Hello!

I'm not sure I understand your question correctly, but here is something about interactions. The 3-way interaction means the 3 factors have certain combinations of each of their levels, which can result in different outcome, than the individual effects would suggest. This may not have a proper physical meaning or dimension.

Let me get you an example.

Let's say you have a chemical process. You want an optimal yield from the reaction. You have 3 factors to change: temperature (T), pressure (p) and stirring (n). You conduct the experiments and analyse it with a 3-way ANOVA (Note: many times the 3-way ANOVA can be avoided with altered experimental design). If you see a "significant" result of the 3-way interaction, that is T*p*n, it means there are certain levels of n giving different yield if T and the p is at a certain level. You can switch the T, p and n as you wish in the last sentence. This would mean you have to optimize your process for the 3 factors together, because they modify eachothers effect. You can say this to managers, if they ask you about interactions.

There are also T*p, n*p and T*n 2-way interactions, look at them in a similar fashion. If an interactions is deemed "insignificant", it is possible to ignore it although not in every context.

Hope this helps!

Hello!

I'm not sure I understand your question correctly, but here is something about interactions. The 3-way interaction means the 3 factors have certain combinations of each of their levels, which can result in different outcome, than the individual effects would suggest. This may not have a proper physical meaning or dimension.

Let me get you an example.

Let's say you have a chemical process. You want an optimal yield from the reaction. You have 3 factors to change: temperature (T), pressure (p) and stirring (n). You conduct the experiments and analyse it with a 3-way ANOVA (Note: many times the 3-way ANOVA can be avoided with altered experimental design). If you see a "significant" result of the 3-way interaction, that is T*p*n, it means there are certain levels of n giving different yield if T and the p is at a certain level. You can switch the T, p and n as you wish in the last sentence. This would mean you have to optimize your process for the 3 factors together, because they modify eachothers effect. You can say this to managers, if they ask you about interactions.

There are also T*p, n*p and T*n 2-way interactions, look at them in a similar fashion. If an interactions is deemed "insignificant", it is possible to ignore it although not in every context.

Hope this helps!

Consider two-way interaction between factors A and B. It means the inconsistency of the performance of A at different levels of B and vice versa. By extension, an AxBxC interaction is the inconsistency of A at the BxC levels or the inconsistency of B at the AxC levels or the inconsistency of C at the AxB levels.