# Main effects in Minitab

I have a multilevel factorial design. I use Minitab to study and analyze this design. One of the outcome of such study is the main effect plot. I get the following :

As I am new to design of experiments and factorial designs, I start searching for the definition and context of "The main effects". In some sources, it is stated that the main effect for factor A at level 1 is

$E_{A1}=$ mean of the response when A is at level 1 - overall mean.

Is this definition correct or I am misunderstanding the exact and right context. Thank you in advance.

• If this is about what Minitab does, then it's a little off-topic. But there's a statistical question here. The trouble is that the great majority of readers don't use Minitab or have access to it. If you could post the data underlying your graph in a universally accessible way then people could check in their own software exactly what is being shown. Further, "some sources" is not an exact reference. You have more than one factor here it seems, but you could be clearer about the structure of the data. – Nick Cox Feb 3 '16 at 10:39
• I guess that these details were inhibiting replies; it is important to realise that a bounty doesn't make an obscure question any clearer. – Nick Cox Feb 3 '16 at 10:39
• @NickCox , Okay I agree with you, may be I stated my question with some ambguity. But let me ask, in general what is the definition (formula) for the main effects in a multi-level full factorial design ? Is it the marginal mean of each level of the factors ? Does every factors has just one main effect ? – Nizar Feb 3 '16 at 11:01
• I don't think there is a universal definition. Your graph is evidence in so far as (I guess) it is showing marginal means and calling that a main effects plot, which seems to me ambiguous if not a little perverse. But (as said) I can't be clear what Minitab is doing as I don't use Minitab (well, not since the 1980s) and I can't see your data. Doesn't Minitab have documentation to explain? If not, it can no longer be taken seriously – Nick Cox Feb 3 '16 at 12:57