Step 1. Build hypotheses

Weight가 number of crackers eaten에 영향을 미칠 것이다.

Fullness가 number of crackers eaten에게 영향을 미칠 것이다.

Weight와 Fullness 두 가지가 동시에 존재함으로써 number of crackers eaten에 영향을 미칠 것이다.

Step 2. Locate the critical range for F-ratio. calculate the dfs

df total: N-1 =80-1=79

df within: df total- df between= 76

df between: 4-1=3

df A: 2-1=1

df B: 2-1=1

df AxB: df between-dfA-dfB= 1

Compute F-ratio SS

SS total= 31836-25920=5916

SS within= 1540+1270+1320+1266=5396

SS between= (440^2)/20+(300^2)/20+(340^2)/20+(360^2)/20-(1440^2)/80

=9680+4500+5780+6480-25920=520

SS A= (740^2)/40+(700^2)/40-(1440^2)/80=13690+12250-25920=20

SS B= (780^2)/40+(660^2)/40-(1440^2)/80=15210+10890-25920=180

SS AxB=SS between- SS A- SS B= 520-20-180=320

MS

MS A=20/1=20

MS B=180/1=180

MS AxB=320/1=320

MS within=5396/76=71

F-ratio

F A (1,76) =20/71=0.282

F B(1,76) =180/71=2.535

F AxB(1,76) =320/71=4.507

*Check F critic

Fcrit(1,76)= 4.00

Fcrit(1,76)= 4.00

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	520	3
- Factor A (weight)	20	1	20	0.282
- Factor B (fullness)	180	1	180	2.535
- A x B interaction	320	1	320	4.507
Within treatment	5396	76	71
Total	5916	79
weigth x fullness factorial design

Fcrit(1,76)= 4.00