====== 개인과제: 크래커 실험 F-test ======

아래의 표를 이용하여 손에 익은 워드프로세서를 이용하여 과제를 수행한 후, 파일 이름을 
  * Assignment_Ftest_yourID.docx 
  * Assignment_Ftest_yourID.pdf
  * Assignment_Ftest_yourID.hwp 중 하나로
저장하고, 이를 업로드 하시기 바랍니다. 업로드 방법은 수업시간에 알려 드립니다. 
<code>{{Assignment_Ftest_yourID.docx|F test Assigment by your id (이름)}}</code>
{{Assignment_Ftest_yourID.docx|F test Assigment by your id (이름)}}

===== 과제 내용 =====
**__과제는 아래를 포함하는 내용이어야 합니다.__** 

^  Factor B: Fullness  ^^^^^^
| Factor A: \\ Weight  |                                                    | Empty                                             | Full                     |   |
| ::: | Normal         | n=20 \\  $\overline{X}=22$  \\ T=440 \\ SS=1540    | n=20 \\  $\overline{X}$ =15  \\ T=300 \\ SS=1270   | $T_\text{Normal}=740$     |   |  
| ::: | Obese          | n=20 \\  $\overline{X}$ = 17  \\ T=340 \\ SS=1320  | n=20 \\  $\overline{X}$ = 18 \\ T=360 \\ SS=1266  | $T_\text{obese} = 700$  |   |  
| ::: |                |  $T_\text{empty} =780$                             | $T_\text{full} = 660$    |  | G=1440 \\ N=80 \\  $\Sigma{X^2}=31836$  |

$\overline{X_{t}}= 18 $ \\
$\overline{X_{t}}^2= 324 $ \\
$N = 80 $ \\
$N*(\overline{X_t}^2) = 25920 $ \\
$\sum{X^2} - N*(\overline{X_t}^2) = 31836 - 25920 = 5916$ \\

step 1. Build hypotheses
step 2. Locate the critical range for F-ratio. calculate the $dfs$ 
  - $df_{total}$
  - $df_{within}$
  - $df_{between}$
    - $df_A$
    - $df_B$
    - $df_{AxB}$

Compute F-ratio
SS
  - $SS_{total}$
$\overline{X_{t}}= 18 $ \\
$\overline{X_{t}}^2= 324 $ \\
$N = 80 $ \\
$N*(\overline{X_t}^2) = 25920 $ \\
$\Sigma{X^2} - N*(\overline{X_t}^2) = 31836 - 25920 = 5916$ \\

  - $SS_{within}$
$SS_{within} = \Sum{SS_{within}} = 1540 + 1270 + 1320 + 1266 = 5396$

  - $SS_{between}$

  - $SS_A$
  - $SS_B$
  - $SS_{AxB}$
MS
  - $MS_{A}$
  - $MS_{B}$
  - $MS_{AxB}$
  - $MS_{Within}$
F-ratio
  - $F_{A}$
  - $F_{B}$
  - $F_{AxB}$

^  Table 1. Mean number of crackers eaten in each treatment condition  ^^^^
|         |          | Fullness         ||
|         |          | Empty stomach       | Full stomach     |
| Weight  | Normal   | M=22 \\ SD=9.00     | M=15 \\ SD=8.18  |
| :::     | Obese    | M=17 \\ SD=8.34     | M=18 \\ SD=8.16  |


^  Table 2. Result  ^^^^^
| Source  | SS  | df  | MS  | F  |
| Between treatment  |   |   |   |  |
| - Factor A (weight)  |   |   |   |  |
| - Factor B (fullness)  |   |   |   |  |
| - A x B interaction  |   |   |   |  |
| Within treatment  |   |   |   |  |
| Total  |   |   |   |  |
| weigth x fullness factorial design  |||||