Discussion
In a \(2^{3}\) factorial design with three treatments A, B, C each at two levels, blocks of 4 plots are available. The design is replicated twice and the allocation of treatment combination is :
| Replication 1 | Replication 2 | ||
|---|---|---|---|
| Block I | Block II | Block I | Block II |
| 1 | b | 1 | a |
| a | c | b | c |
| bc | ab | ac | ab |
| abc | ac | abc | bc |
Hence the two confounded treatment combinations in replication 1 and 2 respectively are :
Answer: D
The confounded effects are BC in replication 1 and AC in replication 2.
A two-factor interaction XY is confounded when one block holds the combinations where X and Y are at the same level and the other block those where they differ.
- Replication 1, block I = {1, a, bc, abc}: b and c are either both absent or both present, so BC is confounded.
- Replication 2, block I = {1, b, ac, abc}: a and c are both absent or both present, so AC is confounded.
AB would need a block {1, ab, c, abc}, and ABC a block {1, ab, ac, bc}; neither appears, which rules out options A, B and C.
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