Question

2x2 between subject a1b1 4,5,5,6,8 a1b2 6,5,6,7,8 a2b1 15,13,13,12,14 a2b2 2,0,3,1,2

Indicate the results of each of the F-tests (significant or not significant) and how it was that you decided (e.g., what comparison did you make to decide).

Answer 1

data

	a1	a2
b1	4	15
	5	13
	5	13
	6	12
	8	14
b2	6	2
	5	0
	6	3
	7	1
	8	2

using excel

data -> data analysis -> anova two way with replication

Anova: Two-Factor With Replication
SUMMARY	a1	a2	Total
b1
Count	5	5	10
Sum	28	67	95
Average	5.6	13.4	9.5
Variance	2.3	1.3	18.5
b2
Count	5	5	10
Sum	32	8	40
Average	6.4	1.6	4
Variance	1.3	1.3	7.555556
Total
Count	10	10
Sum	60	75
Average	6	7.5
Variance	1.777777778	39.83333333
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
B	151.25	1	151.25	97.58065	3.26E-08	4.493998
A	11.25	1	11.25	7.258065	0.015964	4.493998
Interaction	198.45	1	198.45	128.0323	4.8E-09	4.493998
Within	24.8	16	1.55
Total	385.75	19

F > F-critical values in all three factors (A, B and interaction )

hence all factors are significant