‘Two-at-a-Time’ approach with >3 treat­ments [Design Issues]

posted by Shuanghe  – Spain, 2022-06-12 21:02 (167 d 14:36 ago) – Posting: # 23053
Views: 958

Dear Helmut,

I vaguelly recall that for 4x4 William design, each row (sequence) and each column (period) should contain A, B, C, and D each exactly once. I think that there's a typo in the 3rd sequence of your first William design. Your 3rd and 4th column do not seem right. So 3rd period would have 2 Bs and 4th had 2 Ds. CABD should be CADB. So It would be ABCD/BDAC/CADB/DCBA. In such case, it would be balanced for pair-wise comparisons.

$$\small{\begin{array}{c|cccc}
s/p & \text{I} & \text{II} & \text{III} & \text{IV}\\\hline
1 & \text{A} & \text{B} & \text{C} & \text{D}\\
2 & \text{B} & \text{D} & \text{A} & \text{C}\\
3 & \text{C} & \text{A} & \text{D} & \text{B}\\
4 & \text{D} & \text{C} & \text{B} & \text{A}\\
\end{array}{\color{Blue}\mapsto}
\begin{array}{c|cccc}
s/p & \text{I} & \text{II} & \text{III} & \text{IV} \\\hline
1 & \text{A} & {\color{Red}\bullet} & {\color{Red}\bullet} & \text{D}\\
2 & {\color{Red}\bullet} & \text{D} & \text{A} & {\color{Red}\bullet}\\
3 & {\color{Red}\bullet} & \text{A} & \text{D} & {\color{Red}\bullet}\\
4 & \text{D} & {\color{Red}\bullet} & {\color{Red}\bullet} & \text{A}\\
\end{array}{\color{Blue}\wedge}
\begin{array}{c|cccc}
s/p & \text{I} & \text{II} & \text{III} & \text{IV}\\\hline
1 & {\color{Red}\bullet} & \text{B} & {\color{Red}\bullet} & \text{D}\\
2 & \text{B} & \text{D} & {\color{Red}\bullet} & {\color{Red}\bullet}\\
3 & {\color{Red}\bullet} & {\color{Red}\bullet} & \text{D} & \text{B}\\
4 & \text{D} & {\color{Red}\bullet} & \text{B} & {\color{Red}\bullet}\\
\end{array}{\color{Blue}\wedge}
\begin{array}{c|cccc}
s/p & \text{I} & \text{II} & \text{III} & \text{IV}\\\hline
1 & {\color{Red}\bullet} & {\color{Red}\bullet} & \text{C} & \text{D}\\
2 & {\color{Red}\bullet} & \text{D} & {\color{Red}\bullet} & \text{C}\\
3 & \text{C} & {\color{Red}\bullet} & \text{D} & {\color{Red}\bullet}\\
4 & \text{D} & \text{C} & {\color{Red}\bullet} & {\color{Red}\bullet}\\
\end{array}}$$

All the best,
Shuanghe

Complete thread:

UA Flag
Activity
 Admin contact
22,417 posts in 4,692 threads, 1,596 registered users;
18 visitors (0 registered, 18 guests [including 8 identified bots]).
Forum time: 10:38 CET (Europe/Vienna)

To know that we know what we know,
and to know that we do not know what we do not know,
that is true knowledge.    Nicolaus Copernicus

The Bioequivalence and Bioavailability Forum is hosted by
BEBAC Ing. Helmut Schütz
HTML5