Question

The following data were obtained from a two-factor independent-measures experiment with  n = 5 participants in each treatment condition. ​What is the F-value for the interaction/AxB effect
​
                                               B1                       B2                     B3

​ A1	M = 3 T = 15 SS = 18	M = 6 T = 30 SS = 28	M = 9 T = 45 SS = 26
​ A2	M = 1 T = 5 SS = 8	M = 4 T = 20 SS = 20	M = 1 T = 5 SS = 20

Answer 1

The F statistic for interaction of factors A and B is obtained as follows,

Step 1: The ANOVA table for the interaction term is defined as,

ANOVA
Source of Variation	SS	df	MS	F
Interaction
Error

Step 2: Now the sum of square values for interaction and error term is obtained as follow,

Where,

i = represent rows (i = 1,2),

j = represent columns (j = 1 , 2, 3)

k = represent measurement per treatment per condition (k = 1, 2, 3, 4, 5)

represents elements in the column,

represents mean of each group.

represents mean of each row (A1 and A2)

represents mean of each column (B1, B2 and B3)

represents total mean.

r is the number of participants each group (r = 5)

From the data values,

M	B1	B2	B3	Mean
A1	3	6	9	6
A2	1	4	1	2
Mean	2	5	5	4

Step 3: The degree of freedom for interaction and error term is obtained as follow,

Where, a = number of rows, b = number of column.

Step 4: The mean square values for interaction and error term is obtained as follow,

Step 5: The F statistic value for interaction term is,

ANOVA
Source of Variation	SS	df	MS	F
Interaction	48	2	24	4.8
Error	120	24	5