삼원배치법 (혼합모형) (반복없음)

[요인]&nbsp&nbsp $$A$$ 는 [모수인자]

[요인]&nbsp&nbsp $$B$$ 는 [모수인자]

[요인]&nbsp&nbsp $$R$$ 는 [변량인자]

$$ x_{ijk} = \mu + a_{i} + b_{j} + r_{k} + (ab)_{ij} + (ar)_{ik} + (br)_{jk} + e_{ijk} $$

 $$i$$ &nbsp&nbsp : 인자&nbsp&nbsp $$A$$ 의 [수준] 수&nbsp&nbsp $$( i = 1,2, \cdots ,l )$$

 $$j$$ &nbsp&nbsp : 인자&nbsp&nbsp $$B$$ 의 [수준] 수&nbsp&nbsp $$( j = 1,2, \cdots ,m )$$

 $$k$$ &nbsp&nbsp : 인자&nbsp&nbsp $$R$$ 의 [수준] 수&nbsp&nbsp $$( k = 1,2, \cdots ,r )$$

|| '[요인]' || '[제곱합]' $$SS$$ || '[자유도]' $$DF$$ || '[평균제곱]' $$MS$$ || $$E(MS)$$ || $$F_{0}$$ || '기각치' || '[순변동]' $$ S\acute{} $$ || '[기여율]' $$\rho$$ || |||||||||||||||||| || || $$A$$ || $$S_{_{A}}$$ || $$\nu_{_{A}}=l-1$$ || $$V_{_{A}}=S_{_{A}}/\nu_{_{A}}$$ || $$\sigma_{_{E}}^{ \ 2}+m \ \sigma_{_{A \times R}}^{ \ 2}+mr \ \sigma_{_{A}}^{2}$$ || $$V_{_{A}}/V_{_{A \times R}}$$ || $$F_{1-\alpha}(\nu_{_{A}} \ , \ \nu_{_{A \times R}})$$ || $$S_{_{A}}\acute{}$$ || $$S_{_{A}}\acute{}/S_{_{T}}$$ || || $$B$$ || $$S_{_{B}}$$ || $$\nu_{_{B}}=m-1$$ || $$V_{_{B}}=S_{_{B}}/\nu_{_{B}}$$ || $$\sigma_{_{E}}^{ \ 2}+l \ \sigma_{_{B \times R}}^{ \ 2}+lr \ \sigma_{_{B}}^{2}$$ || $$V_{_{B}}/V_{_{B \times R}}$$ || $$F_{1-\alpha}(\nu_{_{B}} \ , \ \nu_{_{B \times R}})$$ || $$S_{_{B}}\acute{}$$ || $$S_{_{B}}\acute{}/S_{_{T}}$$ || || $$R$$ || $$S_{_{R}}$$ || $$\nu_{_{R}}=r-1$$ || $$V_{_{R}}=S_{_{R}}/\nu_{_{R}}$$ || $$\sigma_{_{E}}^{ \ 2}+lm \ \sigma_{_{R}}^{2}$$ || $$V_{_{R}}/V_{_{E}}$$ || $$F_{1-\alpha}(\nu_{_{R}} \ , \ \nu_{_{E}})$$ || $$S_{_{R}}\acute{}$$ || $$S_{_{R}}\acute{}/S_{_{T}}$$ || || $$A \times B$$ || $$S_{_{A \times B}}$$ || $$\nu_{_{A \times B}}=(l-1)(m-1)$$ || $$V_{_{A \times B}}=S_{_{A \times B}}/\nu_{_{A \times B}}$$ || $$\sigma_{_{E}}^{ \ 2}+r \ \sigma_{_{A \times B}}^{2}$$ || $$V_{_{A \times B}}/V_{_{E}}$$ || $$F_{1-\alpha}(\nu_{_{A \times B}} \ , \ \nu_{_{E}})$$ || $$S_{_{A \times B}}\acute{}$$ || $$S_{_{A \times B}}\acute{}/S_{_{T}}$$ || || $$A \times R$$ || $$S_{_{A \times R}}$$ || $$\nu_{_{A \times R}}=(l-1)(r-1)$$ || $$V_{_{A \times R}}=S_{_{A \times R}}/\nu_{_{A \times R}}$$ || $$\sigma_{_{E}}^{ \ 2}+m \ \sigma_{_{A \times R}}^{2}$$ || $$V_{_{A \times R}}/V_{_{E}}$$ || $$F_{1-\alpha}(\nu_{_{A \times R}} \ , \ \nu_{_{E}})$$ || $$S_{_{A \times R}}\acute{}$$ || $$S_{_{A \times R}}\acute{}/S_{_{T}}$$ || || $$B \times R$$ || $$S_{_{B \times R}}$$ || $$\nu_{_{B \times R}}=(m-1)(r-1)$$ || $$V_{_{B \times R}}=S_{_{B \times R}}/\nu_{_{B \times R}}$$ || $$\sigma_{_{E}}^{ \ 2}+l \ \sigma_{_{B \times R}}^{2}$$ || $$V_{_{B \times R}}/V_{_{E}}$$ || $$F_{1-\alpha}(\nu_{_{B \times R}} \ , \ \nu_{_{E}})$$ || $$S_{_{B \times R}}\acute{}$$ || $$S_{_{B \times R}}\acute{}/S_{_{T}}$$ || || $$E$$ || $$S_{_{E}}$$ || $$\nu_{_{E}}=(l-1)(m-1)(r-1)$$ || $$V_{_{E}}=S_{_{E}}/\nu_{_{E}}$$ || $$\sigma_{_{E}}^{ \ 2}$$ || || || $$S_{_{E}}\acute{}$$ || $$S_{_{E}}\acute{}/S_{_{T}}$$ || |||||||||||||||||| || || $$T$$ || $$S_{_{T}}$$ || $$\nu_{_{T}}=lmr-1$$ || || || || || $$S_{_{T}}$$ || $$1$$ ||