Question

1) Suppose you have a 26 factorial experiment that you want to put into 8 blocks.

a. Identify l, where 2l = the number of blocks.

b. What is the block size? Remember we have 64 total treatment combinations that we want to partition into 8 blocks of equal size.

c. How many effects will we need to confound with blocks?

d. Suppose we choose to confound the effects ABC, CDE, and DEF to construct our design. Describe how we construct the blocks assuming we have the contrast table showing all +1 and -1 values for these three effects. You do not need to actually construct the design.

e. If we construct the design in (d), what other effects will we confound with blocks? Remember, generalized interactions could involve two or more effects. Use your answer in (c) to make sure you’ve accounted for every confounded effect.

Answer 1

It's a typing error. It will be a 2⁶ factorial experiment, instead of 26 factorial experiments.

a. Number of blocks is 8 . So, 2l = 8  

so, l = 4

b. The block size is = 2⁶ / 8 = 8

c. The number of effects to be coonfounded with block is (8-1) = 7

e. We found the remaining 4 confounded effects by multiplying the given 3 confounded effects with each other , such as:

ABC*CDE = ABC²DE = ABDE

ABC*DEF= ABCDEF

CDE*DEF= CD²E²F= CF

and ABDE*DEF= ABD²E²F= ABF .

So the 7 confounded effects are :

ABC, CDE,DEF,CF.ABF,ABDE,ABCDEF