Experimentation: Design of Experiments Factor analysis

[eddieray01]

When determining Effect of Factor B on Factor A. Let's say B level 1: is 5 at A level 1 and 9 at A level 2. B at Level 2: is 6 at A level 1 and 10 at A level 2. 1) Assume based on my understanding effect is 7
at B1 minus 8 at B2 = -1? Is that correct it is the difference of marginal means for B1 and B2. Or should this calculation always be largest value minus lower value so B2 minus B1=1? Wanted to clarify if calculating correctly and if order is important since it can change sign on result.

[PaigeMiller]

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@eddieray01 wrote:
When determining Effect of Factor B on Factor A. Let's say B level 1: is 5 at A level 1 and 9 at A level 2. B at Level 2: is 6 at A level 1 and 10 at A level 2. 1) Assume based on my understanding effect is 7
at B1 minus 8 at B2 = -1? Is that correct it is the difference of marginal means for B1 and B2. Or should this calculation always be largest value minus lower value so B2 minus B1=1? Wanted to clarify if calculating correctly and if order is important since it can change sign on result.

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This is difficult to understand as written.

May I suggest you present the data as a simple table, showing clearly the levels of A and B and the result, something like this (obviously this is made-up data)

A    B   Y
1    1   3
1    2   7
2    1   11
etc.

and then state your question clearly.

Thanks!

[eddieray01]

      A1 A2
B1  5    9
B2  6  10

I'm using 1 and 2 as levels for each factor this could be + -

[PaigeMiller]

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@eddieray01 wrote:
      A1 A2
B1  5    9
B2  6  10

I'm using 1 and 2 as levels for each factor this could be + -

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And so what is the question you are asking?

[eddieray01]

Would the effect of B on A be the marginal mean of row 1 minus row 2?  The values in the 2x2 table cells are the result Y for the combinations. 

[PaigeMiller]

In the language of statistics that I am used to using, the phrase "effect of B on A" does not exist and does not make sense to me. There is an effect of B on Y, where going from B1 to B2 yields an average 1 unit increase. There is also an effect of A on Y, where going from A1 to A2 produces an average of a 4 unit increase. There is also an interaction between A and B on Y, which is zero for this data. There is also an effect of B on Y, while holding A to be fixed at 1, and so on.

So I do not understand what you want from the question "effect of B on A".

[eddieray01]

Sorry effect of B on the mean of the response. So with this data B+ rows Minus B- rows.  Would it not be subtracting the marginal means?

[eddieray01]

I think you answered with the unit increase re B of 1 and unit increase of 4 for A. Assuming the unit increase always expressed as a positive number?

[PaigeMiller · Accepted solution]

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@eddieray01 wrote:
I think you answered with the unit increase re B of 1 and unit increase of 4 for A. Assuming the unit increase always expressed as a positive number?

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Not always expressed as a positive number. It depends on how B1 and B2 are defined, and what comparison you want to make.