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--- 삼원배치법_모수모형_반복있음 [2012/07/27 23:34]
moonrepeat [각 [수준]의 [모평균]의 [추정] (주효과만이 유의한 경우)]
+++ 삼원배치법_모수모형_반복있음 [2021/03/10 21:42] (현재)
@@ 줄 1: / 줄 1: @@
 ====== 삼원배치법 (모수모형) (반복있음) ======
 ===== 데이터 구조 =====
- [요인]&nbsp&nbsp $$A$$ 는 [모수인자]
+ [[요인]]  $A$ 는 [[모수인자]]
- [요인]&nbsp&nbsp $$B$$ 는 [모수인자]
+ [[요인]]  $B$ 는 [[모수인자]]
- [요인]&nbsp&nbsp $$C$$ 는 [모수인자]
+ [[요인]]  $C$ 는 [[모수인자]]
+  $y_{ijkp} = \mu + a_{i} + b_{j} + c_{k} + (ab)_{ij} + (ac)_{ik} + (bc)_{jk} + (abc)_{ijk} + e_{ijkp}$
-  $$ y_{ijkp} = \mu + a_{i} + b_{j} + c_{k} + (ab)_{ij} + (ac)_{ik} + (bc)_{jk} + (abc)_{ijk} + e_{ijkp} $$
+  * $y_{ijkp} $:$ A_{i} $와$ B_{j} $그리고$ C_{k}$ 에서 얻은 $p$ 번째 [[측정값]]
+  *  $\mu$   : 실험전체의 [[모평균]]
+  *  $a_{i}$  :  $A_{i}$ 가 주는 효과
+  *  $b_{j}$  :  $B_{j}$ 가 주는 효과
+  *  $c_{k}$  :  $C_{k}$ 가 주는 효과
+  *  $(ab)_{ij}$  :  $A_{i}$ 와  $B_{j}$ 의 [[교호작용]] 효과
+  *  $(ac)_{ik}$  :  $A_{i}$ 와  $C_{k}$ 의 [[교호작용]] 효과
+  *  $(bc)_{jk}$  :  $B_{j}$ 와  $C_{k}$ 의 [[교호작용]] 효과
+  *  $(abc)_{ijk}$  :  $A_{i}$ 와  $B_{J}$  그리고  $C_{k}$ 의 [[교호작용]] 효과
+  *  $e_{ijkp}$  :  $A_{i}$ 와  $B_{j}$  그리고  $C_{k}$ 에서 얻은  $p$ 번째 [[측정값]]의 [[오차]] ( $e_{ijkp} \sim N(0, \sigma_{E}^{ \ 2})$ 이고 서로 [[독립]])
-    $y_{ijkp}$  &nbsp&nbsp : &nbsp&nbsp  $A_{i}$  와&nbsp&nbsp  $B_{j}$  &nbsp&nbsp그리고&nbsp&nbsp  $C_{k}$  에서 얻은&nbsp&nbsp  $p$  번째 [측정값]
+  *  $i$  : [[인자]] $A$의 [[수준]] 수  $( i = 1,2, \cdots ,l )$
+  *  $j$  : [[인자]]  $B$ 의 [[수준]] 수  $( j = 1,2, \cdots ,m )$
-   $ $\mu$ $ &nbsp&nbsp : 실험전체의 [모평균]
+  *  $k$  : [[인자]]  $C$ 의 [[수준]] 수  $( k = 1,2, \cdots ,n )$
+  *  $p$  : 실험의 [[반복]] 수  $( p = 1,2, \cdots ,r )$
-   $$a_{i}$$ &nbsp&nbsp : &nbsp&nbsp  $A_{i}$  가 주는 효과
-    $b_{j}$  &nbsp&nbsp : &nbsp&nbsp  $B_{j}$  가 주는 효과
-    $c_{k}$  &nbsp&nbsp : &nbsp&nbsp  $C_{k}$  가 주는 효과
-    $(ab)_{ij}$  &nbsp&nbsp : &nbsp&nbsp  $A_{i}$  와&nbsp&nbsp  $B_{j}$  의 [교호작용] 효과
-    $(ac)_{ik}$  &nbsp&nbsp : &nbsp&nbsp  $A_{i}$  와&nbsp&nbsp  $C_{k}$  의 [교호작용] 효과
-    $(bc)_{jk}$  &nbsp&nbsp : &nbsp&nbsp  $B_{j}$  와&nbsp&nbsp  $C_{k}$  의 [교호작용] 효과
-    $(abc)_{ijk}$  &nbsp&nbsp : &nbsp&nbsp  $A_{i}$  와&nbsp&nbsp  $B_{J}$  &nbsp&nbsp그리고&nbsp&nbsp $$C_{k}$$ 의 [교호작용] 효과
-    $e_{ijkp}$  &nbsp&nbsp : &nbsp&nbsp  $A_{i}$  와&nbsp&nbsp  $B_{j}$  &nbsp&nbsp그리고&nbsp&nbsp  $C_{k}$  에서 얻은&nbsp&nbsp  $p$  번째 [측정값]의 [오차]  (  $e_{ijkp} \sim N(0, \sigma_{E}^{ \ 2})$  이고 서로 [독립])
-     $i$  &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 $$C$$ 의 [수준] 수&nbsp&nbsp $$( k = 1,2, \cdots ,n )$$
-    $ $p$ $ &nbsp&nbsp : 실험의 [반복] 수&nbsp&nbsp $ $( p = 1,2, \cdots ,r )$ $
-----
 ===== 자료의 구조 =====
- ||<|2> [인자] $ $B$ $ ||<|2> [인자] $ $C$ $ |||||||| [인자] $ $A$ $ ||
+^  [[인자]]\\  $B$   ^  [[인자]]\\  $C$   ^  [[인자]]  $A$   ||||
- ||  $A_{1}$  ||  $A_{2}$  ||  $\cdots$  ||  $A_{l}$  ||
+^:::^:::^   $A_{1}$   ^   $A_{2}$   ^   $\cdots$   ^   $A_{l}$   |
- |||||||||||| ||
+^   $B_{1}$   ^   $C_{1}$   |   $y_{1111}$   |   $y_{2111}$   |   $\cdots$   |   $y_{l111}$   |
- ||<|10>  $B_{1}$  ||<|3>  $C_{1}$  ||  $y_{1111}$  ||  $y_{2111}$  ||  $\cdots$  ||  $y_{l111}$  ||
+^:::^:::|   $\vdots$   |   $\vdots$   |   $\vdots$   |   $\vdots$   |
- ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||
+^:::^:::|   $y_{111r}$   |   $y_{211r}$   |   $\cdots$   |   $y_{l11r}$   |
- ||  $y_{111r}$  ||  $y_{211r}$  ||  $\cdots$  ||  $y_{l11r}$  ||
+^:::^   $C_{2}$   |   $y_{1121}$   |   $y_{2121}$   |   $\cdots$   |   $y_{l121}$   |
- ||<|3>  $C_{2}$  ||  $y_{1121}$  ||  $y_{2121}$  ||  $\cdots$  ||  $y_{l121}$  ||
+^:::^:::|   $\vdots$   |   $\vdots$   |   $\vdots$   |   $\vdots$   |
- ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||
+^:::^:::|   $y_{112r}$   |   $y_{212r}$   |   $\cdots$   |   $y_{l12r}$   |
- ||  $y_{112r}$  ||  $y_{212r}$  ||  $\cdots$  ||  $y_{l12r}$  ||
+^:::^   $\vdots$   |   $\vdots$   |   $\vdots$   |   |   $\vdots$   |
- ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  || ||  $\vdots$  ||
+^:::^   $C_{n}$   |   $y_{11n1}$   |   $y_{21n1}$   |   $\cdots$   |   $y_{l1n1}$   |
- ||<|3>  $C_{n}$  ||  $y_{11n1}$  ||  $y_{21n1}$  ||  $\cdots$  ||  $y_{l1n1}$  ||
+^:::^:::|   $\vdots$   |   $\vdots$   |   $\vdots$   |   $\vdots$   |
- ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||
+^:::^:::|   $y_{11nr}$   |   $y_{21nr}$   |   $\cdots$   |   $y_{l1nr}$   |
- ||  $y_{11nr}$  ||  $y_{21nr}$  ||  $\cdots$  ||  $y_{l1nr}$  ||
+^   $B_{2}$   ^   $C_{1}$   |   $y_{1211}$   |   $y_{2211}$   |   $\cdots$   |   $y_{l211}$   |
- ||<|10>  $B_{2}$  ||<|3>  $C_{1}$  ||  $y_{1211}$  ||  $y_{2211}$  ||  $\cdots$  ||  $y_{l211}$  ||
+^:::^:::|   $\vdots$   |   $\vdots$   |   $\vdots$   |   $\vdots$   |
- ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||
+^:::^:::|   $y_{121r}$   |   $y_{221r}$   |   $\cdots$   |   $y_{l21r}$   |
- ||  $y_{121r}$  ||  $y_{221r}$  ||  $\cdots$  ||  $y_{l21r}$  ||
+^:::^   $C_{2}$   |   $y_{1221}$   |   $y_{2221}$   |   $\cdots$   |   $y_{l221}$   |
- ||<|3>  $C_{2}$  ||  $y_{1221}$  ||  $y_{2221}$  ||  $\cdots$  ||  $y_{l221}$  ||
+^:::^:::|   $\vdots$   |   $\vdots$   |   $\vdots$   |   $\vdots$   |
- ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||
+^:::^:::|   $y_{122r}$   |   $y_{222r}$   |   $\cdots$   |   $y_{l22r}$   |
- ||  $y_{122r}$  ||  $y_{222r}$  ||  $\cdots$  ||  $y_{l22r}$  ||
+^:::^   $\vdots$   |   $\vdots$   |   $\vdots$   |   |   $\vdots$   |
- ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  || ||  $\vdots$  ||
+^:::^   $C_{n}$   |   $y_{12n1}$   |   $y_{22n1}$   |   $\cdots$   |   $y_{l2n1}$   |
- ||<|3>  $C_{n}$  ||  $y_{12n1}$  ||  $y_{22n1}$  ||  $\cdots$  ||  $y_{l2n1}$  ||
+^:::^:::|   $\vdots$   |   $\vdots$   |   $\vdots$   |   $\vdots$   |
- ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||
+^:::^:::|   $y_{12nr}$   |   $y_{22nr}$   |   $\cdots$   |   $y_{l2nr}$   |
- ||  $y_{12nr}$  ||  $y_{22nr}$  ||  $\cdots$  ||  $y_{l2nr}$  ||
+^   $\vdots$   ||   $\vdots$   ||||
- ||||  $\vdots$  ||||||||  $\vdots$  ||
+^   $B_{m}$   ^   $C_{1}$   |   $y_{1m11}$   |   $y_{2m11}$   |   $\cdots$   |   $y_{lm11}$   |
- ||<|10>  $B_{m}$  ||<|3>  $C_{1}$  ||  $y_{1m11}$  ||  $y_{2m11}$  ||  $\cdots$  ||  $y_{lm11}$  ||
+^:::^:::|   $\vdots$   |   $\vdots$   |   $\vdots$   |   $\vdots$   |
- ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||
+^:::^:::|   $y_{1m1r}$   |   $y_{2m1r}$   |   $\cdots$   |   $y_{lm1r}$   |
- ||  $y_{1m1r}$  ||  $y_{2m1r}$  ||  $\cdots$  ||  $y_{lm1r}$  ||
+^:::^   $C_{2}$   |   $y_{1m21}$   |   $y_{2m21}$   |   $\cdots$   |   $y_{lm21}$   |
- ||<|3>  $C_{2}$  ||  $y_{1m21}$  ||  $y_{2m21}$  ||  $\cdots$  ||  $y_{lm21}$  ||
+^:::^:::|   $\vdots$   |   $\vdots$   |   $\vdots$   |   $\vdots$   |
- ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||
+^:::^:::|   $y_{1m2r}$   |   $y_{2m2r}$   |   $\cdots$   |   $y_{lm2r}$   |
- ||  $y_{1m2r}$  ||  $y_{2m2r}$  ||  $\cdots$  ||  $y_{lm2r}$  ||
+^:::^   $\vdots$   |   $\vdots$   |   $\vdots$   |   |   $\vdots$   |
- ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  || ||  $\vdots$  ||
+^:::^   $C_{n}$   |   $y_{1mn1}$   |   $y_{2mn1}$   |   $\cdots$   |   $y_{lmn1}$   |
- ||<|3>  $C_{n}$  ||  $y_{1mn1}$  ||  $y_{2mn1}$  ||  $\cdots$  ||  $y_{lmn1}$  ||
+^:::^:::|   $\vdots$   |   $\vdots$   |   $\vdots$   |   $\vdots$   |
- ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  ||
+^:::^:::|   $y_{1mnr}$   |   $y_{2mnr}$   |   $\cdots$   |   $y_{lmnr}$   |
- ||  $y_{1mnr}$  ||  $y_{2mnr}$  ||  $\cdots$  ||  $y_{lmnr}$  ||
-  $$AB$$ 2원표
+  $AB$  2원표
