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RegisterWilliams’ designs more reliable? [Design Issues]
Dear Ben!
Why should it?
Same number of subjects, same number of degrees of freedom, same design constant. At least if we talk about the usual evaluation. So what mysterious feature should let to more reliable results?
In case we talk about the 'robust' evaluation (aka Senn's basic estimator) we have to analyse the T-R contrasts (in the log domain) via an ANOVA with sequence as effect in the model. The degrees of freedom to use are then N-nseq, where N=number of subjects, nseq=number of sequences.
That gives us:
A slight advantage of the Latin square in case of a 3-treatment-3-period study. Else also identical design features.
❝ ... But due to the design isn't it the case that a Williams design will give more reliable results in any case - even without adjusting for carry over in the model?
Why should it?
Same number of subjects, same number of degrees of freedom, same design constant. At least if we talk about the usual evaluation. So what mysterious feature should let to more reliable results?
In case we talk about the 'robust' evaluation (aka Senn's basic estimator) we have to analyse the T-R contrasts (in the log domain) via an ANOVA with sequence as effect in the model. The degrees of freedom to use are then N-nseq, where N=number of subjects, nseq=number of sequences.
That gives us:
Latin square Williams
3-period N-3 N-6
4-period N-4 N-4A slight advantage of the Latin square in case of a 3-treatment-3-period study. Else also identical design features.
—
Regards,
Detlew
Regards,
Detlew
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