颀备知识28固定效应模型 口可加效应模型 yk=+T;+β1+Eik ,'.,a,J 1.…b.k=1 Ejk i.i. d N(o,o2 ∑τ1=0,∑阝=0
可加效应模型 预备知识2：固定效应模型 ( ) = = = = = = + + + i j i j 2 ijk ijk i j ijk 0, 0 i.i.d N 0, i 1, ,a, j 1, ,b,k 1, ,m y
方差分( analysis of variance ANOVA) 假设 Ho1:T1=τ2=…=Ta=0 阝1=β2 阝b=0 偏差平方和的分解 s:=∑∑-y) =∑∑6-y)+∑∑,-y)+∑∑n-y:-y+y
方差分析（ analysis of variance, ANOVA） 假设 偏差平方和的分解 H : 0 H : 0 02 1 2 b 01 1 2 a = = = = = = = = ( ) ( ) ( ) ( ) = − + − + − − + = − i j 2 ij i. .j 2 i j .j 2 i j i. 2 i j T ij y y.. y y.. y y y y.. SS y y
-sS+s +ss 检验统计量 y1=μ+T1+81,y1=+B1+8jy…=+8 ESS=E∑∑(+B=B) b∑2+(a-1
( ) ( ) 2 i 2 i i j 2 i. .. A i .j .. .j j i. i. i A B e b a 1 ESS E y y y.. SS SS SS = + − = + − = + + = + + = + = + + 检验统计量
同理ESSB=a∑+(b-1)2 ESST=E ∑∑( +阝;+8:-E b∑2+a∑+(ab-1)2 ESS8=(a-1)b-1)2
( ) ( ) ( ) ( )( ) 2 e 2 j 2 j i 2 i i j 2 .. T i j ij 2 j 2 B j ESS a 1 b 1 b a ab 1 ESS E ESS a b 1 = − − = + + − = + + − = + − 同理
EMS SSA I- A E SS EMS E B 2 B b-1 b-1 SS EMS=E 2 (a-1)(b-1) MSA MS B 1 MS MS
( )( ) eB 2 eA 1 e 2 e j 2 2 j B B i 2 2 i A A MS MS F MS MS F a 1 b 1 SS EMS E b 1 a b 1 SS EMS E a 1 b a 1 SS EMS E = = = − − = + − = − = + − = − =