-  ||<|2> [인자] $ $B$ $ |||||||| [인자] $ $A$ $ ||<|2> 합계 ||
+^  [[인자]]  $B$   ^  [[인자]]  $A$   ^^^^  합계  |
-  ||  $A_{1}$  ||  $A_{2}$  ||  $\cdots$  ||  $A_{l}$  ||
+^:::^   $A_{1}$   ^   $A_{2}$   ^   $\cdots$   ^   $A_{l}$   ^:::|
-  |||||||||||| ||
+^   $B_{1}$   |   $T_{11..}$   |   $T_{21..}$   |   $\cdots$   |   $T_{l1..}$   |   $T_{.1..}$   |
-  ||  $B_{1}$  ||  $T_{11..}$  ||  $T_{21..}$  ||  $\cdots$  ||  $T_{l1..}$  ||  $T_{.1..}$  ||
+^   $B_{2}$   |   $T_{12..}$   |   $T_{22..}$   |   $\cdots$   |   $T_{l2..}$   |   $T_{.2..}$   |
-  ||  $B_{2}$  ||  $T_{12..}$  ||  $T_{22..}$  ||  $\cdots$  ||  $T_{l2..}$  ||  $T_{.2..}$  ||
+^   $\vdots$   |   $\vdots$   |   $\vdots$   |   |   $\vdots$   |   $\vdots$   |
-  ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  || ||  $\vdots$  ||  $\vdots$  ||
+^   $B_{m}$   |   $T_{1m..}$   |   $T_{2m..}$   |   $\cdots$   |   $T_{lm..}$   |   $T_{.m..}$   |
-  ||  $B_{m}$  ||  $T_{1m..}$  ||  $T_{2m..}$  ||  $\cdots$  ||  $T_{lm..}$  ||  $T_{.m..}$  ||
+^  합계  ^   $T_{1...}$   ^   $T_{2...}$   ^   $\cdots$   ^   $T_{l...}$   ^   $T$   |
-  |||||||||||| ||
-  || 합계 ||  $T_{1...}$  ||  $T_{2...}$  ||  $\cdots$  ||  $T_{l...}$  ||  $T$  ||
-  $$AC$$ 2원표
+  $AC$  2원표
-  ||<|2> [인자] $ $C$ $ |||||||| [인자] $ $A$ $ ||<|2> 합계 ||
+^  [[인자]]  $C$   ^  [[인자]]  $A$   ^^^^  합계  |
-  ||  $A_{1}$  ||  $A_{2}$  ||  $\cdots$  ||  $A_{l}$  ||
+^:::^   $A_{1}$   ^   $A_{2}$   ^   $\cdots$   ^   $A_{l}$   ^:::|
-  |||||||||||| ||
+^   $C_{1}$   |   $T_{1.1.}$   |   $T_{2.1.}$   |   $\cdots$   |   $T_{l.1.}$   |   $T_{..1.}$   |
-  ||  $C_{1}$  ||  $T_{1.1.}$  ||  $T_{2.1.}$  ||  $\cdots$  ||  $T_{l.1.}$  ||  $T_{..1.}$  ||
+^   $C_{2}$   |   $T_{1.2.}$   |   $T_{2.2.}$   |   $\cdots$   |   $T_{l.2.}$   |   $T_{..2.}$   |
-  ||  $C_{2}$  ||  $T_{1.2.}$  ||  $T_{2.2.}$  ||  $\cdots$  ||  $T_{l.2.}$  ||  $T_{..2.}$  ||
+^   $\vdots$   |   $\vdots$   |   $\vdots$   |   |   $\vdots$   |   $\vdots$   |
-  ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  || ||  $\vdots$  ||  $\vdots$  ||
+^   $C_{n}$   |   $T_{1.n.}$   |   $T_{2.n.}$   |   $\cdots$   |   $T_{l.n.}$   |   $T_{..n.}$   |
-  ||  $C_{n}$  ||  $T_{1.n.}$  ||  $T_{2.n.}$  ||  $\cdots$  ||  $T_{l.n.}$  ||  $T_{..n.}$  ||
+^  합계  ^   $T_{1...}$   ^   $T_{2...}$   ^   $\cdots$   ^   $T_{l...}$   ^   $T$   |
-  |||||||||||| ||
-  || 합계 ||  $T_{1...}$  ||  $T_{2...}$  ||  $\cdots$  ||  $T_{l...}$  ||  $T$  ||
-  $$BC$$ 2원표
+  $BC$  2원표
-  ||<|2> [인자] $ $C$ $ |||||||| [인자] $ $B$ $ ||<|2> 합계 ||
+^  [[인자]]  $C$   ^  [[인자]]  $B$   ^^^^  합계  |
-  ||  $B_{1}$  ||  $B_{2}$  ||  $\cdots$  ||  $B_{m}$  ||
+^:::^   $B_{1}$   ^   $B_{2}$   ^   $\cdots$   ^   $B_{m}$   ^:::|
-  |||||||||||| ||
+^   $C_{1}$   |   $T_{.11.}$   |   $T_{.21.}$   |   $\cdots$   |   $T_{.m1.}$   |   $T_{..1.}$   |
-  ||  $C_{1}$  ||  $T_{.11.}$  ||  $T_{.21.}$  ||  $\cdots$  ||  $T_{.m1.}$  ||  $T_{..1.}$  ||
+^   $C_{2}$   |   $T_{.12.}$   |   $T_{.22.}$   |   $\cdots$   |   $T_{.m2.}$   |   $T_{..2.}$   |
-  ||  $C_{2}$  ||  $T_{.12.}$  ||  $T_{.22.}$  ||  $\cdots$  ||  $T_{.m2.}$  ||  $T_{..2.}$  ||
+^   $\vdots$   |   $\vdots$   |   $\vdots$   |   |   $\vdots$   |   $\vdots$   |
-  ||  $\vdots$  ||  $\vdots$  ||  $\vdots$  || ||  $\vdots$  ||  $\vdots$  ||
+^   $C_{n}$   |   $T_{.1n.}$   |   $T_{.2n.}$   |   $\cdots$   |   $T_{.mn.}$   |   $T_{..n.}$   |
-  ||  $C_{n}$  ||  $T_{.1n.}$  ||  $T_{.2n.}$  ||  $\cdots$  ||  $T_{.mn.}$  ||  $T_{..n.}$  ||
+^  합계  ^   $T_{.1..}$   ^   $T_{.2..}$   ^   $\cdots$   ^   $T_{.m..}$   ^   $T$   |
-  |||||||||||| ||
-  || 합계 ||  $T_{.1..}$  ||  $T_{.2..}$  ||  $\cdots$  ||  $T_{.m..}$  ||  $T$  ||
-   ||  $T_{i...} = \sum_{j=1}^{m} \sum_{k=1}^{n} \sum_{p=1}^{r} y_{ijkp}$  ||  $\overline{y}_{i...} = \frac{T_{i...}}{mnr}$  ||
