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삼원배치법 (혼합모형) (반복없음)

데이터 구조

요인 $A$는 모수인자

요인 $B$는 모수인자

요인 $R$는 변량인자

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

분산분석표

요인 제곱합
$SS$ 		자유도
$DF$ 		평균제곱
$MS$ 		$E(MS)$ $F_{0}$ 기각치 순변동
$S\acute{}$ 		기여율
$\rho$
$$A$$ $$S_{_{A}}$$ $$\nu_{_{A}}=l-1$$ $$V_{_{A}}=S_{_{A}}/\nu_{_{A}}$$ $$\sigma_{_{E}}^{ \ 2}+m \ \sigma_{_{A \times R}}^{ \ 2}+mr \ \sigma_{_{A}}^{2}$$ $$V_{_{A}}/V_{_{A \times R}}$$ $$F_{1-\alpha}(\nu_{_{A}} \ , \ \nu_{_{A \times R}})$$ $$S_{_{A}}\acute{}$$ $$S_{_{A}}\acute{}/S_{_{T}}$$
$$B$$ $$S_{_{B}}$$ $$\nu_{_{B}}=m-1$$ $$V_{_{B}}=S_{_{B}}/\nu_{_{B}}$$ $$\sigma_{_{E}}^{ \ 2}+l \ \sigma_{_{B \times R}}^{ \ 2}+lr \ \sigma_{_{B}}^{2}$$ $$V_{_{B}}/V_{_{B \times R}}$$ $$F_{1-\alpha}(\nu_{_{B}} \ , \ \nu_{_{B \times R}})$$ $$S_{_{B}}\acute{}$$ $$S_{_{B}}\acute{}/S_{_{T}}$$
$$R$$ $$S_{_{R}}$$ $$\nu_{_{R}}=r-1$$ $$V_{_{R}}=S_{_{R}}/\nu_{_{R}}$$ $$\sigma_{_{E}}^{ \ 2}+lm \ \sigma_{_{R}}^{2}$$ $$V_{_{R}}/V_{_{E}}$$ $$F_{1-\alpha}(\nu_{_{R}} \ , \ \nu_{_{E}})$$ $$S_{_{R}}\acute{}$$ $$S_{_{R}}\acute{}/S_{_{T}}$$
$$A \times B$$ $$S_{_{A \times B}}$$ $$\nu_{_{A \times B}}=(l-1)(m-1)$$ $$V_{_{A \times B}}=S_{_{A \times B}}/\nu_{_{A \times B}}$$ $$\sigma_{_{E}}^{ \ 2}+r \ \sigma_{_{A \times B}}^{2}$$ $$V_{_{A \times B}}/V_{_{E}}$$ $$F_{1-\alpha}(\nu_{_{A \times B}} \ , \ \nu_{_{E}})$$ $$S_{_{A \times B}}\acute{}$$ $$S_{_{A \times B}}\acute{}/S_{_{T}}$$
$$A \times R$$ $$S_{_{A \times R}}$$ $$\nu_{_{A \times R}}=(l-1)(r-1)$$ $$V_{_{A \times R}}=S_{_{A \times R}}/\nu_{_{A \times R}}$$ $$\sigma_{_{E}}^{ \ 2}+m \ \sigma_{_{A \times R}}^{2}$$ $$V_{_{A \times R}}/V_{_{E}}$$ $$F_{1-\alpha}(\nu_{_{A \times R}} \ , \ \nu_{_{E}})$$ $$S_{_{A \times R}}\acute{}$$ $$S_{_{A \times R}}\acute{}/S_{_{T}}$$
$$B \times R$$ $$S_{_{B \times R}}$$ $$\nu_{_{B \times R}}=(m-1)(r-1)$$ $$V_{_{B \times R}}=S_{_{B \times R}}/\nu_{_{B \times R}}$$ $$\sigma_{_{E}}^{ \ 2}+l \ \sigma_{_{B \times R}}^{2}$$ $$V_{_{B \times R}}/V_{_{E}}$$ $$F_{1-\alpha}(\nu_{_{B \times R}} \ , \ \nu_{_{E}})$$ $$S_{_{B \times R}}\acute{}$$ $$S_{_{B \times R}}\acute{}/S_{_{T}}$$
$$E$$ $$S_{_{E}}$$ $$\nu_{_{E}}=(l-1)(m-1)(r-1)$$ $$V_{_{E}}=S_{_{E}}/\nu_{_{E}}$$ $$\sigma_{_{E}}^{ \ 2}$$ $$S_{_{E}}\acute{}$$ $$S_{_{E}}\acute{}/S_{_{T}}$$
$$T$$ $$S_{_{T}}$$ $$\nu_{_{T}}=lmr-1$$ $$S_{_{T}}$$ $$1$$