$$ x_{ijk} = \mu + a_{i} + b_{j} + r_{k} + (ab)_{ij} + (ar)_{ik} + (br)_{jk} + e_{ijk} $$
요인 | 제곱합 $SS$ | 자유도 $DF$ | 평균제곱 $MS$ | $E(MS)$ | $F_{0}$ | 기각치 | 순변동 $S\acute{}$ | 기여율 $\rho$ |
---|---|---|---|---|---|---|---|---|
$$A$$ | $$S_{_{A}}$$ | $$\nu_{_{A}}=l-1$$ | $$V_{_{A}}=S_{_{A}}/\nu_{_{A}}$$ | $$\sigma_{_{E}}^{ \ 2}+m \ \sigma_{_{A \times R}}^{ \ 2}+mr \ \sigma_{_{A}}^{2}$$ | $$V_{_{A}}/V_{_{A \times R}}$$ | $$F_{1-\alpha}(\nu_{_{A}} \ , \ \nu_{_{A \times R}})$$ | $$S_{_{A}}\acute{}$$ | $$S_{_{A}}\acute{}/S_{_{T}}$$ |
$$B$$ | $$S_{_{B}}$$ | $$\nu_{_{B}}=m-1$$ | $$V_{_{B}}=S_{_{B}}/\nu_{_{B}}$$ | $$\sigma_{_{E}}^{ \ 2}+l \ \sigma_{_{B \times R}}^{ \ 2}+lr \ \sigma_{_{B}}^{2}$$ | $$V_{_{B}}/V_{_{B \times R}}$$ | $$F_{1-\alpha}(\nu_{_{B}} \ , \ \nu_{_{B \times R}})$$ | $$S_{_{B}}\acute{}$$ | $$S_{_{B}}\acute{}/S_{_{T}}$$ |
$$R$$ | $$S_{_{R}}$$ | $$\nu_{_{R}}=r-1$$ | $$V_{_{R}}=S_{_{R}}/\nu_{_{R}}$$ | $$\sigma_{_{E}}^{ \ 2}+lm \ \sigma_{_{R}}^{2}$$ | $$V_{_{R}}/V_{_{E}}$$ | $$F_{1-\alpha}(\nu_{_{R}} \ , \ \nu_{_{E}})$$ | $$S_{_{R}}\acute{}$$ | $$S_{_{R}}\acute{}/S_{_{T}}$$ |
$$A \times B$$ | $$S_{_{A \times B}}$$ | $$\nu_{_{A \times B}}=(l-1)(m-1)$$ | $$V_{_{A \times B}}=S_{_{A \times B}}/\nu_{_{A \times B}}$$ | $$\sigma_{_{E}}^{ \ 2}+r \ \sigma_{_{A \times B}}^{2}$$ | $$V_{_{A \times B}}/V_{_{E}}$$ | $$F_{1-\alpha}(\nu_{_{A \times B}} \ , \ \nu_{_{E}})$$ | $$S_{_{A \times B}}\acute{}$$ | $$S_{_{A \times B}}\acute{}/S_{_{T}}$$ |
$$A \times R$$ | $$S_{_{A \times R}}$$ | $$\nu_{_{A \times R}}=(l-1)(r-1)$$ | $$V_{_{A \times R}}=S_{_{A \times R}}/\nu_{_{A \times R}}$$ | $$\sigma_{_{E}}^{ \ 2}+m \ \sigma_{_{A \times R}}^{2}$$ | $$V_{_{A \times R}}/V_{_{E}}$$ | $$F_{1-\alpha}(\nu_{_{A \times R}} \ , \ \nu_{_{E}})$$ | $$S_{_{A \times R}}\acute{}$$ | $$S_{_{A \times R}}\acute{}/S_{_{T}}$$ |
$$B \times R$$ | $$S_{_{B \times R}}$$ | $$\nu_{_{B \times R}}=(m-1)(r-1)$$ | $$V_{_{B \times R}}=S_{_{B \times R}}/\nu_{_{B \times R}}$$ | $$\sigma_{_{E}}^{ \ 2}+l \ \sigma_{_{B \times R}}^{2}$$ | $$V_{_{B \times R}}/V_{_{E}}$$ | $$F_{1-\alpha}(\nu_{_{B \times R}} \ , \ \nu_{_{E}})$$ | $$S_{_{B \times R}}\acute{}$$ | $$S_{_{B \times R}}\acute{}/S_{_{T}}$$ |
$$E$$ | $$S_{_{E}}$$ | $$\nu_{_{E}}=(l-1)(m-1)(r-1)$$ | $$V_{_{E}}=S_{_{E}}/\nu_{_{E}}$$ | $$\sigma_{_{E}}^{ \ 2}$$ | $$S_{_{E}}\acute{}$$ | $$S_{_{E}}\acute{}/S_{_{T}}$$ | ||
$$T$$ | $$S_{_{T}}$$ | $$\nu_{_{T}}=lmr-1$$ | $$S_{_{T}}$$ | $$1$$ |