+|  $T_{i...} = \sum_{j=1}^{m} \sum_{k=1}^{n} \sum_{p=1}^{r} y_{ijkp}$  |  $\overline{y}_{i...} = \frac{T_{i...}}{mnr}$  |
-   ||  $T_{.j..} = \sum_{i=1}^{l} \sum_{k=1}^{n} \sum_{p=1}^{r} y_{ijkp}$  ||  $\overline{y}_{.j..} = \frac{T_{.j..}}{lnr}$  ||
+|  $T_{.j..} = \sum_{i=1}^{l} \sum_{k=1}^{n} \sum_{p=1}^{r} y_{ijkp}$  |  $\overline{y}_{.j..} = \frac{T_{.j..}}{lnr}$  |
-   ||  $T_{..k.} = \sum_{i=1}^{l} \sum_{j=1}^{m} \sum_{p=1}^{r} y_{ijkp}$  ||  $\overline{y}_{..k.} = \frac{T_{..k.}}{lmr}$  ||
+|  $T_{..k.} = \sum_{i=1}^{l} \sum_{j=1}^{m} \sum_{p=1}^{r} y_{ijkp}$  |  $\overline{y}_{..k.} = \frac{T_{..k.}}{lmr}$  |
-   ||  $T_{ij..} = \sum_{k=1}^{n} \sum_{p=1}^{r} y_{ijkp}$  ||  $\overline{y}_{ij..} = \frac{T_{ij..}}{nr}$  ||
+|  $T_{ij..} = \sum_{k=1}^{n} \sum_{p=1}^{r} y_{ijkp}$  |  $\overline{y}_{ij..} = \frac{T_{ij..}}{nr}$  |
-   ||  $T_{i.k.} = \sum_{j=1}^{m} \sum_{p=1}^{r} y_{ijkp}$  ||  $\overline{y}_{i.k.} = \frac{T_{i.k.}}{mr}$  ||
+|  $T_{i.k.} = \sum_{j=1}^{m} \sum_{p=1}^{r} y_{ijkp}$  |  $\overline{y}_{i.k.} = \frac{T_{i.k.}}{mr}$  |
-   ||  $T_{.jk.} = \sum_{i=1}^{l} \sum_{p=1}^{r} y_{ijkp}$  ||  $\overline{y}_{.jk.} = \frac{T_{.jk.}}{lr}$  ||
+|  $T_{.jk.} = \sum_{i=1}^{l} \sum_{p=1}^{r} y_{ijkp}$  |  $\overline{y}_{.jk.} = \frac{T_{.jk.}}{lr}$  |
-   ||  $T_{ijk.} = \sum_{p=1}^{r} y_{ijkp}$  ||  $\overline{y}_{ijk.} = \frac{T_{ijk.}}{r}$  ||
+|  $T_{ijk.} = \sum_{p=1}^{r} y_{ijkp}$  |  $\overline{y}_{ijk.} = \frac{T_{ijk.}}{r}$  |
-   ||  $T = \sum_{i=1}^{l} \sum_{j=1}^{m} \sum_{k=1}^{n} \sum_{p=1}^{r} y_{ijkp}$  ||  $\overline{\overline{y}} = \frac{T}{lmnr} = \frac{T}{N}$  ||
+|  $T = \sum_{i=1}^{l} \sum_{j=1}^{m} \sum_{k=1}^{n} \sum_{p=1}^{r} y_{ijkp}$  |  $\overline{\overline{y}} = \frac{T}{lmnr} = \frac{T}{N}$  |
-   ||  $N = lmnr$  ||  $CT = \frac{T^{2}}{lmnr} = \frac{T^{2}}{N}$  ||
+|  $N = lmnr$  |  $CT = \frac{T^{2}}{lmnr} = \frac{T^{2}}{N}$  |
-----
+===== 제곱합 =====
-===== [제곱합] =====
+ 개개의 데이터  $y_{ijkp}$ 와 총평균  $\overline{\overline{y}}$ 의 차이는 다음과 같이 8부분으로 나뉘어진다.
- 개개의 데이터&nbsp&nbsp $$y_{ijkp}$$ 와 총편균&nbsp&nbsp $$\overline{\overline{y}}$$ 의 차이는 다음과 같이 8부분으로 나뉘어진다.
-   $\begin{displaymath}\begin{split} (y_{ijkp}-\overline{\overline{y}}) &= (\overline{y}_{i...} - \overline{\overline{y}}) + (\overline{y}_{.j..} - \overline{\overline{y}}) + (\overline{y}_{..k.} - \overline{\overline{y}}) \\ &+ (\overline{y}_{ij..} - \overline{y}_{i...} - \overline{y}_{.j..} + \overline{\overline{y}}) + (\overline{y}_{i.k.} - \overline{y}_{i...} - \overline{y}_{..k.} + \overline{\overline{y}}) + (\overline{y}_{.jk.} - \overline{y}_{.j..} - \overline{y}_{..k.} + \overline{\overline{y}}) \\ &+ (y_{ijk.} - \overline{y}_{ij..} - \overline{y}_{i.k.} - \overline{y}_{.jk.} + \overline{y}_{i...} + \overline{y}_{.j..} + \overline{y}_{..k.} - \overline{\overline{y}}) \\ &+ (y_{ijkp}-\overline{y}_{ijk.}) \end{split}\end{displaymath}$
+  $\begin{displaymath}\begin{split} (y_{ijkp}-\overline{\overline{y}}) &= (\overline{y}_{i...} - \overline{\overline{y}}) + (\overline{y}_{.j..} - \overline{\overline{y}}) + (\overline{y}_{..k.} - \overline{\overline{y}}) \\ &+ (\overline{y}_{ij..} - \overline{y}_{i...} - \overline{y}_{.j..} + \overline{\overline{y}}) + (\overline{y}_{i.k.} - \overline{y}_{i...} - \overline{y}_{..k.} + \overline{\overline{y}}) + (\overline{y}_{.jk.} - \overline{y}_{.j..} - \overline{y}_{..k.} + \overline{\overline{y}}) \\ &+ (y_{ijk.} - \overline{y}_{ij..} - \overline{y}_{i.k.} - \overline{y}_{.jk.} + \overline{y}_{i...} + \overline{y}_{.j..} + \overline{y}_{..k.} - \overline{\overline{y}}) \\ &+ (y_{ijkp}-\overline{y}_{ijk.}) \end{split}\end{displaymath}$
- 양변을 제곱한 후에 모든&nbsp&nbsp $$i, \ j, \ k, \ p$$ 에 대하여 합하면 아래의 등식을 얻을 수 있다.
+ 양변을 제곱한 후에 모든  $i, \ j, \ k, \ p$ 에 대하여 합하면 아래의 등식을 얻을 수 있다.
