Williams design 3-way [Design Issues]

posted by Relaxation  – Germany, 2021-06-11 12:42 (107 d 17:39 ago) – Posting: # 22409
Views: 1,808

Hi Stefano.

I was a little bit hesitant to answer, as I am and likely will remain a noob in the statistical background. Maybe I also misunderstand your question, which is quite possible.
But there are a lot of people around here to correct the answer, if necessary, and its SOP-Friday...

I think I get your point, but I also think that the period effect is implemented above.
The numbers already include both as mean=µ+π = treatment + period effect.

As an example:
the term s2p2 above is not the treatment mean for A in sequence 2 and period 2 (=1), it is the observed mean and includes the effect of period 2 (1-0.5=0.5).

If we would like to split that up into more detail, when sxpy is the treatment only (defined by combination of sequence and period), we can add Py as the period effect for more clarity.
Then:
A-C = ((s1p1 + P1) + (s2p2 + P2) + (s3p2 + P2) + (s4p3 + P3))
- ((s1p3 + P3) + (s2p3 + P3) + (s3p1 + P1) + (s4p1 + P1)).
See, as in Helmuts post, the period effects are implemented. But in the discussed design (P1+P2+P2+P3 = -0.5) and (P3+P3+P1+P1 = 1) do not completely eliminate each other as they would in a Latin Square. Thus treatment difference is biased (to +0.5 or 3.5/5=0.7) and not easily corrected.

Now, lets both wait and see, whether I got it right :-D.

Best regards,

Relaxation.

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