Please, explain why. I perform an ANOVA such as: y ~ A + B. The p-values for bot
ID: 3052457 • Letter: P
Question
Please, explain why.
I perform an ANOVA such as: y ~ A + B. The p-values for both A and B come up very significant. (< 0.05)
But when I perform the same ANOVA such as : y ~ A * B. The p value of A is still significant (< 0.05). The p value of B is NO MORE significant (> 0.05). And the interaction A*B is also significant (< 0.05).
Can you please provide an explantion why B is no more significant when we consider the interaction of A and B in the model?
Please, be specific and clear in your explanation.
Explanation / Answer
From the explanation of ANOVA analysis it is seen that additive and multiplicative models are applied to the same data and results are mentioned. In the output it is observed that under additive model both the factors A and B are significant whereas in multiplicative model A is significant, B is insignificant and interaction AB is significant.
Now the decision of applying a particular model must not be guess or trial and error based. ANOVA is the last step in supporting DOE. Therefore, the underlying experimental situation is more important to understand clearly. It is general practice to apply simple additive model when two factors are independently performing their worth, but when existence one factor may boost the performance of other factor and vice versa then under such situations multiplicative model is suggested.
In the present explanation details of the experiment are not mentioned. One can also transform the multiplicative model to additive model by log transformation. In the present case a) Additive model is Y ~ A+B
b) Multiplicative model is Y ~ A*B
c) Log model is Log (Y) ~ Log(A) + Log(B)
In model a) both A and B are significant, in model b) A is significant, B is not but AB is. Further the model c) is additive model alike model a) and hence here one can observe logarithmic effect of both A and B is significant. The model c) is now free from term of interaction. Further we know the term of spurious correlation. Therefore in the present example the suitability of the model can be decided based on the experimental situation and conditions.