-   $\begin{displaymath}\begin{split} \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{ijkp}-\overline{\overline{y}})^{2} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{i...} - \overline{\overline{y}})^{2} + \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{.j..} - \overline{\overline{y}})^{2} \\ &+ \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{..k.} - \overline{\overline{y}})^{2} \\ &+ \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{ij..} - \overline{y}_{i...} - \overline{y}_{.j..} + \overline{\overline{y}})^{2} \\ &+ \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{i.k.} - \overline{y}_{i...} - \overline{y}_{..k.} + \overline{\overline{y}})^{2} \\ &+ \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{.jk.} - \overline{y}_{.j..} - \overline{y}_{..k.} + \overline{\overline{y}})^{2} \\ &+ \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{ijk.} - \overline{y}_{ij..} - \overline{y}_{i.k.} - \overline{y}_{.jk.} + \overline{y}_{i...} + \overline{y}_{.j..} + \overline{y}_{..k.} - \overline{\overline{y}})^{2} \\ &+ \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{ijkp}-\overline{y}_{ijk.})^{2} \end{split}\end{displaymath}$
+  $\begin{displaymath}\begin{split} \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{ijkp}-\overline{\overline{y}})^{2} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{i...} - \overline{\overline{y}})^{2} + \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{.j..} - \overline{\overline{y}})^{2} \\ &+ \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{..k.} - \overline{\overline{y}})^{2} \\ &+ \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{ij..} - \overline{y}_{i...} - \overline{y}_{.j..} + \overline{\overline{y}})^{2} \\ &+ \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{i.k.} - \overline{y}_{i...} - \overline{y}_{..k.} + \overline{\overline{y}})^{2} \\ &+ \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{.jk.} - \overline{y}_{.j..} - \overline{y}_{..k.} + \overline{\overline{y}})^{2} \\ &+ \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{ijk.} - \overline{y}_{ij..} - \overline{y}_{i.k.} - \overline{y}_{.jk.} + \overline{y}_{i...} + \overline{y}_{.j..} + \overline{y}_{..k.} - \overline{\overline{y}})^{2} \\ &+ \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{ijkp}-\overline{y}_{ijk.})^{2} \end{split}\end{displaymath}$
- 위 식에서 왼쪽 항은 총변동 $$S_{T}$$ 이고, 오른쪽 항은 차례대로&nbsp&nbsp $$A$$ 의 [변동],&nbsp&nbsp $$B$$ 의 [변동],&nbsp&nbsp $$C$$ 의 [변동],&nbsp&nbsp $$A, \ B$$ 의 [교호작용]의 변동,&nbsp&nbsp $$A, \ C$$ 의 [교호작용]의 변동,&nbsp&nbsp $$B, \ C$$ 의 [교호작용]의 변동,&nbsp&nbsp $$A, \ B, \ C$$ 의 [교호작용]의 변동, [오차변동]인&nbsp&nbsp $$S_{A}$$ , $$S_{B}$$ , $$S_{C}$$ , $$S_{A \times B}$$ , $$S_{A \times C}$$ , $$S_{B \times C}$$ , $$S_{A \times B \times C}$$ , $$S_{E}$$ 가 된다.
+ 위 식에서 왼쪽 항은 총변동  $S_{T}$ 이고, 오른쪽 항은 차례대로  $A$ 의 [[변동]],  $B$ 의 [[변동]],  $C$ 의 [[변동]],  $A, \ B$ 의 [[교호작용]]의 변동,  $A, \ C$ 의 [[교호작용]]의 변동,  $B, \ C$ 의 [[교호작용]]의 [[변동]],  $A, \ B, \ C$ 의 [[교호작용]]의 변동, [[오차변동]]인  $S_{A}$ ,  $S_{B}$ ,  $S_{C}$ ,  $S_{A \times B}$ ,  $S_{A \times C}$ ,  $S_{B \times C}$ ,  $S_{A \times B \times C}$ ,  $S_{E}$ 가 된다.
+  $\begin{displaymath}\begin{split} S_{T} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{ijkp}-\overline{\overline{y}})^{2} \\ &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}y_{ijkp}^{ \ 2} - CT \end{split}\end{displaymath}$
-  $$\begin{displaymath}\begin{split} S_{T} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{ijkp}-\overline{\overline{y}})^{2} \\ &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}y_{ijkp}^{ \ 2} - CT \end{split}\end{displaymath}$$
+ $$\begin{displaymath}\begin{split} S_{A} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{i...}-\overline{\overline{y}})^{2} \\ &= \sum_{i=1}^{l}\frac{T_{i...}^{ \ 2}}{mnr}-CT \end{split}\end{displaymath}$$
-  $$\begin{displaymath}\begin{split} S_{A} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{i...}-\overline{\overline{y}})^{2} \\ &= \sum_{i=1}^{l}\frac{T_{i...}^{ \ 2}}{mnr}-CT \end{split}\end{displaymath}$$
+ $$\begin{displaymath}\begin{split} S_{B} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{.j..}-\overline{\overline{y}})^{2} \\ &= \sum_{j=1}^{m}\frac{T_{.j..}^{ \ 2}}{lnr}-CT \end{split}\end{displaymath}$$
-  $$\begin{displaymath}\begin{split} S_{B} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{.j..}-\overline{\overline{y}})^{2} \\ &= \sum_{j=1}^{m}\frac{T_{.j..}^{ \ 2}}{lnr}-CT \end{split}\end{displaymath}$$
