第三章變異數分析 | anova p value計算
1F-,//F22222121SS1222S12S22v1v2FF-(v1v2)F-(ANOVA)F-testF-F-p-1-way_20101:m(1,..,i,..,m)Data:mnyij---ijGroup1iyi2..y1nyinymnAvg.(1-wayANOVA)1-way_20102yij=i+ij,i=1,..,m,j=1,..,nij,N(0,2)H01=2=.2=mH1(ijij)SST=SSt+SSEMSt=SSt/(m-1)H0=2MSE=SSE/(N-m)()MSE21-way_20103F=MSt/MSE1.H0FF(m-1,N-m)2.MStFFp-value=P(F->F)p-value
1 F- ,//F 22222121 SS 12 22 S12 S22 v1 v2 F F- (v1 v2 ) F- (ANOVA) F-test F- F- p- 1-way_2010 1 : m ( 1 , .., i , .., m ) Data : m n yij --- i j Group1 i yi2 ..y1n yinymnAvg. (1-way ANOVA) 1-way_2010 2 yij = i + ij , i= 1,.., m, j= 1,.., n ij , N ( 0, 2 ) H0 1= 2=.
2 = m H1 ( i j i j) SST = SSt+ SSE MSt = SSt/(m-1) H0 = 2 MSE = SSE /(N -m) ( ) MSE 2 1-way_2010 3 F = MSt / MSE 1. H0 F F (m-1, N-m) 2. MSt F F p-value = P( F- > F ) p-value< treatment p-value 1 treatment 2 Q : ?
3 ? ? 1-way_2010 4 SourceSSdfMSF- p- TreatmentSStm-1 MStF =MSt/MSEE rrorSSEN-mMSET otalSSTN-1 ANOVA table for 1-way model ANOVA Table 1 F- p- F- df p- df p- p- - p- < 2 p- m 1-way_2010 5 A B C (p42) 1234 A78546B98657C1013111011 : 1-way ANOVA SourceSSdfMSF- p- 8211 ANOVA table p-value = .00569 < 3 (level) 4 1-way_2010 6 A: 67 68 69 70 71 B: 70 71 72 73 74 C: D: 72 E.
4 74 + | | | | | | | 73 + +-----+ | | | | | | | | +-----+ | | | | | | 72 + *--+--* | *--+--* | | | | | | | | | +-----+...