Question

A 2^3 design is confounded in 4 blocks of size 2. The principal block contains treatments (1) and abc. Another block contains a. What is the second element of that block. (b, c, ab, ac, or bc?)

Answer 1

In this question we have to find 4 blocks in size 2. Here we have to select two effect to confound.If we consider two effect to be confounded only two degree of freedom.So if we confound two effects then we confound interaction between these two factors.

ABC as one of the effects Then, it would seem logical to pick one of the 2-way interactions as the other confounding factor. Let's say we use AB. If we do this, remember, we also confound the interaction between these two effects.The interaction between ABC and AB is C.

The 2-way interactions such as AB and AC. The interaction of these is BC. In this case you have not confounded a main effect, but instead have confounded the three two-way interactions. The four combinations of the AB and AC

Treatment	I	A	B	C	AB	AC	BC	ABC	Block
(1)	+	-	-	-	+	+	+	-	4
a	+	+	-	-	-	-	+	+	1
b	+	-	+	-	-	+	-	+	3
ab	+	+	+	-	+	-	-	-	2
c	+	-	-	+	+	-	-	-	2
ac	+	+	-	+	-	+	-	-	3
bc	+	-	+	+	-	-	+	-	1
abc	+	+	+	+	+	+	+	+	4

Here we get (1) and abc in principal block then we can find a with other bc in block 1

Blocks	1	2	3	4
	a	ab	b	(1)
	bc	c	ac	abc