+ $$\begin{displaymath}\begin{split} S_{C} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{..k.}-\overline{\overline{y}})^{2} \\ &= \sum_{k=1}^{n}\frac{T_{..k.}^{ \ 2}}{lmr}-CT \end{split}\end{displaymath}$$
-  $$\begin{displaymath}\begin{split} S_{C} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{..k.}-\overline{\overline{y}})^{2} \\ &= \sum_{k=1}^{n}\frac{T_{..k.}^{ \ 2}}{lmr}-CT \end{split}\end{displaymath}$$
+ $$\begin{displaymath}\begin{split} S_{A \times B} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{ij..}-\overline{y}_{i...}-\overline{y}_{.j..}+\overline{\overline{y}})^{2} \\ &= S_{AB} - S_{A} - S_{B} \end{split}\end{displaymath}$$
-  $$\begin{displaymath}\begin{split} S_{A \times B} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{ij..}-\overline{y}_{i...}-\overline{y}_{.j..}+\overline{\overline{y}})^{2} \\ &= S_{AB} - S_{A} - S_{B} \end{split}\end{displaymath}$$
+ $$\begin{displaymath}\begin{split} S_{AB} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{ij..}-\overline{\overline{y}})^{2} \\ &= \sum_{i=1}^{l}\sum_{j=1}^{m} \frac{T_{ij..}^{ \ 2}}{nr} -CT \end{split}\end{displaymath}$$
-  $$\begin{displaymath}\begin{split} S_{AB} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{ij..}-\overline{\overline{y}})^{2} \\ &= \sum_{i=1}^{l}\sum_{j=1}^{m} \frac{T_{ij..}^{ \ 2}}{nr} -CT \end{split}\end{displaymath}$$
+ $$\begin{displaymath}\begin{split} S_{A \times C} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{i.k.}-\overline{y}_{i...}-\overline{y}_{..k.}+\overline{\overline{y}})^{2} \\ &= S_{AC} - S_{A} - S_{C} \end{split}\end{displaymath}$$
-  $$\begin{displaymath}\begin{split} S_{A \times C} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{i.k.}-\overline{y}_{i...}-\overline{y}_{..k.}+\overline{\overline{y}})^{2} \\ &= S_{AC} - S_{A} - S_{C} \end{split}\end{displaymath}$$
+ $$\begin{displaymath}\begin{split} S_{AC} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{i.k.}-\overline{\overline{y}})^{2} \\ &= \sum_{i=1}^{l}\sum_{k=1}^{n} \frac{T_{i.k.}^{ \ 2}}{mr} -CT \end{split}\end{displaymath}$$
-  $$\begin{displaymath}\begin{split} S_{AC} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{i.k.}-\overline{\overline{y}})^{2} \\ &= \sum_{i=1}^{l}\sum_{k=1}^{n} \frac{T_{i.k.}^{ \ 2}}{mr} -CT \end{split}\end{displaymath}$$
+ $$\begin{displaymath}\begin{split} S_{B \times C} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{.jk.}-\overline{y}_{.j..}-\overline{y}_{..k.}+\overline{\overline{y}})^{2} \\ &= S_{BC} - S_{B} - S_{C} \end{split}\end{displaymath}$$
-  $$\begin{displaymath}\begin{split} S_{B \times C} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{.jk.}-\overline{y}_{.j..}-\overline{y}_{..k.}+\overline{\overline{y}})^{2} \\ &= S_{BC} - S_{B} - S_{C} \end{split}\end{displaymath}$$
+ $$\begin{displaymath}\begin{split} S_{BC} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{.jk.}-\overline{\overline{y}})^{2} \\ &= \sum_{j=1}^{m}\sum_{k=1}^{n} \frac{T_{.jk.}^{ \ 2}}{lr} -CT \end{split}\end{displaymath}$$
-  $$\begin{displaymath}\begin{split} S_{BC} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(\overline{y}_{.jk.}-\overline{\overline{y}})^{2} \\ &= \sum_{j=1}^{m}\sum_{k=1}^{n} \frac{T_{.jk.}^{ \ 2}}{lr} -CT \end{split}\end{displaymath}$$
+ $$\begin{displaymath}\begin{split} S_{A \times B \times C} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{ijk.}-\overline{y}_{ij..}-\overline{y}_{i.k.}-\overline{y}_{.jk.}+\overline{y}_{i...}+\overline{y}_{.j..}+\overline{y}_{..k.}-\overline{\overline{y}})^{2} \\ &= S_{ABC}-(S_{A}+S_{B}+S_{C}+S_{A \times B}+S_{A \times C}+S_{B \times C}) \end{split}\end{displaymath}$$
-  $$\begin{displaymath}\begin{split} S_{A \times B \times C} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{ijk.}-\overline{y}_{ij..}-\overline{y}_{i.k.}-\overline{y}_{.jk.}+\overline{y}_{i...}+\overline{y}_{.j..}+\overline{y}_{..k.}-\overline{\overline{y}})^{2} \\ &= S_{ABC}-(S_{A}+S_{B}+S_{C}+S_{A \times B}+S_{A \times C}+S_{B \times C}) \end{split}\end{displaymath}$$
+ $$\begin{displaymath}\begin{split} S_{ABC} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{ijk.}-\overline{\overline{y}})^{2} \\ &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\frac{T_{ijk.}^{ \ 2}}{r} -CT \end{split}\end{displaymath}$$
-   $\begin{displaymath}\begin{split} S_{ABC} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{ijk.}-\overline{\overline{y}})^{2} \\ &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\frac{T_{ijk.}^{ \ 2}}{r} -CT \end{split}\end{displaymath}$
