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RegisterWilliams’ designs more reliable? [Design Issues]
Dear Detlew,
Good question, next queston!
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
❝ So give me an impression what this could be and how to quantify this?
Good question, next queston!
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
Complete thread:
- Replicated cross over with fixed number of periods martin 2012-11-05 17:31 [Design Issues]
![[Mix]](https://static.bebac.at/img/mix.png "open in Mix view")
- Additional information martin 2012-11-06 11:50
- Quick Q for my clarification ElMaestro 2012-11-06 12:09
- Quick Q for my clarification martin 2012-11-06 12:29
- 5 periods ElMaestro 2012-11-06 12:43
- Latin Squares ↔ Williams’ designs Helmut 2012-11-06 14:07
- Latin Squares ↔ Williams’ designs Ben 2012-11-07 21:10
- Williams’ designs more reliable? d_labes 2012-11-08 08:29
- Williams’ designs more reliable? Ben 2012-11-09 18:20
- Williams’ designs more reliable? d_labes 2012-11-11 14:14
- Williams’ designs more reliable?Ben 2012-11-18 13:20
- Frequentists vs. Bayesians Helmut 2012-11-18 14:48
- Frequentists vs. Bayesians Ben 2012-11-18 15:28
- Frequentists vs. Bayesians Helmut 2012-11-18 14:48
- Williams’ designs more reliable?Ben 2012-11-18 13:20
- Williams’ designs more reliable? d_labes 2012-11-11 14:14
- Williams’ designs more reliable? Ben 2012-11-09 18:20
- Williams’ designs more reliable? d_labes 2012-11-08 08:29
- Latin Squares ↔ Williams’ designs Ben 2012-11-07 21:10
- Quick Q for my clarification martin 2012-11-06 12:29
- Quick Q for my clarification ElMaestro 2012-11-06 12:09
- Additional information martin 2012-11-06 11:50
Ing. Helmut Schütz