## Related questions with answers

Consider the

$2^6$

factorial design. Set up a design to be run in four blocks of 16 runs each. Show that a design that confounds three of the four-factor interactions with blocks is the best possible blocking arrangement.

Solution

VerifiedWe have to consider $2^6$ factorial design. We need to set up design to be run in four blocks of 16 runs each. Also, we have to show that a design that confounds three of the four factor interactions with blocks is the best possible blocking arrangement.

We constructed the design by using defining contrast for $ABCD$ and $CDEF.$ To assign the treatment combinations to the four blocks, substitute them into the defining contrast, so

$\begin{align*} &L_1=1(0)+1(0)+1(0)+1(0)=0=0(\text{mod}\enskip 2)\\ &L_2=1(0)+1(0)+1(0)+1(0)=0=0(\text{mod}\enskip 2). \end{align*}$

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