+  $\begin{displaymath}\begin{split} S_{E} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{ijkp}-\overline{\overline{y}})^{2} \\ &= S_{T} - S_{ABC} \end{split}\end{displaymath}$
+===== 자유도 =====
-   $\begin{displaymath}\begin{split} S_{E} &= \sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}\sum_{p=1}^{r}(y_{ijkp}-\overline{\overline{y}})^{2} \\ &= S_{T} - S_{ABC} \end{split}\end{displaymath}$
-----
-===== [자유도] =====
   $\nu_{A}=l-1$
@@ 줄 175: / 줄 150: @@
   $\nu_{T}=lmnr-1=N-1$
-----
+===== 평균제곱 =====
-===== [평균제곱] =====
   $V_{A}=\frac{S_{A}}{\nu_{A}}$
@@ 줄 192: / 줄 166: @@
   $V_{E}=\frac{S_{E}}{\nu_{E}}$
-----
+===== 평균제곱의 기대값 =====
-===== [평균제곱의 기대값] =====
   $E(V_{A})=\sigma_{E}^{ \ 2} +mnr \sigma_{A}^{ \ 2}$
@@ 줄 209: / 줄 182: @@
   $E(V_{E})=\sigma_{E}^{ \ 2}$
-----
 ===== 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]]\\  $\rho$   |
- |||||||||||||||||| ||
+|   $A$   |   $S_{_{A}}$   |   $\nu_{_{A}}=l-1$   |   $V_{_{A}}=S_{_{A}}/​\nu_{_{A}}$   |   $\sigma_{_{E}}^{ \ 2}+mnr \ \sigma_{_{A}}^{2}$   |   $V_{_{A}}/​V_{_{E}}$   |   $F_{1-\alpha}(\nu_{_{A}} \ , \ \nu_{_{E}})$   |   $S_{_{A}}\acute{}$   |   $S_{_{A}}\acute{}/​S_{_{T}}$   |
- ||  $A$  ||  $S_{_{A}}$  ||  $\nu_{_{A}}=l-1$  ||  $V_{_{A}}=S_{_{A}}/​\nu_{_{A}}$  ||  $\sigma_{_{E}}^{ \ 2}+mnr \ \sigma_{_{A}}^{2}$  ||  $V_{_{A}}/​V_{_{E}}$  ||  $F_{1-\alpha}(\nu_{_{A}} \ , \ \nu_{_{E}})$  ||  $S_{_{A}}\acute{}$  ||  $S_{_{A}}\acute{}/​S_{_{T}}$  ||
+|   $B$   |   $S_{_{B}}$   |   $\nu_{_{B}}=m-1$   |   $V_{_{B}}=S_{_{B}}/​\nu_{_{B}}$   |   $\sigma_{_{E}}^{ \ 2}+lnr \ \sigma_{_{B}}^{2}$   |   $V_{_{B}}/​V_{_{E}}$   |   $F_{1-\alpha}(\nu_{_{B}} \ , \ \nu_{_{E}})$   |   $S_{_{B}}\acute{}$   |   $S_{_{B}}\acute{}/​S_{_{T}}$   |
- ||  $B$  ||  $S_{_{B}}$  ||  $\nu_{_{B}}=m-1$  ||  $V_{_{B}}=S_{_{B}}/​\nu_{_{B}}$  ||  $\sigma_{_{E}}^{ \ 2}+lnr \ \sigma_{_{B}}^{2}$  ||  $V_{_{B}}/​V_{_{E}}$  ||  $F_{1-\alpha}(\nu_{_{B}} \ , \ \nu_{_{E}})$  ||  $S_{_{B}}\acute{}$  ||  $S_{_{B}}\acute{}/​S_{_{T}}$  ||
+|   $C$   |   $S_{_{C}}$   |   $\nu_{_{C}}=n-1$   |   $V_{_{C}}=S_{_{C}}/​\nu_{_{C}}$   |   $\sigma_{_{E}}^{ \ 2}+lmr \ \sigma_{_{C}}^{2}$   |   $V_{_{C}}/​V_{_{E}}$   |   $F_{1-\alpha}(\nu_{_{C}} \ , \ \nu_{_{E}})$   |   $S_{_{C}}\acute{}$   |   $S_{_{C}}\acute{}/​S_{_{T}}$   |
- ||  $C$  ||  $S_{_{C}}$  ||  $\nu_{_{C}}=n-1$  ||  $V_{_{C}}=S_{_{C}}/​\nu_{_{C}}$  ||  $\sigma_{_{E}}^{ \ 2}+lmr \ \sigma_{_{C}}^{2}$  ||  $V_{_{C}}/​V_{_{E}}$  ||  $F_{1-\alpha}(\nu_{_{C}} \ , \ \nu_{_{E}})$  ||  $S_{_{C}}\acute{}$  ||  $S_{_{C}}\acute{}/​S_{_{T}}$  ||
+|   $A \times B$   |   $S_{_{A \times B}}$   |   $\nu_{_{A \times B}}=(l-1)(m-1)$   |   $V_{_{A \times B}}=S_{_{A \times B}}/​\nu_{_{A \times B}}$   |   $\sigma_{_{E}}^{ \ 2}+nr \ \sigma_{_{A \times B}}^{2}$   |   $V_{_{A \times B}}/​V_{_{E}}$   |   $F_{1-\alpha}(\nu_{_{A \times B}} \ , \ \nu_{_{E}})$   |   $S_{_{A \times B}}\acute{}$   |   $S_{_{A \times B}}\acute{}/​S_{_{T}}$   |
- ||  $A \times B$  ||  $S_{_{A \times B}}$  ||  $\nu_{_{A \times B}}=(l-1)(m-1)$  ||  $V_{_{A \times B}}=S_{_{A \times B}}/​\nu_{_{A \times B}}$  ||  $\sigma_{_{E}}^{ \ 2}+nr \ \sigma_{_{A \times B}}^{2}$  ||  $V_{_{A \times B}}/​V_{_{E}}$  ||  $F_{1-\alpha}(\nu_{_{A \times B}} \ , \ \nu_{_{E}})$  ||  $S_{_{A \times B}}\acute{}$  ||  $S_{_{A \times B}}\acute{}/​S_{_{T}}$  ||
+|   $A \times C$   |   $S_{_{A \times C}}$   |   $\nu_{_{A \times C}}=(l-1)(n-1)$   |   $V_{_{A \times C}}=S_{_{A \times C}}/​\nu_{_{A \times C}}$   |   $\sigma_{_{E}}^{ \ 2}+mr \ \sigma_{_{A \times C}}^{2}$   |   $V_{_{A \times C}}/​V_{_{E}}$   |   $F_{1-\alpha}(\nu_{_{A \times C}} \ , \ \nu_{_{E}})$   |   $S_{_{A \times C}}\acute{}$   |   $S_{_{A \times C}}\acute{}/​S_{_{T}}$   |
- ||  $A \times C$  ||  $S_{_{A \times C}}$  ||  $\nu_{_{A \times C}}=(l-1)(n-1)$  ||  $V_{_{A \times C}}=S_{_{A \times C}}/​\nu_{_{A \times C}}$  ||  $\sigma_{_{E}}^{ \ 2}+mr \ \sigma_{_{A \times C}}^{2}$  ||  $V_{_{A \times C}}/​V_{_{E}}$  ||  $F_{1-\alpha}(\nu_{_{A \times C}} \ , \ \nu_{_{E}})$  ||  $S_{_{A \times C}}\acute{}$  ||  $S_{_{A \times C}}\acute{}/​S_{_{T}}$  ||
+|   $B \times C$   |   $S_{_{B \times C}}$   |   $\nu_{_{B \times C}}=(m-1)(n-1)$   |   $V_{_{B \times C}}=S_{_{B \times C}}/​\nu_{_{B \times C}}$   |   $\sigma_{_{E}}^{ \ 2}+lr \ \sigma_{_{B \times C}}^{2}$   |   $V_{_{B \times C}}/​V_{_{E}}$   |   $F_{1-\alpha}(\nu_{_{B \times C}} \ , \ \nu_{_{E}})$   |   $S_{_{B \times C}}\acute{}$   |   $S_{_{B \times C}}\acute{}/​S_{_{T}}$   |
