In: Statistics and Probability
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).
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