Williams’ designs more reliable? [Design Issues]

posted by Ben – 2012-11-18 12:20 (2935 d 08:07 ago) – Posting: # 9544
Views: 3,911

Dear Detlew,

» So give me an impression what this could be and how to quantify this?

Good question, next queston! :lookaround:
Intuitively, since each treatment precedes each other treatment the same number of times as it follows each other treatment any carry-over from say, for example treatment A should be averaged over all other treatments. Even though we are not able to estimate the carry-over effects (since not included in the model), we should have balanced out potential carry-over effects. That was my initial thoughts, unfortunately I am struggling to quantify that. [Moreover, maybe one can add an additional argument, namely the fact that all pairwise treatment comparisons have the same variance: In a Latin square one treatment comparison can be much worse (by chance due to higher variability) than the other one, you simply don't know. This cannot happen in a Williams design, results are more reliable in the sense that you know a priori all comparisons will behave equally.]

Best,
Ben

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