3 = ) ( ) F- ( ) (controlled expermental error rate) ( α) c = t( t ) / Fsher s Least Sgnfcant Dfference c c parwse o parwse ( ) o LSD Tukey W procedure o studentzed range dstrbuton: W = max( y ) mn( y ) s q = w / o Student-Newman-Keuls procedure o Tukey (crtcal value) Tukey Duncan Multple range test o Tukey ( α) r o r [00 ] http://wolfpackhannamackr Nonparametrc 76
Scheffe s S method o (contrast) Dunnett s procedure o control ( ) ( : placebo,, ) parwse (contrast) o, 3? : Q = u ( u + 3 ) /? Q = y ( y + 3 ) / u y ( Q) : F = ~ F(, n t) where c c c MSE( ) n = c o 4? Q = u + u ) ( u + ) c =, c =, c =, c = ( 4 u3 3 4 [00 ] http://wolfpackhannamackr Nonparametrc 77
SAS [00 ] http://wolfpackhannamackr Nonparametrc 78
HOMEWORK# (due May 4) (Research and Development ) (Hgh, Moderate, Low) (0 ) (SAS ) Low 76 8 68 58 69 66 77 6 Moderate 67 8 94 86 78 77 89 79 83 87 7 84 Hgh 85 97 0 78 96 95 Box-Plot Bar parwse (Tukey ) Hgh, (Low + Moderate) [00 ] http://wolfpackhannamackr Nonparametrc 79
6 Medan Medan? + ( ) + 3 k M, M, K M k, : H M = M = K = 0 : M k : k > O O O k A O O O k B n n n k N 3 {> } { } ( O E ) 4 T = ~ χ ( df = k ) ( )??? E E = [00 ] http://wolfpackhannamackr Nonparametrc 80
χ ( df = k ) (crtcal value: ) EXAMPLE (05 α = 0 ) 85 87 09 94 75 97 88 85 89 93 76 95 69 83 85 79 9 04 9 34 33 94 09 95 ) : H 0 : M = M = M ) : 3) : 935 3 > 3 8 5 7 0 8 8 8 4 (3 4) T = 4 (5 4) + 4 (0 4) + + 4 4) : (3) χ ( df =, α = 005) = 5 99 = 3 HOMEWORK#3 (due June 5) 4 Medan ( : hand calculaton) =005 A 7 6 9 4 6 30 9 6 B 44 34 43 47 35 5 37 9 C 7 45 8 3 36 3 4 4 5 D 5 9 30 50 47 40 43 44 54 [00 ] http://wolfpackhannamackr Nonparametrc 8
63 Kruskal-Walls 3 ( ) Mann-Whtney k M, M, K M k, : H M = M = K = 0 : M k : 3 R 4 : T = 3( N + ) N( N + ) n N = R = n = Kruskal-Walls K-W 5 3 5, K-W χ ( df = k ) [00 ] http://wolfpackhannamackr Nonparametrc 8
EXAMPLE 3 Kruskal-Walls ( =005) 6 307 33 454 339 304 54 87 356 465 50 455 355 468 36 3 343 77 07 048 838 687 ) : H 0 : M = M = M ) : 3) : 3 4 7 3 8 4 9 6 5 69 6 8 5 7 3 90 3 0 0 9 94 R 69 90 94 T = 3( N + ) = [ + + ] 3( + ) = 93 N( N + ) n ( + ) 0 6 6 4) : (3) χ ( df =, α = 005) = 5 99 HOMEWORK#3 ( due June 5) 3 ( : ) Kruskal-Walls ( : hand calculaton) =005 Control 340 340 356 386 386 40 40 47 433 495 557 LSD 94 35 35 340 356 37 385 40 UML 63 309 340 356 37 37 40 47 [00 ] http://wolfpackhannamackr Nonparametrc 83