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삼원배치법_혼합모형_반복없음 [2012/07/26 21:57] moonrepeat 새로 만듦 |
삼원배치법_혼합모형_반복없음 [2021/03/10 21:42] (현재) |
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| ====== 삼원배치법 (혼합모형) (반복없음) ====== | ====== 삼원배치법 (혼합모형) (반복없음) ====== | ||
| ===== 데이터 구조 ===== | ===== 데이터 구조 ===== | ||
| - | [요인]   $$A$$ 는 [모수인자] | + | [[요인]] $A$는 [[모수인자]] |
| - | [요인]   $$B$$ 는 [모수인자] | + | [[요인]] $B$는 [[모수인자]] |
| - | [요인]   $$R$$ 는 [변량인자] | + | [[요인]] $R$는 [[변량인자]] |
| + | $$ x_{ijk} = \mu + a_{i} + b_{j} + r_{k} + (ab)_{ij} + (ar)_{ik} + (br)_{jk} + e_{ijk} $$ | ||
| - | $$ x_{ijk} = \mu + a_{i} + b_{j} + r_{k} + (ab)_{ij} + (ar)_{ik} + (br)_{jk} + e_{ijk} $$ | + | * $i$ : [[인자]] $A$의 [[수준]] 수 $( i = 1,2, \cdots ,l )$ |
| - | + | * $j$ : [[인자]] $B$의 [[수준]] 수 $( j = 1,2, \cdots ,m )$ | |
| - | + | * $k$ : [[인자]] $R$의 [[수준]] 수 $( k = 1,2, \cdots ,r )$ | |
| - | $$i$$    : 인자   $$A$$ 의 [수준] 수   $$( i = 1,2, \cdots ,l )$$ | + | |
| - | + | ||
| - | $$j$$    : 인자   $$B$$ 의 [수준] 수   $$( j = 1,2, \cdots ,m )$$ | + | |
| - | + | ||
| - | $$k$$    : 인자   $$R$$ 의 [수준] 수   $$( k = 1,2, \cdots ,r )$$ | + | |
| ===== 분산분석표 ===== | ===== 분산분석표 ===== | ||
| - | || '''[요인]''' || '''[제곱합]''' $$SS$$ || '''[자유도]''' $$DF$$ || '''[평균제곱]''' $$MS$$ || $$E(MS)$$ || $$F_{0}$$ || '''기각치''' || '''[순변동]''' $$ S\acute{} $$ || '''[기여율]''' $$\rho$$ || | + | ^ [[요인]] ^ [[제곱합]]\\ $SS$ ^ [[자유도]]\\ $DF$ ^ [[평균제곱]]\\ $MS$ ^ $E(MS)$ ^ $F_{0}$ ^ [[기각치]] ^ [[순변동]]\\ $S\acute{}$ ^ [[기여율]]\\ $\rho$ | |
| - | |||||||||||||||||| || | + | | $$A$$ | $$S_{_{A}}$$ | $$\nu_{_{A}}=l-1$$ | $$V_{_{A}}=S_{_{A}}/\nu_{_{A}}$$ | $$\sigma_{_{E}}^{ \ 2}+m \ \sigma_{_{A \times R}}^{ \ 2}+mr \ \sigma_{_{A}}^{2}$$ | $$V_{_{A}}/V_{_{A \times R}}$$ | $$F_{1-\alpha}(\nu_{_{A}} \ , \ \nu_{_{A \times R}})$$ | $$S_{_{A}}\acute{}$$ | $$S_{_{A}}\acute{}/S_{_{T}}$$ | |
