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태연 최
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1 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 ] Nonparametrc 73

2 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 ] Nonparametrc 74

3 3 m (ppm) 0 Lake Observaton 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 ] Nonparametrc 75

4 ( ) 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 ] Nonparametrc 76

5 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 ] Nonparametrc 77

6 SAS [00 ] Nonparametrc 78

7 HOMEWORK# (due May 4) (Research and Development ) (Hgh, Moderate, Low) (0 ) (SAS ) Low Moderate Hgh Box-Plot Bar parwse (Tukey ) Hgh, (Low + Moderate) [00 ] Nonparametrc 79

8 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 ] Nonparametrc 80

9 χ ( df = k ) (crtcal value: ) EXAMPLE (05 α = 0 ) ) : H 0 : M = M = M ) : 3) : > (3 4) T = 4 (5 4) + 4 (0 4) ) : (3) χ ( df =, α = 005) = 5 99 = 3 HOMEWORK#3 (due June 5) 4 Medan ( : hand calculaton) =005 A B C D [00 ] Nonparametrc 8

10 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 ] Nonparametrc 8

11 EXAMPLE 3 Kruskal-Walls ( =005) ) : H 0 : M = M = M ) : 3) : R T = 3( N + ) = [ + + ] 3( + ) = 93 N( N + ) n ( + ) ) : (3) χ ( df =, α = 005) = 5 99 HOMEWORK#3 ( due June 5) 3 ( : ) Kruskal-Walls ( : hand calculaton) =005 Control LSD UML [00 ] Nonparametrc 83

nonpara1.PDF

nonpara1.PDF Chapter 1 Introduction 1 Introduction (parameter) (assumption) (rank), (median) p-value distribution free, assumption free, statistical inference based on ranks 11 Nonparametric? John Arbuthnot (1710)