Question

Examine the following two-factor analysis of variance table (shown below). Determine if interaction exists between factor A and factor B. Use alpha = 0.05.

Source	SS	df	MS	F-Ratio
Factor A	162.79	4
Factor B			28.12
AB Interaction	262.31	12
Error	________	___
Total	1,298.74	84

Answer 1

Null Hypothesis A and B are independent of each other

ALternative Hypothesis A and B are not independent

ANOVA Table :

Source	SS	df	MS	F-Ratio	F at 5% level
Factor A	162.79	4	162.79/4 =40.70	40.70/12.143=3.352	F(4,65) =2.513
Factor B	28.12*3 =84.36	12/4 =3	28.12	28.12/12.143=2.316	F(3,65) =2.746
Interaction A B	262.31	12	262.31/12 =21.86	21.86/12.143=1.800	F(12,65)=1.904
Error	1298.74-(162.79+84.36+262.31)=789.28	84-(4+3+12)=65	789.28/65=12.143
Total	1298.74	84

Since F calculated for Interaction is less than F tabulated. Fail to Reject H0.

Hence A and B are independent to each other.