- ||  $B \times C$  ||  $S_{_{B \times C}}$  ||  $\nu_{_{B \times C}}=(m-1)(n-1)$  ||  $V_{_{B \times C}}=S_{_{B \times C}}/​\nu_{_{B \times C}}$  ||  $\sigma_{_{E}}^{ \ 2}+lr \ \sigma_{_{B \times C}}^{2}$  ||  $V_{_{B \times C}}/​V_{_{E}}$  ||  $F_{1-\alpha}(\nu_{_{B \times C}} \ , \ \nu_{_{E}})$  ||  $S_{_{B \times C}}\acute{}$  ||  $S_{_{B \times C}}\acute{}/​S_{_{T}}$  ||
+|   $A \times B \times C$   |   $S_{_{A \times B \times C}}$   |   $\nu_{_{A \times B \times C}}=(l-1)(m-1)(n-1)$   |   $V_{_{A \times B \times C}}=S_{_{A \times B \times C}}/​\nu_{_{A \times B \times C}}$   |   $\sigma_{_{E}}^{ \ 2}+r \ \sigma_{_{A \times B \times C}}^{ \ 2}$   |   $V_{_{A \times B \times C}}/​V_{_{E}}$   |   $F_{1-\alpha}(\nu_{_{A \times B \times C}} \ , \ \nu_{_{E}})$   |   $S_{_{A \times B \times C}}\acute{}$   |   $S_{_{A \times B \times C}}\acute{}/​S_{_{T}}$   |
- ||  $A \times B \times C$  ||  $S_{_{A \times B \times C}}$  ||  $\nu_{_{A \times B \times C}}=(l-1)(m-1)(n-1)$  ||  $V_{_{A \times B \times C}}=S_{_{A \times B \times C}}/​\nu_{_{A \times B \times C}}$  ||  $\sigma_{_{E}}^{ \ 2}+r \ \sigma_{_{A \times B \times C}}^{ \ 2}$  ||  $V_{_{A \times B \times C}}/​V_{_{E}}$  ||  $F_{1-\alpha}(\nu_{_{A \times B \times C}} \ , \ \nu_{_{E}})$  ||  $S_{_{A \times B \times C}}\acute{}$  ||  $S_{_{A \times B \times C}}\acute{}/​S_{_{T}}$  ||
+|   $E$   |   $S_{_{E}}$   |   $\nu_{_{E}}=lmn(r-1)$   |   $V_{_{E}}=S_{_{E}}/​\nu_{_{E}}$   |   $\sigma_{_{E}}^{ \ 2}$   |    |    |   $S_{_{E}}\acute{}$   |   $S_{_{E}}\acute{}/​S_{_{T}}$   |
- ||  $E$  ||  $S_{_{E}}$  ||  $\nu_{_{E}}=lmn(r-1)$  ||  $V_{_{E}}=S_{_{E}}/​\nu_{_{E}}$  ||  $\sigma_{_{E}}^{ \ 2}$  ||  ||  ||  $S_{_{E}}\acute{}$  ||  $S_{_{E}}\acute{}/​S_{_{T}}$  ||
+|   $T$   |   $S_{_{T}}$   |   $\nu_{_{T}}=lmnr-1$   |    |    |    |    |   $S_{_{T}}$   |   $1$   |
- |||||||||||||||||| ||
+===== 분산분석 =====
- ||  $T$  ||  $S_{_{T}}$  ||  $\nu_{_{T}}=lmnr-1$  ||  ||  ||  ||  ||  $S_{_{T}}$  ||  $1$  ||
+ [[인자]]  $A$ 에 대한 [[분산분석]]
-----
-===== [분산분석] =====
- 인자&nbsp&nbsp $$A$$ 에 대한 [분산분석]
-   $F_{0}=\frac{V_{_{A}}}{V_{_{E}}}$
+  * $$F_{0}=\frac{V_{_{A}}}{V_{_{E}}}$$
+ [[기각역]] : $F_{0} > F_{1-\alpha}(\nu_{_{A}},\nu_{_{E}})$
-  [기각역] :&nbsp&nbsp  $F_{0} > F_{1-\alpha}(\nu_{_{A}},​\nu_{_{E}})$
 ----
- 인자&nbsp&nbsp $$B$$ 에 대한 [분산분석]
+ [[인자]]  $B$ 에 대한 [[분산분석]]
-   $F_{0}=\frac{V_{_{B}}}{V_{_{E}}}$
+  * $$F_{0}=\frac{V_{_{B}}}{V_{_{E}}}$$
+ [[기각역]] : $F_{0} > F_{1-\alpha}(\nu_{_{B}},\nu_{_{E}})$
-  [기각역] :&nbsp&nbsp  $F_{0} > F_{1-\alpha}(\nu_{_{B}},​\nu_{_{E}})$
 ----
- 인자&nbsp&nbsp $$C$$ 에 대한 [분산분석]
+ [[인자]]  $C$ 에 대한 [[분산분석]]
+  *  $F_{0}=\frac{V_{_{C}}}{V_{_{E}}}$
-  $$F_{0}=\frac{V_{_{C}}}{V_{_{E}}}$$
+ [[기각역]] : $F_{0} > F_{1-\alpha}(\nu_{_{C}},\nu_{_{E}})$
-  [기각역] :&nbsp&nbsp  $F_{0} > F_{1-\alpha}(\nu_{_{C}},​\nu_{_{E}})$
 ----
- 인자&nbsp&nbsp $$A , \ B$$ 의 [교호작용] 대한 [분산분석]
+ [[인자]]  $A , \ B$ 의 [[교호작용]]에 대한 [[분산분석]]
-   $F_{0}=\frac{V_{_{A \times B}}}{V_{E}}$
+  * $$F_{0}=\frac{V_{_{A \times B}}}{V_{E}}$$
+ [[기각역]] : $F_{0} > F_{1-\alpha}(\nu_{_{A \times B}},\nu_{_{E}})$
-  [기각역] :&nbsp&nbsp  $F_{0} > F_{1-\alpha}(\nu_{_{A \times B}},​\nu_{_{E}})$
 ----
- 인자&nbsp&nbsp $$A , \ C$$ 의 [교호작용] 대한 [분산분석]
+ [[인자]]  $A , \ C$ 의 [[교호작용]]에 대한 [[분산분석]]
-   $F_{0}=\frac{V_{_{A \times C}}}{V_{E}}$
+  * $$F_{0}=\frac{V_{_{A \times C}}}{V_{E}}$$
+ [[기각역]] : $F_{0} > F_{1-\alpha}(\nu_{_{A \times C}},\nu_{_{E}})$
-  [기각역] :&nbsp&nbsp  $F_{0} > F_{1-\alpha}(\nu_{_{A \times C}},​\nu_{_{E}})$
 ----
- 인자&nbsp&nbsp $$B , \ C$$ 의 [교호작용] 대한 [분산분석]
+ [[인자]]  $B , \ C$ 의 [[교호작용]]에 대한 [[분산분석]]
-   $F_{0}=\frac{V_{B \times C}}{V_{E}}$
+  * $$F_{0}=\frac{V_{B \times C}}{V_{E}}$$
+ [[기각역]] : $F_{0} > F_{1-\alpha}(\nu_{_{B \times C}},\nu_{_{E}})$
-  [기각역] :&nbsp&nbsp  $F_{0} > F_{1-\alpha}(\nu_{_{B \times C}},​\nu_{_{E}})$
 ----
- 인자&nbsp&nbsp $$A , \ B , \ C$$ 의 [교호작용] 대한 [분산분석]
+ [[인자]]  $A , \ B , \ C$ 의 [[교호작용]]에 대한 [[분산분석]]
-   $F_{0}=\frac{V_{A \times B \times C}}{V_{E}}}$
+  *  $F_{0}=\frac{V_{A \times B \times C}}{V_{E}}}$
-  [기각역] :&nbsp&nbsp $ $F_{0} > F_{1-\alpha}(\nu_{A \times B \times C},​\nu_{_{E}})$ $
+ [[기각역]] :  $F_{0} > F_{1-\alpha}(\nu_{A \times B \times C},​\nu_{_{E}})$
-----
 ===== 각 수준의 모평균의 추정 (주효과만이 유의한 경우) =====
  주효과인 [[인자]]  $A, B, C$ 만이 유의한 경우 [[교호작용]]들이 모두 오차항에 [[풀링]]되어 버린다.

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