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Analysing 2-factor 2-level design as if it was 4 different treatment design

Hello!

 

Just curious why we see different results in such cases.

 

Here we have a classic 2-factor 2-level factorial design which we can analyze using Nominal regression/logistic regression.

 

 

Analysis shows that only interaction is significant :

 

 

However, if we transform this data as if there were 4 factors A1, B1, C (A1*B1), D (A0*B0),

 

 

then we will see that main effects are significant?

 

How can we explain and interpret this?

 

PS
Datasets are in attachments. These results are from real experiment.

 

DOERe: Analysing 2-factor 2-level design as if it was 4 different treatment design

You do not really have four factors. Your construction over-specifies the model, so JMP arbitrarily zeros the last 'factor' and indicates that the first three are biased.

 

The equivalent to two two-level factors would be one four-level factor, not four two-level factors.

Re: Analysing 2-factor 2-level design as if it was 4 different treatment design

Yep, as Mark says...you have 3 degrees of freedom in 4 treatments.

Re: Analysing 2-factor 2-level design as if it was 4 different treatment design

I am sorry.

I have corrected the file to 1-factor 4-level. Now it shows that level A (which is factor A) is significant: