A Chemist plans to investigate the effects of four types of
catalyst and three types
of reagents on the rate of a chemical reaction. Suppose that
the amount of each type of
catalyst and reagent, if decided to add, is fixed. Also, at
most one type of catalyst and one type of
reagent can be added simultaneously.
Before planning the experiment she seeks your advice on how to
run the experiment. She has written
to you as follows:
“I intend to study the catalysts first and then the reagents.
However, I am restricted to fewer than
or equal to 50 observations in total. In the first experiment
I could use 6 replicates of each catalyst
and in the second experiment I could use 8 replicates of each
reagent. Then, I have 4*6 + 3*8 = 48
observations from this experimental plan. Alternatively, I
could use 7 replicates of each catalyst in
the first experiment, and 6 replicates of each reagent in the
second experiment. Then, I totally use
4*7 + 3*6 = 46 observations from this experimental plan. Which
of the two experimental plans
would be best?”
You have made an appointment to see her in order to discuss
this. Make clear notes on the most
important points to discuss with her at your meeting. Explain
the statistical motives for discussing
these points. You do not need to restrict the discussion to
her specific question and you should
include a preliminary recommendation of a plan for the
experiment