| - | || $$A$$ || $$S_{_{A}}$$ || $$\nu_{_{A}}=l-1$$ || $$V_{_{A}}=S_{_{A}}/\nu_{_{A}}$$ || $$\sigma_{_{E}}^{ \ 2}+m \ \sigma_{_{A \times R}}^{ \ 2}+mr \ \sigma_{_{A}}^{2}$$ || $$V_{_{A}}/V_{_{A \times R}}$$ || $$F_{1-\alpha}(\nu_{_{A}} \ , \ \nu_{_{A \times R}})$$ || $$S_{_{A}}\acute{}$$ || $$S_{_{A}}\acute{}/S_{_{T}}$$ || | + | | $$B$$ | $$S_{_{B}}$$ | $$\nu_{_{B}}=m-1$$ | $$V_{_{B}}=S_{_{B}}/\nu_{_{B}}$$ | $$\sigma_{_{E}}^{ \ 2}+l \ \sigma_{_{B \times R}}^{ \ 2}+lr \ \sigma_{_{B}}^{2}$$ | $$V_{_{B}}/V_{_{B \times R}}$$ | $$F_{1-\alpha}(\nu_{_{B}} \ , \ \nu_{_{B \times R}})$$ | $$S_{_{B}}\acute{}$$ | $$S_{_{B}}\acute{}/S_{_{T}}$$ | |
| - | || $$B$$ || $$S_{_{B}}$$ || $$\nu_{_{B}}=m-1$$ || $$V_{_{B}}=S_{_{B}}/\nu_{_{B}}$$ || $$\sigma_{_{E}}^{ \ 2}+l \ \sigma_{_{B \times R}}^{ \ 2}+lr \ \sigma_{_{B}}^{2}$$ || $$V_{_{B}}/V_{_{B \times R}}$$ || $$F_{1-\alpha}(\nu_{_{B}} \ , \ \nu_{_{B \times R}})$$ || $$S_{_{B}}\acute{}$$ || $$S_{_{B}}\acute{}/S_{_{T}}$$ || | + | | $$R$$ | $$S_{_{R}}$$ | $$\nu_{_{R}}=r-1$$ | $$V_{_{R}}=S_{_{R}}/\nu_{_{R}}$$ | $$\sigma_{_{E}}^{ \ 2}+lm \ \sigma_{_{R}}^{2}$$ | $$V_{_{R}}/V_{_{E}}$$ | $$F_{1-\alpha}(\nu_{_{R}} \ , \ \nu_{_{E}})$$ | $$S_{_{R}}\acute{}$$ | $$S_{_{R}}\acute{}/S_{_{T}}$$ | |
| - | || $$R$$ || $$S_{_{R}}$$ || $$\nu_{_{R}}=r-1$$ || $$V_{_{R}}=S_{_{R}}/\nu_{_{R}}$$ || $$\sigma_{_{E}}^{ \ 2}+lm \ \sigma_{_{R}}^{2}$$ || $$V_{_{R}}/V_{_{E}}$$ || $$F_{1-\alpha}(\nu_{_{R}} \ , \ \nu_{_{E}})$$ || $$S_{_{R}}\acute{}$$ || $$S_{_{R}}\acute{}/S_{_{T}}$$ || | + | | $$A \times B$$ | $$S_{_{A \times B}}$$ | $$\nu_{_{A \times B}}=(l-1)(m-1)$$ | $$V_{_{A \times B}}=S_{_{A \times B}}/\nu_{_{A \times B}}$$ | $$\sigma_{_{E}}^{ \ 2}+r \ \sigma_{_{A \times B}}^{2}$$ | $$V_{_{A \times B}}/V_{_{E}}$$ | $$F_{1-\alpha}(\nu_{_{A \times B}} \ , \ \nu_{_{E}})$$ | $$S_{_{A \times B}}\acute{}$$ | $$S_{_{A \times B}}\acute{}/S_{_{T}}$$ | |
| - | || $$A \times B$$ || $$S_{_{A \times B}}$$ || $$\nu_{_{A \times B}}=(l-1)(m-1)$$ || $$V_{_{A \times B}}=S_{_{A \times B}}/\nu_{_{A \times B}}$$ || $$\sigma_{_{E}}^{ \ 2}+r \ \sigma_{_{A \times B}}^{2}$$ || $$V_{_{A \times B}}/V_{_{E}}$$ || $$F_{1-\alpha}(\nu_{_{A \times B}} \ , \ \nu_{_{E}})$$ || $$S_{_{A \times B}}\acute{}$$ || $$S_{_{A \times B}}\acute{}/S_{_{T}}$$ || | + | | $$A \times R$$ | $$S_{_{A \times R}}$$ | $$\nu_{_{A \times R}}=(l-1)(r-1)$$ | $$V_{_{A \times R}}=S_{_{A \times R}}/\nu_{_{A \times R}}$$ | $$\sigma_{_{E}}^{ \ 2}+m \ \sigma_{_{A \times R}}^{2}$$ | $$V_{_{A \times R}}/V_{_{E}}$$ | $$F_{1-\alpha}(\nu_{_{A \times R}} \ , \ \nu_{_{E}})$$ | $$S_{_{A \times R}}\acute{}$$ | $$S_{_{A \times R}}\acute{}/S_{_{T}}$$ | |
| - | || $$A \times R$$ || $$S_{_{A \times R}}$$ || $$\nu_{_{A \times R}}=(l-1)(r-1)$$ || $$V_{_{A \times R}}=S_{_{A \times R}}/\nu_{_{A \times R}}$$ || $$\sigma_{_{E}}^{ \ 2}+m \ \sigma_{_{A \times R}}^{2}$$ || $$V_{_{A \times R}}/V_{_{E}}$$ || $$F_{1-\alpha}(\nu_{_{A \times R}} \ , \ \nu_{_{E}})$$ || $$S_{_{A \times R}}\acute{}$$ || $$S_{_{A \times R}}\acute{}/S_{_{T}}$$ || | + | | $$B \times R$$ | $$S_{_{B \times R}}$$ | $$\nu_{_{B \times R}}=(m-1)(r-1)$$ | $$V_{_{B \times R}}=S_{_{B \times R}}/\nu_{_{B \times R}}$$ | $$\sigma_{_{E}}^{ \ 2}+l \ \sigma_{_{B \times R}}^{2}$$ | $$V_{_{B \times R}}/V_{_{E}}$$ | $$F_{1-\alpha}(\nu_{_{B \times R}} \ , \ \nu_{_{E}})$$ | $$S_{_{B \times R}}\acute{}$$ | $$S_{_{B \times R}}\acute{}/S_{_{T}}$$ | |
| - | || $$B \times R$$ || $$S_{_{B \times R}}$$ || $$\nu_{_{B \times R}}=(m-1)(r-1)$$ || $$V_{_{B \times R}}=S_{_{B \times R}}/\nu_{_{B \times R}}$$ || $$\sigma_{_{E}}^{ \ 2}+l \ \sigma_{_{B \times R}}^{2}$$ || $$V_{_{B \times R}}/V_{_{E}}$$ || $$F_{1-\alpha}(\nu_{_{B \times R}} \ , \ \nu_{_{E}})$$ || $$S_{_{B \times R}}\acute{}$$ || $$S_{_{B \times R}}\acute{}/S_{_{T}}$$ || | + | | $$E$$ | $$S_{_{E}}$$ | $$\nu_{_{E}}=(l-1)(m-1)(r-1)$$ | $$V_{_{E}}=S_{_{E}}/\nu_{_{E}}$$ | $$\sigma_{_{E}}^{ \ 2}$$ | | | $$S_{_{E}}\acute{}$$ | $$S_{_{E}}\acute{}/S_{_{T}}$$ | |
| - | || $$E$$ || $$S_{_{E}}$$ || $$\nu_{_{E}}=(l-1)(m-1)(r-1)$$ || $$V_{_{E}}=S_{_{E}}/\nu_{_{E}}$$ || $$\sigma_{_{E}}^{ \ 2}$$ || || || $$S_{_{E}}\acute{}$$ || $$S_{_{E}}\acute{}/S_{_{T}}$$ || | + | | $$T$$ | $$S_{_{T}}$$ | $$\nu_{_{T}}=lmr-1$$ | | | | | $$S_{_{T}}$$ | $$1$$ | |
| - | |||||||||||||||||| || | + | |
| - | || $$T$$ || $$S_{_{T}}$$ || $$\nu_{_{T}}=lmr-1$$ || || || || || $$S_{_{T}}$$ || $$1$$ || | + | |