Look at the scenario that is presented below and discuss what type model it is,

Question

Look at the scenario that is presented below and discuss what type model it is, whether you think that the model that was used is the best one for the design purpose stated, and other comments you wish to make about the model.

An experiment was conducted to determine the effects of the following factors on the gain of a semiconductor device Factor A. Location of Assembly B. Partial Pressure of Controlling Material C. Relative Humidity Level 0 Laboratory 10-15 196 Level 1 Production Line 104 30% The experiment was run in two blocks with the allocation of treatments to blocks In replication 1, BC is confounded with blocks. In replication 2, ABC is confounded with blocks. The result for each replicate is below Replicate 1 (BC) Block 1 Block 2 31.8 47.0 43.8 45.6 168.2 43.2 43.7 48.2 58.2 193.3 ABC ac Replicate 2 (ABC) Block 1 Block 2 39.0 40.9 29.3 34.9 144 51.4 40.3 40.5 52.9 185.1 ac abc

Explanation / Answer

The above design is a 22 factorial design.

For now we will just consider two treatment factors of interest. It looks almost the same as the randomized block design model only now we are including an interaction term:

Yijk=+i+j+()ij+eijk

where i = 1, ..., a, j = 1, ..., b, and k = 1, ..., n. Thus we have two factors in a factorial structure with n observations per cell. As usual, we assume the eijk N(0, 2), i.e. independently and identically distributed with the normal distribution. Although it looks like a multiplication, the interaction term need not imply multiplicative interaction.

And this the best model to design the purpose stated.

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